Episteme 6 vol 2

EPISTEME Physis e Sophia nel III millennio An International Journal of Science, History and Philosophy

N. 6 - 21 dicembre 2002

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Redazione (bartocci@dipmat.unipg.it) "Episteme" c/o Dipartimento di Matematica e Informatica UniversitĂ degli Studi Via Vanvitelli - 06100 Perugia

Direttore Responsabile

Euro Roscini (Supplemento semestrale ad: Arte in Foglio, Pubblicazione registrata presso il Tribunale di Perugia, N. 36/1991)

http://www.robotics.it/episteme http://www.dipmat.unipg.it/~bartocci (per ottenere ~ tenere premuto Alt mentre si compone il numero 126 con i simboli numerici nella parte destra della tastiera)

Numeri arretrati on line: http://itis.volta.alessandria.it/episteme PORZI editoriali

ISSN 1593-3482

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PARTE II/ SECOND SECTION

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EPISTEME Physis e Sophia nel III millennio/Physis and Sophia in the III millennium An International Journal of Science, History and Philosophy

N. 6 - 21 dicembre 2002 / 21st Dec. 2002 [La diffusione via Internet di sezioni della rivista avviene prima della data indicata - Sections of Episteme are available in Internet even before the previous date]

Parte I Informazioni editoriali/Editorial Policy Pubblicazioni ricevute/Received books and journals 1 - Lia Mangolini: La vera natura del "magico Shamìr" - A proposito di un'antichissima tecnologia per la lavorazione della pietra senza l'uso di strumenti metallici 2 - Emilio Spedicato: L'Eden riscoperto: geografia, questioni numeriche ed altre storie 3 - Felice Vinci: L'optimum climatico, il paradiso indoeuropeo e il giardino dell'Eden 4 - Sabato Scala: Il culto gnostico della Maddalena - Dal mosaico di Otranto alle basiliche paleocristiane di Cimitile, attraverso opere letterarie ed architettoniche, fino agli ultimi custodi, i Catari ed i Templari 5 - Arcangelo Papi: La facciata profetica del Duomo di S. Rufino in Assisi 6 - Prospero Calzolari: Presenza occulta e manifesta dell'Imperatore Federico II nella Basilica di San Francesco ad Assisi - Frate Elia e la congiura del silenzio 7 - Giuseppe Pirazzo, Francesco Vitale: Il mistero degli indiani Mandan 8 - Ludwik Kostro: When, Where, and How Was Decalogue Created? - Historical Origins and Evolution of the Ten Commandments 9 - Umberto Bartocci: La vera identità di Cristoforo Colombo - Osservazioni e congetture 10 - Pier Costanzo Brio: Cristoforo Colombo, la nascita - Verità storica e leggenda purista 11 - Ezio Albrile: Una eresia di luce 12 - Rosario Vieni: Sul termine greco ανθρωπος … e dintorni 13 - Oktawian Nawrot: Liberty as a Relation 14 - Sante Anfiboli: Il canto delle gru - Un racconto iniziatico

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15 - Bruno d'Ausser Berrau: Ατοπον − Relazioni spazio-temporali e metafisica tradizionale 16 -

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: Solvet saeclum in favilla - In attesa del Dies Irae?

17 - Umberto Lucia: Il ruolo del trasferimento tecnologico nello sviluppo sostenibile Reprints Paolo Manzelli, Mariagrazia Costa: Il tempo come coordinata - Gli studi di Giorgio Piccardi (1895-1972) Omero Speri, Piero Zorzi: Atomo, Energia, Uomo Commenti ricevuti/Received Comments Sante Anfiboli: A proposito del Vexillum Templi, e altra simbolica templare...

Alberto Bolognesi: Il Big Bang ha fatto flop?

Lino Lista: Le tre Grazie - Una chiave per dischiudere il giardino della Primavera Arcangelo Papi: Il caso Majorana - L'<<ipotesi Klingsor>> Francesco Pullia: Manlio Farinacci, studioso fuori dal coro Recensioni/Reviews Luca Bianchini, Anna Trombetta: Goethe, Mozart e Mayr, fratelli illuminati Paolo Cortesi: Alla ricerca della Pietra Filosofale - Storia e segreti dell'alchimia (Gerardina Cesarano) Gianni Grana: L'invenzione di Dio

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Parte II (Sezione speciale, tutta dedicata alla teoria della relatività, e "filiazioni"... - A special section, wholly dedicated to the theory of relativity, and "derivations"...)

- A Letter from the Editor to the Readers - Alternative Physics On Line 1 - Umberto Bartocci: Looking for Special Relativity's Possible Experimental Falsifications 2 - Christopher Jon Bjerknes: S. Tolver Preston's Explosive Idea - E = mc 2 and the Huyghens-Leibnitz Mass/Energy Identity as a Heuristic Principle in the Nineteenth Century 3" " " : Einstein's Irrational Ontology of Redundancy - The Special Theory of Relativity and Its Many Fallacies of Petitio Principii 4 - Alberto Bolognesi: La nuova teoria del cielo - La cosmologia osservativa di Halton Arp 5 - George Galeczki: Beyond Maxwell-Lorentz Electrodynamics 6 - Delbert J. Larson: The State of Experimental Evidence for Length Contraction, 2002 7-

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: The Most General Fundamental Failures of Modern Physics

8 - Emidio Laureti: Le basi sperimentali della propulsione non Newtoniana 9 - Rocco Vittorio Macrì: Neopitagorismo e Relatività 10 - Jarosław Mrozek: Did Einstein Claim That Nature Has Mathematical Structure?

11 - Francisco J. Müller: The Problem of Reciprocity and Non-Reciprocity in Relativity Theory 12 - Vladimir Onoochin: On the Impossibility to Describe the Fields of the System of Uniformly Moving Charges in the Frame of Special Relativity 13 - Sabato Scala: Simmetrizzazione delle equazioni di Maxwell con l'introduzione del campo gravitazionale, un'idea bizzarra?

14 - Gianfranco Spavieri, Miguel Rodríguez, Edgar Moreno: Recent Developments in the Relativistic Electrodynamics Controversy 15 - Tuomo Suntola: Dynamic Space Converts Relativity Into Absolute Time and Distance 16 - Paramahamsa Tewari: Nature of Energy, Light, and Einstein's Light Principle in Special Theory of Relativity 17 -

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: On the Space-Vortex Structure of Cosmic Bodies

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18 - Theo Theocharis: Louis T. More, Prophet of the 20th Century 19 -

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: Ultimate Creative Ignorance

20 - Tom Van Flandern: What the Global Positioning System Tells Us about the Twin's Paradox Reprints Emilio Almansi: Sulle attrazioni newtoniane di origine idrodinamica Stefan Marinov: Annus Horribilis - (The Story of) A Payed Advertisement Published by Nature N. Moisseiev: Intorno alla legge di resistenza al moto dei corpi in un mezzo pulviscolare Carl A. Zapffe: Exodus of Einstein's Special Theory in Seven Simple Steps Recensioni/Reviews Christopher Jon Bjerknes: Albert Einstein, The Incorrigible Plagiarist (Thomas E. Phipps, Jr., from Infinite Energy Magazine, N. 47, 6 October, 2002) (A brand new Appendix to the book: A Short History of the Concept of Relative Simultaneity in the Special Theory of Relativity) Franco Selleri (a cura di): La natura del tempo (Propagazioni super-luminali - Paradosso dei gemelli - Teletrasporto)

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INFORMAZIONI EDITORIALI Episteme è soprattutto una rivista "non convenzionale" on-line, reperibile presso i seguenti siti: http://www.robotics.it/episteme http://www.dipmat.unipg.it/~bartocci (Numeri arretrati: http://itis.volta.alessandria.it/episteme).

Articoli, commenti e altro materiale sono benvenuti, e possono essere presentati per la pubblicazione da parte di ciascuna persona interessata. La spedizione può essere effettuata vuoi a mezzo Internet, a: bartocci@dipmat.unipg.it (inviare eventuali attachments soltanto in formato txt, o doc - si prega di non usare tex! - ed eventuali figure, tabelle, etc. in formato jpg), vuoi facendo pervenire un dischetto tramite posta ordinaria, all'indirizzo: "Episteme" Dipartimento di Matematica e Informatica, Università 06100 Perugia - Italy.

Respingendo ogni forma di "monopolio linguistico", Episteme intende mantenersi plurilingue, pertanto i lavori potranno essere redatti in qualsiasi (quasi!) lingua, vale a dire Francese, Inglese, Italiano, Spagnolo, Tedesco (etc.?!).

L'accettazione degli articoli è decisa dagli organizzatori - in base alla conformità con la linea della rivista - che ne informeranno in modo tempestivo i proponenti, riservandosi eventualmente di acquisire pareri di esperti (le opinioni ricevute saranno eventualmente rese note agli interessati), e/o di chiedere agli autori chiarimenti o modifiche.

Il materiale ricevuto anche se non utilizzato non si restituisce.

- La diffusione via Internet di parti della rivista avviene in qualche caso prima della data prevista per la pubblicazione ordinaria, dopo la quale però ogni correzione ai lavori messi a disposizione in rete viene segnalata in un apposito Errata Corrige.

- Si fa notare che la versione on-line di Episteme è talora necessariamente "semplificata" rispetto a quella a stampa (per esempio in presenza di caratteri o simboli speciali). Il file originale in formato doc dei vari articoli (o dell'intero fascicolo) verrà inviato gratuitamente dalla redazione (come attachment) a chiunque ne farà richiesta.

"Episteme" è più in generale un "progetto culturale", che non ha fini di lucro, e non è finanziato da alcun ente, pubblico o privato. Gli organizzatori se ne ripartiscono le spese secondo le personali momentanee disponibilità. Sovvenzioni per tenere in vita l'iniziativa sono ovviamente ben gradite, e possono essere inviate via vaglia postale o assegno (intestati ad Episteme) al sopra citato indirizzo.

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Oltre alla diffusione on-line, si produce anche un certo numero di copie cartacee della rivista, tra l'altro per distribuirle, a cura e spese degli organizzatori, presso Biblioteche, Istituzioni, etc.. Tali copie potranno essere ottenute da singoli rivolgendone specifica richiesta agli indirizzi sopra menzionati, al prezzo di 15 Euro cadauna. Detta somma va intesa esclusivamente quale rimborso (assai parziale!) per le spese di stampa, rilegatura e spedizione postale, e come contributo generale per la gestione e il mantenimento in vita del progetto. Si ringraziano pertanto in anticipo coloro che vorranno richiedere la versione a stampa della rivista.

EDITORIAL POLICY Episteme is mostly an on-line publication, but it does produce even printed copies. In order to obtain some of these (15$ each), a request should be sent to the editor, at one of the addresses indicated below.

Episteme is interested in publishing papers which illustrate unconventional points of view that is to say, which do not usually appear in other academic journals - in Science, History and Philosophy.

Since Episteme is thought of as a multi-linguistic journal, papers are accepted and possibly published in Deutsch, French, English, Italian, Spanish (etc.?!).

Episteme will communicate to contributors as soon as possible whether submitted papers are in agreement with the journal's criteria, or not.

Files of the papers, in doc or txt format (please avoid tex!), together with possible illustrations in jpg format, should be sent either by attachment, to: bartocci@dipmat.unipg.it or by diskette, through ordinary mail, to: "Episteme" Dipartimento di Matematica e Informatica UniversitĂ , 06100 Perugia - Italy.

Episteme can be found at the following web sites: http://www.robotics.it/episteme http://www.dipmat.unipg.it/~bartocci (Back numbers: http://itis.volta.alessandria.it/episteme).

- Sections of this journal are available in Internet even before the publication of the printed version; afterwards, any modification of the material made available in the web is registered in a suitable Errata Corrige.

- The Internet version of Episteme can sometimes be defective, in presence for instance of special characters or symbols. The original file in doc format of the various articles (or of the journal's whole issue) will be sent free (as an attachment) from the editorial office to every people asking for it.

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A Letter from the Editor to the Readers This special number of Episteme, attached to the ordinary December 2002 issue, is intended to celebrate the first three years of the journal (which has grown up more and more from its first number, meeting encouraging appreciation from an increasing number of readers), and to face - in as "professional" way as possible - one of the greater obstacles to the diffusion of the principles of Cartesian rationality. Namely, the assertion that man, conceived as a "young animal", and as a recent and still "simple" product of blind evolution and chance from nonliving matter, has not (at least in the present moment of his history, but perhaps he will never have) an intellect able to make an intuitive image of the real underlying structure of the Universe. This is, in our opinion, the answer to the question which Theocharis [a well known physicist, who is present in this number of Episteme, as well as in N. 4, Sep. 2002] asks in: "Where science has gone wrong"?1 The turning point could be in fact recognized in the 1859 publication, and worldwide success, of Darwin's theory2, which immediately led to the 1872 "revolution" in the foundations of mathematics (the voluntary renouncing of intuition in favour of a formalistic point of view, which first of all destroyed the foundational r么le of euclidean geometry3), and shortly afterwards to the 1905 relativistic revolution (fostered once again by mathematicians, those people which one could call the G枚ttingen men4). As a matter of fact, relativity was the first physical theory to introduce the idea that one could not anymore interpret all natural phenomena in a "classical way" (the reason for that would be that man's intellect does not have experience of the large, and small, scale universe), and thus supported the necessity of unconventional mathematics in physics 5 (the famous successive Einstein's "qualms of conscience", in front of a physics which had rapidly grown up highly counter-intuitive, appear entirely adequate to his "original sin").

No more explicit manifesto of this philosophy we could find but in the words of a leading XXth Century physicist, the 1965 Nobel prize winner Richard Feynman, who warns that: "What I am going to tell you about is what we teach our physics students [...] and you think I'm going to explain it to you so you can understand it? No, you are not going to be able to understand it. [...] It is my task to convince you not to turn away because you don't understand it. You see, my physics students don't understand it either. That is because I don't understand it. Nobody does. [...] It's a problem that physicists have learned to deal with: They've larned to realized that whether they like a theory or they don't like a theory is not the essential question. Rather, it is whether or not the theory gives predictions that agree with experiment. [...] The theory of quantum Electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees full with experiment. So I hope you can accept Nature as She is - absurd "6.

In front of a Nature which is irreparably "absurd", and can be only manipulated, but not understood, a rather nihilistic-irrational7 drift has spread in "natural philosophy", and from physics it has "infected" all fields of science and of Western Weltanschauung. This trend has given rise to a sort of epistemological resignation8, which has supported the common feeling that purely practical satisfaction should be the only consequence of the scientific enterprise. It also implies the supremacy of practical-echonomical values (or even simply aesthetical) over ethical, as well as metaphysical, ones (regarding as such the pursuit of pure knowledge). And this is one of the worst "sins" of our "advanced" civilization, which aims to propose itself sometimes even resorting to the force - as the unique, and the best, for the whole mankind.

Perhaps, another interesting quotation 9 would be useful in order to realize what kind of epistemology is born from such premises.

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Constructing a scientific theory means forging a new system of concepts for interpreting the world.

Such a construction has a great deal in common with the process of creating a fictional world [...] In either a work of fiction or a work of science, the task of creation is the same [...] "the boundary line between the two is not as clear as is generally believed" [here the author quotes Vladimir Nabokov's Lectures in Literature, ed. by Fredson Bowers, Harcourt Brace Jovanovich, New York 1980] [...]

There is no discontinuity between the thinking processes underlying modern science and the thinking represented in the ancient myths. [...] The scientist is a mythopoet who constructs a system of concepts for interpreting experience and weaves them into a coherent story. But science adds the discipline of prediction, testing, and building upon the results of the others. Science is mythology plus discipline. [...] Even physics, the standard of precision for all experimental science, is a mythology created by human minds guided by the paradigms of the day. [...] In modern western culture, science has largely taken the place of traditional religions [...] Many millennia ago, orally recited myths represented the best scientific thought of the time. Today, "objective" science is one of our most widely accepted myths.

The author goes on describing the shock that some students experience when confronted with this "truth", and explaining the reason for the "success" of only a few of them.

Bright students with high scores in mathematical aptitude arrive eager to learn all the wonderful truths of science. For the first two years, they really believe it. But in the third year, they study issues in the philosophy of science and discover that it is all a myth. It is a myth with high predictive value, and no other myth has been found to be more accurate. Yet it is not an Eternal verity, but simply our best guess about the universe works. When they come to that realization, many of the students go through a profound emotional crisis. Some of them never recover. But the best ones emerge with a deeper understanding of science and a better ability to do original research.

These "skeptical" opinions (which are similar in some sense to those of the well known epistemologist Paul K. Feyerabend) are of course in part right, in part wrong, and in part, moreover, paradoxical. Yes, even if most of contemporary physics could be well described indeed as a work of idealistic "fiction", all the same the aim of any "true" science should always be, at the contrary, to try to assemble (as far as it is possible) a rational image of the world, which, at least in principle, cannot be but the same for all human beings, since they share the same experiences and thought-categories10. That is to say, even if a scientist should always show himself well aware of the limits of his knowledge, and of its possible hypothetical nature, science cannot but reduce the space for arbitrariness of opinions, and a "proof" of this is the fact that very often quite independent scientists, coming from all the parts of the world, and from absolutely different cultures, elaborate the same kind of scientific theories, as this volume shows in some extent.

The "paradox" arises when one takes note of the existence of a curious factual situation [see for instance the paper of Bolognesi about the "big-bang", or the professional experiences sketched in Marinov's reprint], namely that, this "liberal" epistemology notwithstanding, scientific paradigma are defended by the establishment like dogmas, critical research on the "foundations" is discouraged, official journals would not take even in consideration papers like most of the ones published here, for instance those which express doubts about relativity, under the conviction that this theory is "beyond a shadow of a doubt" 11, and that only a crank would challenge Einstein. Briefly, the paradox is that a self pretended (in words) liberal environment, shows itself quite illiberal in the facts!

It is not difficult to realize how much of this debate is influenced even by politicalsociological purposes, since the appreciated value of tolerance would be, in the persuasion of many, better favoured by the absence of any "truth", including "scientific" ones. As a matter of fact, there are instead effective arguments concerning the possible coexistence of freedom

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and truth, for instance that there are not too many truths to be afraid of12, or that every generation has anyway the right, even better the duty, to doubt (this is the Cartesian methodological doubt) any opinion received from the previous generation. As Federigo Enriques brilliantly says: "For the values of the spirit, as well as for those of economy, a degradation law holds: men cannot peacefully enjoy their hereditary possession, but must renew and recreate these values, in an effort to understand and to get over them"13.

Carrying on this discussion, we would risk to write down a manifesto of proto-modern epistemology, opposed both to modern and post-modern (an example of this is given by the quoted Feynman and Sowa), not to say pre-modern!, epistemologies; that is to say, to make explicit the general aptitude, and expectations, which inspired the rational work of people like Galilei, Descartes, etc., and so we stop here, spending instead a few words in order to make understood how the editor (who is a mathematician, and not a physicist!) came to realize the unexpected influence of a reductionist materialist philosophy on the "foundations" of mathematics and physics, and of the existence of strong (usually overlooked) connections between the last two. He used to teach modern formalistic mathematics, telling his students as it is usual under these circumstances - that the highly sophisticated approach they were called to follow (since the very foundations), was necessary, due to the "well known" great achievements of physical research at the beginning of XXth Century. Most teachers roughly satisfy the need of motivations in this way, but the editor decided, at some point of his career, to study with more attention the previous statement, in order to be able to persuade better (mostly himself!) that the renunciation to intuition, which was demanded by the formalistic approach to the "nature" of mathematical objects, was rather justified, and wise notwithstanding his long personal teaching experience, which, quite at the contrary, had shown very clearly to him that mathematics could have been taught in a quite simpler way by using at the beginning the intuition of ordinary space (euclidean geometry, measuring, real numbers) and time (arithmetics, counting, natural numbers, order), instead of abstract structures. So he went on studying the physical connection, analysing in some detail the famous historical experiments, which led people such as Feynman to claim that "classical" explanations were " absolutely impossible". When he started this research he was quite sure that he would have found all in perfect order, and that he would have come back to his beloved pure mathematics in a very short time: but 20 and more years have elapsed since then, and he has found himself more and more sinking into a deep bog, and he was persuaded at last that the "magnificence", and the experimental ground, of some theories as relativity, or quantum mechanics (in its widespread "irrational" Copenhagen interpretation) was more an effect of propaganda, rather than of objective science (namely, a science which is based on certain experimental data, and deductions), or of logical "impossibilities".

This persuasion of the necessity of a new literal re-volution, of the restoration of ordinary rationality in Natural Philosophy, appears - we would dare say - a common thread connecting the papers collected in this volume, wholly dedicated to criticism and alternative to the pillars of XXth Century physics, relativity, relativistic cosmology, etc.. We must admit that we are well aware of the fact that some of this criticism could be in its turn criticized, since not always the arguments are free of errors, or of misunderstandings. All the same, in our opinion, this does not diminish the interest of such attempts for a long overdue renewal of science, since we are not in front of mathematics, where a mistake in a line of a proof of a theorem usually makes the whole discussion worthless. Matters in physics appear more complex, and subtle, and one can take advantage of even "unperfect" papers, which however express good ideas14.

We are ending this "foreword" explaining briefly the criteria which inspired the choice of the reprints. As Friedwart Winterberg says very keenly, the promising attempts of physics at

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the end of XIXth Century, aimed towards a knowledge of the aether's structure, "were brought to an abrupt end by Einstein's rejection of the ether and its replacement by his well-known postulates"15. Both the papers of Almansi and of Moisseiev appeared as a good example of this assertion, even if they, especially the second one, were written after the publication, and the rather fast acceptance16, of Einstein's theory. "Explanation" of gravitation as a possible phenomenon of hydrodynamical origin, and the analysis of the resistance to the motion through a fluid medium, could have been quite well proposed as studies concerning possible properties of "physical space" (pressure, pressure waves, resistance, etc.), supposed either a continuous or a powdery (an hypothesis which we personally find more likely) medium. The publication of Marinov's "paid advertisement" in Nature, was something due, a tribute to the memory of on unforgotten friend, and in most sense a "master". Not all his opinions appear acceptable, since he never believed in an "aether", yet he defined himself an "absolutist", a situation which led him to statements like: there are no "fields", there is no (finite speed) propagation of interaction, there exists energy coming from "nothing", and so on. The same applies for the choice of Zapffe's "exodus": a commemoration of a physicist which always disputed relativity as a an adequate "model" of physical reality 17. His magnetospheric theory sounds quite attractive, unfortunately one must repeat what has been said in Marinov's case, not all his opinions appear acceptable18.

Notes 1 - Nature, 1987, 329; Nature, 1988, 333 and 389.

2 - The connection with darwinism is essential in order to understand all the development of Western science and culture during the last 150 years. A very interesting virtual book [Adnan Oktar (Harun Yahya), The Evolution Deceit] dealing with this matter is freely available at the web page: http://www.evolutiondeceit.com/ . Needless to say, this does not mean that everything before was quite good, and that were not irrational obstacles interposed against free thought - which is the indispensable condition for the progress of any knowledge - but the Darwinistic pessimism and aggressiveness had a very bad influence on the field itself of "rationality".

3 - U. Bartocci and J.P. Wesley eds., Proceedings of the Conference on Foundations of Mathematics & Physics in 20th Century: the Renunciation to Intuition, Benjamin Wesley Publ., Blumberg, Germany, 1990.

4 - See for instance the very interesting Lewis Pyenson's book, The Young Einstein - The advent of relativity (Adam Hilger Ltd, Bristol and Boston, 1985), in particular Chapter 5: "Physics in the shadow of mathematics".

5 - Ibidem, p. 83.

6 - QED - The strange theory of light and matter, Princeton University Press, 1985, pp. 9-10.

Feynman goes over on this opinion at the beginning of his celebrated lectures about Quantum Mechanics (The Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965): "We choose to examine a phenomen which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery". Of course, from an aether-theoretical point of view, all the pretended "impossibilities" are rooted instead on the post-relativity disappearance of the concept of aether, as responsible for all quantum phenomena. B.H. Lavenda and E. Santamato assert for instance that: "Quantum indeterminism is explainable in terms of the random interactions between quantum particles and the underlying medium in which they supposedly move" ("The Underlying Brownian Motion of Nonrelativistic Quantum Mechanics", Foundations of Physics, Vol. 11, N. 9/10, 1981, p. 654); and elsewhere that: "It might perhaps be possible to develop a completely classical formulation of quantum mechanics based upon the irregular motion of a single Brownian particle immersed in a suspension of lighter particles" ("Stochastic Interpretations of Nonrelativistic Quantum Theory", Int. J. of Th. Physics, Vol. 23, N. 7, 1984).

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7 - The word "irrational", which could evocatively qualify some contemporary physical theories, is introduced just in opposition to "classical physics", namely to physics which makes use only of ordinary rationality (that is to say, founded on ordinary space, time, causality), but we must explicitely remark that to go beyond this ordinary rationality does not necessarily mean to fall into inner contradictions, as some too naif criticism - for instance of relativity - seems to believe. The situation is similar to the famous case of non-euclidean geometries. They are logically acceptable intellectual constructions, but they do not describe the intuition of ordinary space which is "rooted" in man's mind. Exactly as non-euclidean geometries show that there are many possible "models" of space which could be thought of, relativity show that it is possible to conceive many abstract mathematical models of space-time, and the important question to ask is not whether these counter-intuitive spacetimes are "illogical" in themselves (since after all they are mathematical models, and thus they are "logical" in the same measure as all mathematics is logical), but if their introduction is really necessary in order to describe Nature's laws.

8 - As it has been called by Franco Selleri, in La causalità impossibile - L'interpretazione realistica della fisica dei quanti, Ed. Jaca Book, Milano, 1987, p. 13.

9 - From the chapter "Science as a Mythology", in John F. Sowa: Conceptual Structures - Information Processing in Mind and Machine, Addison Wesley, 1984, pp. 353-356.

10 - "There can exist but one correct method of viewing any subject or question whatever", see in this same Episteme's issue the paper of C.J. Bjerknes dedicated to S. Tolver-Preston.

11 - From the title of the Chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will, Was Einstein right?, Oxford University Press, 1988. No less enthusiastic appears the famous mathematician Hermann Weyl (which the author appreciates very much in different contexts), when he claims (in Space - Time - Matter, Dover Pub., NY, 1952) that: "Einstein's Theory of Relativity has advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us from Truth has collapsed" ("Truth" has a capital initial letter in the original English text, but one should take into account that in the German original the corresponding term "Wahrheit" had to be written with a capital initial by a general rule of that language). Nevertheless, orthodox physicists are not so unwise do not acknowledge that any physical theory cannot be a perennial certainty, and that it could be shown wrong in certain respects, an approximation of limited validity to reality. For example, many physicists would easily accept that the theory of relativity (both special and general) may be imprecise when applied in the domain of very small distances, or that it may not be adequate when applied to extremely large ones (for instance, of the order of the presumed "size" of the universe). But, even if these possible breakdowns would not cause concern, it appears very unlikely that the establishment would be willing to recognize that relativity gave a quite misleading image of the universe, and that they followed a completely wrong path for more than 100 years.

12 - We would say, either of a logical-mathematical nature, or of an experimental one, while "general theories" do almost always depend on the choice of principles a priori, which as such are obviously free. Any discussion acknowledging the different rôles of hypotheses, facts and deductions (or even inductions and abductions), should always develop with extreme tolerance, very often establishing not one single truth, but just a graph of possibilities, which was the the ideal of Leibniz's calculemus.

13 - Le matematiche nella storia e nella cultura, Ed. Zanichelli, Bologna, 1936, p. 153. Editor's translation, with obvious apologies, here and elsewhere, for the poor English!

14 - We could add that, in the worst case, some mistakes have the instructive consequence to show how a counter-intuitive treatment of physics could lead even educated scholars into intellectual bewilderment.

15 - "The Goal Towards Unified Theory of Elementary Particles and the Ether Hypothesis" (in Physical Interpretations of Relativity Theory. Proceedings, London, 1988).

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16 - At least from the greatest part of the scientific Western establishment, with some curious exceptions, which would not today politically correct to discuss with absolute freedom of opinion and expression.

17 - He was even one of the contributors to the Proceedings of the International Conference "What Physics for the Next Century?", Ischia, 1991, Ed. Andromeda, Bologna: "Bradley Aberration and Einstein Space-Time", pp. 197-198.

18 - For instance, as numerous critics of relativity, he falls in the "trap" of the so-called Dingle Syllogism, which is unfortunately not so good a weapon against special relativity (it would just emphasize that relativity is not completely a "relativistic" theory, since the difference between inertial and accelerated motions is an "absolute feature" in Minkowski space-time; see for instance our "Most Common Misunderstandings About Special Relativity", at the web page: http://www.dipmat.unipg.it/~bartocci/ERRORSVF.htm).

***** The following words, coming from a private communication, seem to be very appropriate to put an end to this Introduction.

Aether as a continuum is the Solution Glory to experts in Aether models! While people are wondering how the universe began and evolved, The Answer seems to depend upon Aether as the continuum in Fluid Mechanics.

Hydrodynamics provides an analogy to the physical pictures of simplicity in fundamental Nature. In the simplest continuum analogous to vacuum, quantum uncertainty is not yielding particles but actually, mini vortices. Vortices are stable, interactive, and able to form particlelike patterns. Vortices are actually spinning strings in Superstring Theory.

The beginning of the Universe is just the quantum fluctuation of Aether or the fabric of space.

Quantum field is a vacuum continuum. While other physicists are still searching for the reality of superstring, aether continuum physicists or fluid mechanics physicists are keen on the reality and application of vortices.

[Wishing a prosperous development and promotion of Aether models], Wu Chi Kay - Aether model developer

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Alternative Physics On Line As stated in the previous "Letter to the Readers" which opens this volume, during the second half of the last Century (after World War II, and after the worldwide consecration of Albert Einstein's "authority"- by the way, due to a doubtful connection between relativity, the famous formula E = mc2 , and the construction of the atomic bomb - as a result of the nuclear explosions at Hiroshima and Nagasaki), the publication of papers expressing criticism of or alternatives to relativity has almost been banned by "normal" scientific journals (justified by the claim that: only a crank would challenge Einstein). This attitude has on the one side almost totally discouraged the production of free critical thought, and on the other side has crystallized the foundations of established Physics in a system of dogmatic immobility - a situation which forced many intellectuals (not only physicists) to understand scientific knowledge as a kind of "religion" (a thought system in which beliefs cannot be checked by laymen, or not even really "understood" - see for instance, in this same issue of Episteme, Marinov's complaints, or Theocharis' contributions).

Even today, things are continuing in this manner, as far as leading scientific journals are concerned, but the increasing diffusion of the Internet has allowed greater freedom of expression and communication, and this has supported the acquisition of unconventional news and points of view, thus showing that discomfort towards the actual establishment's philosophy of Nature and of Science is rather widespread. In this page, we offer some interesting examples of this "resistance", which becomes more and more worth of attention, the more some investigations could lead to unexpected and very positive practical consequences (see for instance Aspden's mention below of an "unseen sea of energy that we inhabit in ignorance of its overwhelming power").

We are ending this short presentation with an almost obvious consideration: while censorship of ideas has become less effective, the web's information content has become so large that even a willing reader is at risk of getting lost in a maze of too many inputs, some of which must truly be classified in the realm of day dreams, if not of voluntary disinformation...

[Thanks to Josef Hasslberger, Francisco J. M端ller, Delbert Larson, for their valuable support and cooperation] *****

"Unconventional" Scientific Journals On Line and General Web Sites 1) Aetherometry - The Science of the Metrics of the Aether, http://www.aetherometry.com/ 2) Aether Sites, http://www.aethro-kinematics.com/wc_sites.html 3) Apeiron - Studies in infinite nature, http://redshift.vif.com/ 4) (Various papers about) Extracting Energy from the Active Vacuum, http://jnaudin.free.fr/html/meg.htm 5) Galilean Electrodynamics, http://www.galileanelectrodynamics.com/

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6) Infinite Energy Magazine, http://www.infinite-energy.com 7) Journal of New Energy, http://www.padrak.com/ine/ 8) Journal of Theoretics, http://www.journaloftheoretics.com 9) Astronomy Research - Scientifically viable challenges to mainstream paradigms, http://metaresearch.org/ Something has gone wrong in the field of astronomy. Many widely held beliefs fly in the face of observational evidence. Theories go through such contortions to resolve inconsistencies that the ideas can no longer be explained in simple language. Alternative ideas are often rejected out of hand simply because they challenge the status quo. The result... many of today's theories are unnecessarily complex. Meta Research is dedicated to bringing some common sense back to this field. Here we challenge ideas that have consistently failed to make successful predictions, examine new paradigms, and advocate the ideas found to be most worthy of further consideration and testing. [...]

10) Modern Scientific Theories of the ancient Aether, http://www.magna.com.au/~prfbrown/aetherqr.htm 11) Natural Philosophy Alliance, http://mywebpages.comcast.net/deneb The Natural Philosophy Alliance (NPA) is devoted mainly to broad-ranging, fully openminded criticism, at the most fundamental levels, of the often irrational and unrealistic doctrines of modern physics and cosmology; and to the ultimate replacement of these doctrines by much sounder ideas developed with full respect for evidence, logic, and objectivity. Such reforms have long been urgently needed; and yet there is no area of scholarship more stubbornly censorial, and more reluctant to reform itself.

Reigning paradigms in physics and cosmology have for many decades been protected from open challenge by extreme intolerance, excluding debate about the most crucial problems from major journals and meetings. But the founding of the NPA in 1994 provided those struggling against this irrationality and intolerance with the strength, visibility, and credibility that comes from numbers and from collaborative, purposeful effort. It has also enabled them to share, expand, and refine their individual knowledge through contact with many other critical scholars, at NPA general meetings--held at least once per year since 1994--and by phone and mail, both postal and electronic. [...]

12) Sapere Aude, http://www.btinternet.com/~sapere.aude/ (from Dec. 2002: http://www.dipmat.unipg.it/~bartocci/fis/sapere_aude.html) Reclaiming the common sense foundations of knowledge The site seeks to further the debate about the foundations of knowledge by facilitating access to the arguments of critics of orthodoxy. Because of the perennially central role the natural sciences, critical arguments focus on the presuppositions, concepts and methods of modern physics, and especially on the cognitive revolution associated with special relativity ("antirelativity").

13) The Subspace Project, http://www.martinelli.org/ Why an Aether? Its almost a commonly known fact that the aether was disproven by an experiment done almost one hundred years ago, by a couple of physicists whom we know as Michelson and Morely (see "Is the Speed of Light Constant" ). Given that, An obvious question might be then, "why should we re-visit this idea?". There are a few reasons why we should. The first point I should make is that the aether theory that was disproven by the

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Michelson and Moreley experiment was that conceived by 19th century physicists. This only means the first aether conception was wrong, not that there is no aether.

Furthermore, new scientific research is a process of "turning over stones". We are simply not smart enough to know which 'stones to turn' or what we will find underneath. Sometimes we can find things of interest , most times not -- but, sometimes you get "spin-offs".

When it comes to basic research it is unfortunately hard to guess at any kind of a return on investment. The Michelson and Morley experiment is one example of an unexpected ROI. They were doing basic research - just doing the sweeping - after all the great discoveries had finally been made. They were measuring the drift velocity of the earth through the aether.

Every physicist expected that the Michelson and Morley experiment (because of the extremely precise Michelson Interferometer) would give some number for the earth's drift velocity through the aether. This number was the expected ROI. Instead they found no drift velocity whatsoever. In fact, if we were to use their results to calculate the velocity of the earth with respect to the aether we would have to say that the earth is at absolute rest - not even orbiting the sun!. This was far more interesting and valuable than the expected ROI. They found 'gold' - a new principle - a new physical law. â&#x20AC;Ś "the speed of light is constant for all frames." With this new law, physics took a very unexpected turn. This find was one of the key ingredients to today's modern physics. It gave Einstein the foundation upon which all of his work was built. And this gives us another observationâ&#x20AC;Ś As the turn of the century was approaching, physicists believed that physics was nearly done. This turned out to be wrong way wrong. This is a pattern in science history. In fact, it is not too far off to state this as a principle, that "established science is often wrong". [...]

Are There Aether Atoms? Yes, but they are not what you might expect. [...]

14) Sur la piste de l'Energie Libre, http://quanthomme.free.fr/CHERCHEURS1.htm 15) 21st Century Science & Technology, http://www.21stcenturysciencetech.com

Some Interesting Papers On Line 1) http://www.energyscience.co.uk/index.html Aether Science Papers by: Harold Aspden This is not a commercial website. It is an educational site operated on a non-profit basis by Energy Science Ltd. under the direction of Dr. Harold Aspden, who in his retirement years provides the financial support needed to sustain this venture. Dr. Aspden acknowledges his gratitude to the Internet facility for providing the means to tell the world about his lifelong exploration of the unseen sea of energy that we inhabit in ignorance of its overwhelming power.

The book Aether Science Papers was published in 1996. [...] The 14 papers, reproduced in A4 format from the scientific periodicals in which they were first published, constitute the main section of the book. The front section of the book is a 68 page commentary entitled The Creative Vacuum. In view of the importance of making scientists aware of this work, it has been decided to publish the opening 68 pages here in these Web pages.

About the Title: The 'aether' is a word which says that there is no such thing as empty space.

To say there is no aether is therefore to assert that space can be truly empty, meaning it contains nothing of an electrical character, it now being a well established fact that there is nothing having a physical existence that lacks electrical properties. If a scientist expresses doubt by reference to the 'neutron', I say that the neutron has magnetic properties which are seated in the motion of electric charge. Otherwise, you need to explain why it has a magnetic

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moment. If that scientist then mentions the 'neutrino', then I say that the 'neutrino' was only a notion, a figment of imagination invented as a devious way of declaring that the aether could absorb or shed energy and momentum without admitting that the aether exists. If that scientist says that the consensus opinion of professors of physics who deny the reality of the aether can surely not be discarded, then I ask "Why not?" and can but point to a report on page 12, 6 May 1996 issue, of The Times newspaper in U.K. Science correspondent Nigel Hawkes wrote under a heading 'The possibility of getting something for nothing': "A physicist at Cambridge University has produced a new and daring explanation for an old puzzle. If she is right, it could be the first convincing evidence that it is possible to get something from nothing. The question Claudia Eberlein addresses in a forthcoming issue of Physical Review Letters is that of sonoluminescence. If you expose water to a blast of ultrasound, you get a flash of light.

This is deeply puzzling, because visible light has so much more energy than sound that the energy of the sound has somehow to be boosted by a trillionfold. The wavelength of the light emitted implies that the source is at a temperature of tens of thousands of degrees C. Ms Eberlein suggests that the emission of light is a quantum vacuum effect - energy given off by the vacuum. Quantum theory says that there is in reality no such thing as a vacuum and that empty space teems with 'virtual particles' including photons which flit in and out of existence.

The theory is open to test. If it turns out to be right, her explanation will be a major coup, the first observable manifestation of quantum vacuum radiaton."

The energetic vacuum is, therefore, a live issue. The 'aether' is a reality and I believe that it can, like a fluid crystal, form structure and dissolve that structure, as it latches onto material substance, but if that substance vibrates excessively then even the aether is confounded and, in its confusion, it sheds energy! I have, accordingly, chosen the title Aether Science Papers with deliberation, knowing that, in the end, the 'aether', per se, will have to be recognized, even though that will confound the non-believers who constitute the modern generation of physicists.

2) http://mujweb.cz/veda/babiakjoz/MMX%20New%20view.htm Michelson-Morley's Experiment - A New View by: Jozef Babiak Michelson-Morley's experiment carried out in 1887 should determine absolute velocity of the Earth around the Sun in the hypothetical "aether". Negative results of this experiment, why the shift of the interference fringes does not appear when rotating the interferometer in the angle of 900, explained in 1892 Fitzgerald and independently of him Lorentz with the contraction hypothesis. Einstein in 1905 built his Special Theory of Relativity on validity of the contraction hypothesis and on the principle of constant velocity of light in vacuum. [...]

The calculation of the shift of the interference fringes that should appear by absolute velocity of the Earth around the Sun, is in literature given as follows: [...] This calculation of the shift of the interference fringes in the Michelson - Morley's experiment is incorrect, because it is calculated according to the laws of the classic Newton's mechanics - using Galileo's transformations. Michelson - Morley's experiment is a physical experiment with light, therefore calculation of the shift of the interference fringes should be calculated according to the optics' laws. Light in its nature (photons, electromagnetic oscillation) and with its way of propagating in the solid environment (Snell's law, Huygens' principle) differentiates with its characteristics from solid bodies to that are valid the laws of the Newton's mechanics. Light photons - are atom particles which by interactions with atoms of the solid environment create the optics' laws, therefore we can not describe the propagation of the light in the solid environment using the laws of the classic Newton's mechanics. Snell's law defines the velocity of light beams in the solid environment as c / na , where na is refractive index of light in the solid environment. In the calculation of the shift of the interference fringes is the velocity of light beams in the interferometer arms stated incorrectly as c, which is the velocity of light in vacuum. In the Michelson-Morley's experiment there is no vacuum in the

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interferometer arms. I present here an argument, that is often presented, that the velocity of light in the air is just a few less than in vacuum and has no significant meaning for this experiment. The velocity of light beams in the air in the Earth's atmosphere is less by c - c / na = 79 km/s than the velocity of light in vacuum c. Michelson's inteferometer can measure he change of the velocity of light from the shift of the inteference fringes with the accuracy 1 m/s on the length of one meter. Therefore is unavoidable to state the precise value of the velocity of light in the arms of the Michelson's interferometer. Huygens' principle of propagation of the light in the solid environment defines, that every point to which the oscillation comes, becomes the source of the elementary oscillation. Huygens' principle avoids adding the velocity of light beams with the velocity of light, because the source of the light oscillation becomes each point of the solid environment which the oscillation reaches. Sound is propagated in the solid environment using the same principle. Pressure wave - sound is propagated in the solid environment progressively from point to point with the velocity given by the parameters of the solid environment. We can observe this phenomenon very well and graphically on the flying plane. The velocity of the sound coming from the flying plane is not added to the velocity of the plane, the sound is propagated from the flying plane in the air with the velocity given by the air parameters. The velocity of the movement of the sound source has no influence to the velocity of the sound. Only the sound frequency is changing, according to the Doppler's principle. Michelson-Morley's experiment has been measured in the air, therefore the light beams in both interferometer arms were moving in the air. The air in both interferometer arms is at rest with respect to the interferometer, therefore the velocity of the light beams with the respect to the interferometer is in both arms c / na . [...]

3) http://www.paradox-paradigm.com/ From Paradox to Paradigm by: Johan Bakker Foreword: Quantum mechanics and the Relativity Theory are incompatible. Somewhere something must be wrong. In 1727 Bradley observed the star y-Draconis and measured the stellar aberration. Science concluded unjustly from these measurements that the influential ether could not exist. Michelson and Morley proved without doubt, with their famous experiment in 1887, that absolute ether could not exist.

After both ethers were denied the Special Relativity Theory of Einstein was inevitable. The propagation of forces and light through vacuum became mysterious and almost unexplainable; time and space became relative.

In the 20th century quantum mechanics developed and gained momentum through the rapid development of computer science, mathematics and technological development. The mathematical solutions are staggering, though even the greatest scientists admit they do not comprehend the physical implications of quantum mechanics totally. In atomic and subatomic physics math has taken over. The flaw of quantum mechanics is the lack of physical understanding; it's become an empirical science.

When we consider that science unjustly rejected the hypothesis of the influential ether, in theory the possibility of this alternative still exists. Exploring the possibilities of the influential ether, it was "easy" to find mathematical and physical explanations for relativistic observations and the Lorentz factor. The scientific explanations the ether gives for unexplained and mysterious physical phenomena are vast.

Elementary and atomic particles like electron, positron, proton, neutron, deuteron, photon and neutrinos reveal their existence in simple non-relativistic mathematics. The physical background of quantum mechanics becomes clear. The dual character of particles and uncertainty principle of quantum mechanics coincides with the ether. Nuclear fusion is better understood. Even the cause for gravity emerges.

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Theoretical physicists are not able to disprove the ether theory. They however, understandable, reject the possibility of ether because it differs too much with the present scientific perception; their opinion is pre-determined. [...]

Summary: The concrete indications science should look in depth at the possibilities of the ether theory are: - In the 19th and 20th century science did not give enough attention to the possibility of the influential ether after this medium was denied prematurely. The influential ether describes the stellar aberration perfectly and therefore science should admit the ether theory is a possible alternative theory.

- The drag coefficient of Fresnel was confirmed by the experiment of Fizeau. This confirmation had no scientific meaning at all, because the drag coefficient was introduced ad hoc without a valid physical explanation. It was already certain a "drag factor" would be measured after Arago's observations. The perfect match of the experiment of Fizeau with the assumption of ether is a different case and should puzzle scientists.

- The ether theory, described in a simple basic manner in the previous chapters, give all the explanations you need to explain relativistic observations.

- The inert qualities of the ether gives an explanation for the observed, yet unexplained, synchrotron radiation.

Often one hears scientists declare the more simple a theory is the more valid it becomes. The ether theory, with only two forms of energy and related forces, is extremely simple and explains a lot. Why do scientists reject the ether theory without validated arguments? The comfort the ether theory explains the revelation of stable particles from ether should mean something to scientists and produce wondering. The, in a simple way, derived radius of the neutron combined with the basic equation of the energy of an oscillation eliminates the constant of Planck and derives a simple classical non relativistic presentation of the mysterious photon. What is the chance this can happen if it is pure coincidence? The strong magnetic force, the electrostatic force and the electromagnetic oscillation energy in the deuteron, the aligned proton and neutron, gives a basic explanation for the quantum mechanic properties of atomic nuclei and particles. The speculative, but yet simple and consistent, explanation of gravity emerging from atomic nuclei in matter opens the possibility the ether theory becomes "the theory of everything" when science gives it proper attention.

Measurements on magnetic currents with directed magnetic spin indicate that there might be a relation between mass and magnetic energy that exceeds the relation E=Mc2 .

These are the arguments I found pro "ether", by assuming there might be ether after all. The described ether can explain many othernot mentioned phenomena. For example it is not hard to see that it is impossible for a proton to merge with an electron when conditions are not extreme dense. The properties of the mysterious neutrino become clear etc.

Also in favor for the ether theory are contradictions like: - The Relativity Theory and quantum mechanics contradict each other. There must be something wrong somewhere!

- The American spacecraft's, the Pioneer 10 and 11 moves through space with a different direction than calculated with the Relativity Theory. The differences are small but undeniable and unexplained.

- In astronomy calculations bare large uncertainties. The estimations of the age of the universe are between 7 and 20 billion years. Factors of importance in astronomy are speed, distance, mass and time. All the astronomic measurements need relativistic corrections, which corrections will differ slightly when ether is assumed. Possible the accuracy of these calculations increases when astronomic data is corrected, according to ether, in a slightly different way?

- And "last but not least" there are the paradoxes the Relativity Theory and quantum mechanics imply. If there is no other explanation, the paradoxes have to be real, but without

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having to explain the paradoxes, the outcome of science is much clearer and therefore much more preferable.

When I started to write "From Paradox to Paradigm" I just knew in what direction I had to look. I was not satisfied with the perception of science of the world we do not experience.

Science does not yet have all the answers. When you look what science achieved the last century you have to be impressed. The information technology and mathematics opened a world that was fast explored. Scientists eager to explore the unknown had found the code to decrypt the inexplicable. It had to be the truth what they discovered because the math matched the experience so well and suddenly what we experienced was no longer valid. Scientists use the validated argument that what we see is not necessary correct. But they misuse a similar argument when they say that math describes the data and therefore must be true. They forget that math is only a tool to describe the events observed and therefore only describes the mathematical solution of that part of reality. Quantum mechanics describe the experienced atomic and subatomic world very well. The achievement of science in this area is enormous.

One has to be impressed, but science is also the achievement of men and therefore there is a change it overestimates itself: science itself can become arrogant. Science should be aware of its limitations. Quantum mechanics describe the behavior of (sub) atomic physics very well, this however does not mean that quantum mechanics are the answer to the whole truth. It is not, nothing is. It describes only a part, the observed in a mathematical way, and can therefore not be absolute. Quantum mechanics are even more limited in its revelations when derived relations are extrapolated. The value of extrapolated mathematical solutions is seriously limited by the fact that one does not know what the math describes exactly. It is a mathematical solution for a limited outcome of part of the process. Quantum mechanics describe the mathematical relation between observed data. These mathematical solutions do not explain the physical process that takes place. Quantum mechanics has no validation to pretend to describe the physical processes completely.

It would be arrogant to state that the ether is a better way to understand physics, but it is not when you state that it might be. As long as science denies the possibilities of the ether without valid arguments science is arrogant. In theoretical physics there are many contradictions that cannot be resolved, and therefore set aside. The possibilities of the ether theory to combine the uncertainty principle and duality of quantum mechanics and the deterministic aspects of classical physics are vast.

The main reason to write "From Paradox to Paradigm" is not be "right" or "wrong". If science took a path that is not completely correct, the perception quantum mechanics provides may not be totally valid. The consequence will be that we are not able to foresee that some interpretations are not entirely correct. We cannot adjust, because the only hold we have is the math and math only describes the direct relation of the data in a mathematical way. The ether described in this book gives strong indications that nuclear fusion will not be achieved, in an economic profitable way, by means of thermal nuclear fusion. The approach according to the ether should be totally different.

When atomic nucleus are captured and guided by strong magnetic fields the uncertainty principle can be contained and Controlled Cold Nuclear Fusion (CCNF) becomes theoretically possible. No one denies the necessity of abundant and clean nuclear fusion energy for our modern society. The high costs, pollution, global warming and limited reserves of natural energy resources will become disastrous in due time. And yet science denies society to explore this possibility by not taking the ether seriously.

[The book is accessible and can be printed, free of charge, at the web site above] 4) http://www.einsteinontrial.com/ Einstein on Trial, Or Metaphysical Principles of Natural Philosophy - A collection of essays written over a period of a quarter of a century

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by: Jorge Céspedes-Curé.

In 1905, Einstein set the scientific community on an innovative and, at the time, controversial course abandoning the Newtonian concept of space and time and upholding the MaxwellLorentz electrodynamics. Was this a leap forward or has the 20th century followed a misleading course? In a thoroughly readable and exhaustively philosophical analysis, backed by rigorous mathematical arguments, Jorge C. Curé places Einstein's conceptions on historic scrutiny. By unifying the Newtonian and classical relativistic conceptions of nature, he establishes a New Physics. A fitting revolution for the new millennium.

In Chapter 1, the author examines the philosophical knowledge Einstein had about the ontological and epistemological foundations of physics. He finds, in this respect, that Einstein was one of the few creators of 20th century physics who knew precisely what he was doing in the philosophical foundations of physics. In Chapter 2, Curé deduces a generalized HamiltonJacobi equation (HJ) from Newton's axiom of motion. This generalized HJ equation contains an extra term, which Curé calls the "quantum collective potential" (QCP). Curé goes on to show the ontological origin of the QCP based on a philosophical consideration when applying Newton's axiom of motion. He then shows that Schrödinger's equation is a particular case of the generalized HJ equation. In this chapter, Einstein is found not guilty, at all, in accusing quantum mechanics for being an incomplete theory. In Chapter 3, a vast collection of Electrokinetics (EK) and Electrodynamics (ED), which were scattered in the history of physics of the 19th and 20th centuries, are examined. They are classified and also translated to a modern vector notation. In Chapter 4, Newton's three principles are extended from three to five. Curé accepts Einstein's challenge to deduce "formally and logically" a Newtonian Gravitodynamics and Electrodynamics. Then he shows theoretically and experimentally the existence of a new ED field proportional to the square of the electric current. He also presents the revival of Eddington's model of the neutron as a miniature hydrogen atom. In Chapter 5, Curé re-examines the cosmic ether concept, discovering how Einstein himself resuscitated the concept in 1920. The author explains the light deflection of remote stars by the solar energy field, using the classical phenomenon of refraction. Curé's calculations show a much better agreement with Merat's empirical law of solar light deflection, than Einstein's calculations. In Chapter 6, Curé demonstrates that Newton provided, in his Principia of 1687, an original explanation about the perihelic rotation of planet Mercury. Curé defends General Relativity Theory (GRT), in the event that the sun is oblate. Curé uses the measured starlight deflection by the energy field of the sun to determine the stellar density of energy. At the end of this chapter, the author speculates on an alternative explanation of the starlight redshift. This work has profound implications on the Big Bang theory and modern cosmology. In the last Chapter 7, Curé begins with the analyses of four essays written by Einstein, between 1930 and 1948, about "Science and Religion." The author points out that Einstein, through the four essays, foresaw the advent of a future scientific theology. Einstein believed that through a "cosmic religious experience" man could acquire transrational knowledge by a transcendental reconnection with the Supreme Intelligence. In the rest of this chapter, Curé pursues, to its finality, the consequences of these initial theological intuitions of Einstein. In this way, Curé establishes the foundations of "Cosmotheism" or Scientific Theology.

5) http://ourworld.compuserve.com/homepages/jlnaudin/html/elecmtr.htm Electrogravitics - Experiment With A Motor By: Patrick Cornille 6) http://www.orgonelab.org/miller.htm Dayton Miller's Ether-Drift Experiments: A Fresh Look by: James DeMeo The history of science records the 1887 ether-drift experiment of Albert Michelson and Edward Morley as a pivotal turning point, where the energetic ether of space was discarded

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by mainstream physics. Thereafter, the postulate of "empty space" was embraced, along with related concepts which demanded constancy in light-speed, such as Albert Einstein's relativity theory. The now famous Michelson-Morley experiment is widely cited, in nearly every physics textbook, for its claimed "null" or "negative" results. Less known, however, is the far more significant and detailed work of Dayton Miller.

Dayton Miller's 1933 paper in Reviews of Modern Physics details the positive results from over 20 years of experimental research into the question of ether-drift, and remains the most definitive body of work on the subject of light-beam interferometry. Other positive etherdetection experiments have been undertaken, such as the work of Sagnac (1913) and Michelson and Gale (1925), documenting the existence in light-speed variations (c+v > c-v), but these were not adequately constructed for detection of a larger cosmological ether-drift, of the Earth and Solar System moving through the background of space. Dayton Miller's work on ether-drift was so constructed, however, and yielded consistently positive results.

Miller's work, which ran from 1906 through the mid-1930s, most strongly supports the idea of an ether-drift, of the Earth moving through a cosmological medium, with calculations made of the actual direction and magnitude of drift. By 1933, Miller concluded that the Earth was drifting at a speed of 208 km/sec. towards an apex in the Southern Celestial Hemisphere, towards Dorado, the swordfish, right ascension 4 hrs 54 min., declination of -70° 33', in the middle of the Great Magellanic Cloud and 7° from the southern pole of the ecliptic. (Miller 1933, p.234) This is based upon a measured displacement of around 10 km/sec. at the interferometer, and assuming the Earth was pushing through a stationary, but Earth-entrained ether in that particular direction, which lowered the velocity of the ether from around 200 to 10 km/sec. at the Earth's surface. Today, however, Miller's work is hardly known or mentioned, as is the case with nearly all the experiments which produced positive results for an ether in space. Modern physics today points instead to the much earlier and less significant 1887 work of Michelson-Morley, as having "proved the ether did not exist". [...] http://www.orgonelab.org/ 7) http://www.norbertfeist.de/english.htm#Absatz4 Ether Theory or Relativity Theory? by: Norbert Feist The missing aberration of terrestrial sources, a new analysis of the Michelson Experiment and analogous acoustic experiments with the result of a new identical propagation equation for light and sound call the premises of relativity theory into question. They speak for the existence of a luminiferous ether as absolute frame of reference and propagation medium for electromagnetic waves.

8) http://rosarioclub.com/ciencia.htm La Aventura del Razonamiento - Ciencia & Descubrimiento by: Ricardo Gómez Kenny La comunidad cientifica, si bien evoluciona, es cerrada, ciega y sorda. El inesperado descubrimiento, anunciado por un argentino hace ya varios años, hoy deja sin respuesta a los matemàticos. Entre las opiniones que han podido recibirse - todas con alguna excusa - se puede leer "entre lìneas" , algo asì como...".!Ah, yo no fuì! Dirìjase a fulano." Si el error puntualizado llama la atenciòn, (por lo simple y razonable), la causa de todo sorprende mucho màs aùn. Los equipos de cientìficos, oficialmente reconocidos y que dicen "estar a favor de la acciòn interdiciplinaria", nunca quisieron tomar en cuenta la opiniòn racional de los grupos llamados comunmente "proyectistas". En sìntesis: Segùn este investigador ... todos los dibujos que representan experiencias en los libros de fisica, (En el tema Relatividad), estan mal confeccionados. No responden a las reglas preestablecidas para objetos en movimiento.

Obviamente, la crìtica no se refiere a errores propios del dibujante sino de aquèl que concibiò

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dicha forma de representaciòn.¿Tienen validez los razonamientos que le siguen? Podrìamos resumir toda esta situaciòn en esta frase: "Un arquitecto moviò la estanterìa. Los matemàticos, desconcertados, se reùsan a debatir". [...]

9) http://www.hasslberger.com/ Vortex - The Natural Movement - Considerations on Light, Matter, Gravity And Magnetism by: Josef Hasslberger Physics, the science which should be explaining to us how the universe came about and what it consists of, seems to have arrived at the end of a blind alley. Its descriptions of the origin and the workings of our universe get more and more complex, less and less agreed-upon and they are definitely not going to accompany us into the 21st century. We are at the beginning of the space-age. In order to survive in that new age, we need clear and unequivocal descriptions of physical phenomena. [...] The trouble is not where physicists commonly look.

It seems to be more a question of philosophical or religious outlook. Our view of nature was conditioned first by the great philosophers of ancient Greece and then, for a long time, by the orthodox religions prevalent in current western civilization. Ironically, the physicist who denies the action of a creator, just by this very denial limits the scope of his investigations. He has become "inversely religious", which to an independent scientific investigation is no less limiting than the stand of the dogmatic religionist. So it might be that progress in our time has become dependent again on philosophy, on that science of thinking, of looking at basics and drawing conclusions that is unencumbered by the specialization so prevalent in the physical sciences. The following is a speculative description, in simple terms, of the basic workings of the universe. [...]

10) http://www.dipmat.unipg.it/~bartocci/H&KPaper.htm Hafele & Keating Tests; Did They Prove Anything? by: A.G. Kelly Abstract: The original test results were not published by Hafele & Keating, in their famous 1972 paper; they published figures that were radically different from the actual test results which are here published for the first time. An analysis of the real data shows that no credence can be given to the conclusions of Hafele & Keating. ... A leader in Nature in 1972 [11] said that "the agreement between theory and experiment was most satisfactory". ... The Hafele 1971 report said "Most people (myself included) would be reluctant to agree that the time gained by any one of these clocks is indicative of anything" and "the difference between theory and measurement is disturbing" ...

11) http://personales.ya.com/carlosla/model/ EVE, a model of the aether by: Carlos Laborde Introduction: The main purpose of this work is to define a model of aether within a given description scheme. The description scheme used is considered a matter of free election. This election must only be judged "a posteriori" by its power to organize in an economic and simple way as much knowledge of the physical world as possible. The description scheme is the following classical one: - The space/geometry chosen for the description is the Euclidean with three dimensions.

- The time concept chosen for the description is the Absolute Time.

Such Space and Time are well defined mathematical concepts that behave according to the postulates. This does not necessarily imply that, in the absence of known external forces, every material mechanism used in some local context as a clock and that every, so called, rigid bar should always behave classically (i.e. remain constant when compared with standards). It must be considered satisfactory enough if the experimental behaviour of such

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clocks and rigid rods can be described in a consistent way within the description scheme chosen, invoking perhaps some new phenomena. Clocks are used to measure time, not Time, and rigid rods are used to measure space, not Space, (in a similar way that gas pressures, electric currents, etc, are measured by the corresponding instruments). The Time and Space are theoretical bricks of the description that are not measured in the physical world but defined in the model world.

It is considered that the goal of adjusting the physical laws to a classic descriptive scheme should not be abandoned since it promises more advantages than the relativistic point of view which adjusts the description scheme to some crude experimental observations. First, when seeking a global description of the positions and movements of the celestial bodies, the use of General Relativity seems condemned to lead to circular arguments due to the fact that the metric used in the description is itself altered by the gravitation fields of the bodies that aim to be installed in that metric. Second, if succeeding instead to describe the Universe with a 3-D Euclidean metric together with an absolute Time, the models so constructed are easily understood by our minds (used to treat with these kinds of relations in our everyday life). In this case, intuition becomes a powerful tool to suggest new inferences.

The descriptive point of view defended in this work is the same adopted by the majority of physicists before the arrival of Relativity. It is not ignored that the theory of Relativity became a safety raft when the efforts made at the beginning of the 20th century failed to explain the new experimental facts within the classical description frame. This work may be considered just a call to make one more effort in the old line impelled by two new facts: First, our knowledge of physical phenomena is now greater (quantum mechanics, vacuum fluctuations, existence of a preferred reference frame associated with the dipolar anisotropy of cosmic microwave radiation...). Second, today's official description of Physics seems again unsatisfactory to an increasing number of physicists.

Abstract: A very simple aether is postulated. This aether is represented by an ensemble of moving point entities (aetherinos) that pervade all space. The aetherinos are not material particles. They have no intrinsic material properties (mass, charge, magnetic moment, spin...) but are responsible for the appearance of these properties in matter, which is postulated to be an ensemble of entities of another kind (Simple Particles). In principle this aether is fully described by its aetherino's velocity distribution (which can change in space and in time) and by an hypothesis about the effects of the collisions of the aetherinos with matter. (The aetherinos do not collide with themselves).

No attempt is made in this work to deduce the exact local distribution consistent with the experimental facts. With the help of a plausible example distribution and a very simplistic model of matter it is "shown" nevertheless that many fundamental laws of physics can be "explained" instead of just stated. [...]

Light is considered a space - time modulation in the aetherino's velocity distribution. The "spread out" space - time propagation of the disturbance resembles more the idea of light as a wave than that of light as a particle (photon). The corpuscular properties of light should then be ascribed only to its emission and absorption by matter and explained by its cooperative / destructive interaction with the wave-type disturbance. [...]

12) http://www.dipmat.unipg.it/~bartocci/larson.htm A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical Aether by: Delbert J. Larson Abstract: Maxwell's equations are derived from a postulated, mechanical, two-component aether.

[Two more papers by the same author at http://www.dipmat.unipg.it/~bartocci/listafis.htm, point N. 20]

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13) http://www.geocities.com/hlindner1/Writings/Space/Physics.htm Flowing Space by: Henry H. Lindner Abstract: A simple theory of Cosmic space and motion explains the experimental results, unifies our understanding of the effects of motion and of gravity, produces no paradoxes, and makes more predictions than Relativity.

Key words: absolute space, atomic clocks, black holes, entrainment, gravity, inertia, light, mass, motion, paradoxes, principle of equivalence, Relativity, space, time. http://www.geocities.com/Athens/Atrium/8041/ 14) http://www.scientificexploration.org/jse/articles/mccausland/toc.html Anomalies in the History of Relativity by: Ian McCausland Abstract: In November 1919 it was announced to the world that observations of a solar eclipse that occurred in May 1919 supported Albert Einstein's general theory of relativity.

That announcement was one of the most influential events of 20th-century science, since Einstein's instant rise to enormous fame arose directly from it. In spite of the confidence with which the announcement was made, however, it was later realized that the accuracy of the observations was insufficient to constitute a reliable confirmation of the phenomenon that was predicted. Furthermore, another of the formulas published in the general theory, for the variation in the perihelion of the planet Mercury, had already been derived by another scientist several years earlier using another method. In spite of the fact that the experimental evidence for relativity seems to have been very flimsy in 1919, Einstein's enormous fame has remained intact and his theory has ever since been held to be one of the highest achievements of human thought. The resulting deification of Einstein has had some unfortunate effects: critics of his theory are often dismissed as cranks, and the search for better theories has been inhibited. It is suggested that the announcement of the eclipse observations in 1919 was not a triumph of science as it is often portrayed, but rather an obstacle to objective consideration of alternatives.

Abstract (first page of article) - Introduction - The General Theory of Relativity - The Eclipse Expeditions & their Observations - Announcement of the Eclipse Results - The Perihelion of Mercury - The Special Theory of Relativity - Discussion - Acknowledgement - References 15) http://www.aetherpress.com/ Aether and Gyrons by: Frank Meno Present physical theories are based on numerous postulates for such things as forces, momenta, energy, mass, charge, etc., which are not defined in terms of comprehensible concepts. For example, a force that causes attraction through empty space is clearly impossible to comprehend. Although one can obtain some useful results by manipulating mathematical expressions based on such postulates, this approach has neither yielded progress in philosophy, nor has it enabled further progress in practice. Common sense tells us that, to investigate something effectively, we should know what we are dealing with. As I describe in my book [Cats, Atoms, Gyrons, Aether, and the Universe], the ancient Greeks have delineated the basic questions, but they failed to develop the required mathematics, and have not performed the necessary experiments to verify their hypotheses before their civilization collapsed. Nevertheless, the Greek philosophers came to the correct conclusion that there exists a fundamental substance which must be atomistic. This means that the ultimate constituent parts of this substance must not be further divisible. Furthermore, since the observed physical reality is changing, these fundamental entities, which they called atomos,

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must be in perpetual motion. The issue that was not effectively resolved regards the shape and size of these 'atoms' (gyrons). [...]

Aether Gyron Each gyron moves in a straight line while at the same time rotating around its center. These gyrons, colliding with each other, comprise the gas called aether. Gyrons are very small on our scale, their length probably corresponds to the Planck length, which is 1.6 x10^-35 m. In comparison, the diameter of a proton is 1.5 x10^-15 m. The gyrons are spread throughout the universe, and the majority of them are undergoing random collisions with each other. In this condition they are comprising what we call the vacuum. Thus, vacuum is not empty, it contains the random moving gyrons whose motion represents the potential energy. The average gyron speed corresponds to the speed of light, while some of them move slower, and some faster.

Like in material substances, if the equilibrium condition is disturbed, waves can propagate in the aether. The most commonly observed aether waves are called electromagnetic waves, to which belongs light. In these waves the gyrons move as a group in a non-random spiral pattern which is called a photon. The intensity of light depends on the number of photons moving together. If the spiral trajectories of the participating photons move in unison, then the light is termed coherent. Coherent light is generated in lasers, while incoherent light comes from the sun and common illumination.

As in material fluids, there can also exist vortices in the aether. In an aether vortex the gyrons move non-randomly in a closed circular pattern. The simplest aether vortex is called electron.

Since there are possible only right-handed, and left-handed rotations, we have also only two kinds of electrical charge. The charge is conserved because the rotation in the vortex is conserved. However, if a right-handed, and a left-handed vortex meet, the rotation cancels, and charge disappears. This is termed annihilation of matter with anti-matter. The disturbance associated with such an event causes the generation of photons. The images below show the organized trajectories of gyrons manifested as photons, and electrons. [...]

16) http://mywebpages.comcast.net/deneb/muller.htm An Experimental Disproof of Special Relativity Theory (Unipolar Induction) by: Francisco J. Mﾃｼller Here is an experiment that invalidates Relativistic Electrodynamics. To facilitate understanding it will be presented in two parts, each one in turn subdivided into a rotational case and a translational one. [...]

17) http://jnaudin.free.fr/html/troutnbl.htm A Successful Trouton-Noble experiment by: Jean-Louis Naudin and Patrick Cornille 18) http://www.ece.drexel.edu/ECE/AR/Aether_Model.pdf An Aether Model of the Universe by: Allen Rothwarf Abstract: An aether model based upon a degenerate Fermion fluid, composed primarily of electrons and positrons in a negative energy state relative to the null state or true vacuum, is proposed and its consequences are explored for physics and cosmology. The model provides both insight and quantitative results for a large number of phenomena for which conventional theory provides no answers or unsatisfactory answers. Among the concepts treated are: waveparticle duality, the nature of spin (a vortex in the aether), the derivation of Hubbleﾃ不 law; electric fields (polarization of the aether); Zitterbewegung (a bare particle orbiting within a vortex core); inflation in cosmology; the arrow of time; the Pauli exclusion principle (repulsion between parallel spin vortices); the nature of the photon (a region of rotating polarized aether propagating with a screw-like motion); neutrinos (a spin vortex with no

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particle in its core); redshifts; g-ray bursters; and a number of other topics. A key assumption is that the speed of light is the Fermi velocity of the degenerate electron-positron plasma that dominates the aether. As a consequence the speed of light decreases with time on the scale of the age of the universe.

Keywords: Aether, Quantum Mechanics, Cosmology, Relativity, red-shift, Hubble's law, speed of light, vortices, wave-particle duality.

1. Introduction We live in a universe of interacting fluids. While oceans in which gases are dissolved, and an oxygen-nitrogen atmosphere with water vapor and other trace gases are readily accepted, the third fluid, the aether, which penetrates everything is ridiculed as a relic of a bygone era in science. Yet, while rejecting an aether, the science establishment has no problems swallowing waves in vacuum, mysterious probability waves, ad hoc cosmological constants, vacuum fluctuations that can generate anything, and time and space expanding and shrinking. To the true believer, the fact that they work is the only justification for the major theories in physics; Maxwell's equations, the Schrodinger equation, and Relativity, and is used as evidence that we know everything, that Science is Dead, and humanity's brightest should move on to more challenging tasks. Some of us, however, are heretics. We would actually like to understand the physics, rather than just use it as a magic wand to create technology. In this pursuit of understanding, which is also ridiculed by the establishment as asking meaningless questions, we have found that the aether is not only a useful concept, but that it is a real substance with an origin that coincides with the birth of our universe and whose properties determine the speed of light, the other physical constants, and the missing insight lacking in present theories.

Before expounding upon the aether and how it explains so many phenomena in a simple way, let me point out that contrary to popular belief, science is not logically based. Instead, it, like all human activity is based upon chance and trial and error. [...] http://www.ece.drexel.edu/ECE/AR/Rothwarf_home.html 19) http://get.ilja-schmelzer.net/ General Lorentz Ether Theory By: Ilya Schmelzer An old and seemingly discredited notion of ether has found its new incarnation in a "metric theory of gravity" by I. Schmelzer, who managed to find for his new ether a consistent and instructive interpretation in terms of condensed matter physics. (Prof.V.A. Petrov) General Lorentz ether theory (GLET) is a metric theory of gravity with a predefined Newtonian framework with preferred coordinates Xi, T. It generalizes Lorentz-Poincare Ether Theory to Gravity. The ether has density, velocity and stress tensor, and fulfills the classical conservation laws [...]

20) http://www.journaloftheoretics.com/Links/Papers/Seto.pdf Unification of Physics By: Ken H. Seto Abstract: In the final days of his life, Einstein tried in vain to unite gravity with the electromagnetic force. The reason for his failure was due to his incomplete understanding of the physical space. A new description of physical space along with a new understanding of matter was formulated. This new model of the current universe gives rise to a new theory of gravity and at the same time it unite gravity with the electromagnetic force naturally. Also this new model predicts the existence of a new fifth force - called the CRE force. In addition, the unification of all physics is within the scope of this model. http://www.erinet.com/kenseto/

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[The author is already known to Episteme's readers for his article "The Resurrection of the Light Conducting Medium for Modern Physics" which appeared in the issue N. 3, April 2001] 21) http://metaresearch.org/cosmology/speed_of_gravity.asp The Speed of Gravity - What the Experiments Say By: Tom Van Flandern Abstract: Standard experimental techniques exist to determine the propagation speed of forces. When we apply these techniques to gravity, they all yield propagation speeds too great to measure, substantially faster than light speed. This is because gravity, in contrast to light, has no detectable aberration or propagation delay for its action, even for cases (such as binary pulsars) where sources of gravity accelerate significantly during the light time from source to target By contrast, the finite propagation speed of light causes radiation pressure forces to have a non-radial component causing orbits to decay (the "Poynting-Robertson effect"); but gravity has no counterpart force proportional to v/c to first order. General relativity (GR) explains these features by suggesting that gravitation (unlike electromagnetic forces) is a pure geometric effect of curved space-time, not a force of nature that propagates. [...] *****

Call for papers for a book of essays The Editors of a proposed book on classical electrodynamics to be published

by Rinton Press, Inc. (USA) invite submission of papers.

The name of the compilation will be Has the last word been said on classical electrodynamics?

(Classical electrodynamics: new horizons) All papers to be submitted by e-mail to dr. Andrew E. Chubykalo (preferable) andrew_chubykalo@terra.com.mx or to Dr. Vladimir Onoochin a33am@dol.ru or to Dr. Roman Smirnov-Rueda Roman_Smirnov@Mat.UCM.Es or to Dr. Augusto Espinoza drespinozag@terra.com.mx

in LaTeX, LaTeX"\documentstyle" format is preferable (i.e. not "\documentclass"!).

Figures for papers should be presented in eps-format (encapsulated postscript format). Page size should not be more than 22.86 x 15.24 Ń Đź. Papers should be approximately 15 pages in length and must not exceed 20 pages (except special cases agreed with the Editors).

All received papers will be evaluated by independent referees.

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Deadline is 1st of June, 2003

After publication of the book all contributors receive two printouts of their contributions.

EDITORIAL AIMS AND OBJECTIVES In the last decade, it is observed an emergence of revived interests towards classical electrodynamics. While the conventional Maxwell's theory remains one of the few cornerstones of modern physics and cradle of Einstein's relativity, an throughout study on it may lead us to a better and deeper understanding on electromagnetism which has a nearly two century history and may bring us nice surprises. In spite of all its visible successes, there are still reasons to believe that either Maxwell's equations or the conceptual background of electromagnetism needs to be modified.

There are also attempts in these directions. R. Feynman was one of these who had some doubts on the completeness of classical electrodynamics, and he once commented: "… this tremendous edifice (classical electrodynamics), which is such a beautiful success in explaining so many phenomena, ultimately falls on its face. When you follow any of our physics too far, you find that it always gets into some kind of trouble. …the failure of the classical electromagnetic theory. Classical mechanics is a mathematically consistent theory; it just doesn't agree with experience. It is interesting, though, that the classical theory of electromagnetism is unsatisfactory theory all by itself. There are difficulties associated with the ideas of Maxwell's theory which are not solved by and not directly associated with quantum mechanics…".

Many unresolved and forbidden problems of classical electrodynamics seem to be more serious in view of frustrated intentions to make fully compatible Einstein's relativity (based mainly on Maxwell's equations) with quantum mechanics. According to Bohm, this significant incommensurability has to lead to discover an entirely new order to physics at a fundamental level with all its implications for classical theory. It will be helpful if there is a forum where arguments of both for and against modification of standard Maxwell's approach are presented, and thus, an objective discussion of all possible alternative views logically sound and based on a rigorous mathematical ground is conducted.

This review volume as entitled above will provide such a forum. The editors would call scientists who are actively working in electromagnetic theory to send in your review or research papers on classical electrodynamics, especially these on unsolved and annoying problems.

The Editors: Dr. Andrew E. Chubykalo (Mexico) Dr. Augusto Espinoza (Mexico) Dr. Vladimir Onoochin (Russia) Dr. Roman Smirnov-Rueda (Spain)

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Looking for Special Relativity's Possible Experimental Falsifications (Umberto Bartocci) 1 - Introduction We already had the opportunity to describe, in the Letter... which opens this special number of Episteme, the fundamental reasons which should inspire a general criticism of relativity, or, better, of the "philosophy" which was (and is) the ground of Einstein's success. This paper is an attempt to analyse the strictly physical (phenomenological) situation, in order to give a suggestion where to look for possible experimental falsifications of the theory (from now on SR, special relativity1), in the conviction that this is the only possible manner to show that the main assumption of "abstract physics" supporters is wrong: namely, that the renouncing to ordinary space, time, causality, was not a "nihilistic caprice", but a necessity forced by facts2.

This analysis is not so easy as it could appear, since to decide whether a given experiment, or phenomenon (two paradigmatic examples: annual stellar aberration, Sagnac's experiment), could be explained in a relativistic manner or not (or else, from the other side, that it could not be explained in a "classical" way), is an engagement which can be pursued only with a great care, and a good knowledge of the theory one is aiming to prove or to disprove3.

Our main points will be that: I - There are not so many convincing (direct) experimental arguments in favour or SR, as it is vice versa usually emphasized by "orthodox" physicists - which sometimes add, on these premises, that a pretended phenomenon possibly disproving SR would be like a vox clamantis in deserto, and that this justifies the cautious establishment's response in front of such claims.

II - Moreover, there is not even a crowd of experimental data against Einstein's physics. In simple words, we do not have until now enough evidence in favour of neither a point of view, which shows that it would be rather unwise, at least for the moment, to dismiss all attempts aiming to provide a "rational" description of how Nature works.

1.A Cartesian Physics vs Special Relativity In order to achieve our goal, let us give a sketch of what relativity essentially is. First of all, it is a theory which, contrarily to the common opinion, should be considered more conservative than revolutionary in its essence. In order to explain this assertion, we must go back to the very beginning of physics as a science, and to the opposition between Cartesian conception of space as a plenum, and Newtonian contrary point of view4, an empty space not endowed of any physical objective, measurable, property. Of course, from this quite simple starting point5, divergences grow up in an increasing complexity, but the substance of all conflict is there. After the success of Newton on Descartes, the image of the empty space - in which a mysterious action at a distance ruled the trajectories of all celestial bodies, and in which movement could only be relative, according to Galileo's famous ship's argument6 dominated the scene of science for more than one Century. The conception of a space acting as an indispensable medium for all physical interactions, came back during electromagnetic studies in XIX Century: Ampère, Oersted, Faraday, Neumann, the great Maxwell's Treatise, etc.. At the end of that Century the situation in theoretical physics was indeed an

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uncomfortable one. There was the image of the world given by Newtonian mechanics, which marked, even in a symbolical way, the "victory" of science over the supporters of darkness and superstition. But there was an aether too, which was clearly "seen" for instance in the lines of force surrounding a magnet. When Einstein appears on the stage 7, a solution was really needed, and there were only two possible way out. Either to accept the evidence for an electromagnetic aether, to refuse the principle of relativity (from now on PR), and to frankly acknowledge that Newton's party was wrong; or, at the contrary, to maintain the foundation of Newton's physics8, even in a quite different space-time set up, really undreamed of until Einstein's age (and this would be the "revolution").

It is obvious that, from our point of view, the really true courage would have been to choose the first option, while Enstein did exactly the opposite. He maintained Newton's empty space, proposing PR as one of the essential Nature's laws, and at the same time "borrowed" from aether's physics concepts like the independence of light's speed from the speed of the source, the finiteness of the speed of propagation of all aether's "disturbances" (fields), etc.. He showed in such a way that it was possible to assemble a general theory, but he was forced, however, to give up ordinary space and time conceptions. Thus, it is not a "paradox" to assert that Einstein followed rather closely Newton's tracks9, and that its only true opponent is Cartesian fluid-dynamical physics10. One could as well assert that SR is similar to a proof ab absurdo: the only way to keep together the abstract RP, and the experimental electromagnetism, is to abandon ordinary space-time, and since this is absurd, we must choose between the principle and the facts. Needless to say which should have been, in our opinion, the right choice.

1.B Special Relativity's True "Heart" As we have mentioned, SR is made up of two postulates (Voraussetzungen), RP plus LSP (Light's Speed Principle)11. In an empty space RP is "acceptable", because of a kind of insufficient reason principle: there is no reason why an inertial observer 12 should experience a physics different from another one, seeing that there exists nothing which could decide which one is really moving, or still. In an aether theory, and in a wave theoretical approach to the nature of light (perhaps not the only possible one), LSP is acceptable (even in a stronger form, see the next section 4). So, from the point of view of a critic of SR, this is 50% correct, and it is not LSP the assertion which should require a careful scrutiny, but SR's true foundation, that is to say PR13. Indeed, it is PR which, added to LSP, makes LSP quite counter-intuitive, and such that all the attention of people goes to the very qell known strange features of relativistic speeds, but, we repeat it, LSP has nothing wrong in itself, and it becomes "bad" when one changes the independence from the speed of the source with the independence from the speed of the observer!

At this point, the fundamental question is: which are the direct experimental arguments in favour of PR? We believe that an "honest" answer should be, at least for the moment being, that there are not. The greatest part of the pretended experiments in favour of SR - whose correctness one could even accept, mostly if he is not a professional physicist, like the present writer - could be, first of all, easily re-interpreted in an aether theory, finding in fact in such a context their better (proper) "explanation" (the "increasing" of the inertial mass as a phenomenon of "resistance"; the finiteness of the speed of propagation of interactions, perhaps equal for many different phenomena, the consequent "retardation", etc., obvious; for the so-called "time dilation", see the next section 3; and so on, we must confess that we find most of all worth of some attention the claims about the experimental validity od the so-called transverse Doppler effect). Second, that part of experiments which seem to validate PR, have only used the

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hypothetical motion of the Earth through the aether 14, thus showing that theoretical physics has not made, in this field, a great progress since XVII Century! The possibility that this motion does not exist at all - or that it is too small to be detected 15 - is seldom taken into consideration in popular divulgations of Einstein's theory, while Descartes-Leibniz's vortex theory16 implies exactly this inexistence. Only experiments performed in reciprocally moving laboratories would give some evidence in favour of the one or of the other conflicting points of view, and these experiments have been almost never done 17! In 20 years study of this problem, and innumerable discussions with colleagues (usually worried to avert a friend from bad companies), the author has never heard of such experiments, while at the contrary everybody claimed that it was practically impossible to reach those speeds which could have been significant in order to test RP. Moreover, they added that the required accuracy of measures would have been irreparably disturbed by the forced movement (see even Marinov's remarks, in the next section 2.A).

And so then? Why one should believe in something which has not yet been proved beyond a shadow of a doubt18??

It is at this point unavoidable the doubt that the motivations of Einstein's followers are not of a strictly scientific nature (mathematicians for instance greeted with enthusiasm the "birth" of SR, since it showed that their sophisticated tools would have shown their practical utility too19), and we feel obliged to carry on a long research work like the present one.

1.C The Theory of the "Dragging Aether" It is clear from the above that the general theory which we feel the most trustworthy opponent of SR is the so-called theory of the dragged aether20, a denomination which shows nevertheless an implicit relativistic conditioning. If we consider a physically active aether, why should we accept - in obedience to the opinion that any motion could not be but relative that it would be the same thing to say either that the aether is dragged, or that the aether is dragging, as it is quite more likely? This misunderstanding is not only of a linguistic nature, since it is at the origin of a pretended "proof" against the theory we are aiming to propose as the possibly "true" one. As a matter of fact, most text-books recall the famous Fizeau's experiment as a "crucial" one proving that the aether is not (at least completely) dragged by moving bodies (in this case water, forced to move in a pipe), but this has really nothing to do with Descartes-Leibniz's theory21!

At this point one could ask whether there are other arguments against the dragging aether (the usual name for an hypothesis of this kind is Stokes theory, but we believe, as we have said, that we are in front of similar but different theories), and one would be perhaps surprised acknowledging that, according to the well known Resnick's book 22, only Fizeau's experiment and annual stellar aberration are quoted as such "proofs". Of the first one we have just said, the other one appears as a possible new great misunderstanding, one of the many which affect theoretical physics, which the author, not accustomed to this kind of situation in mathematics, discovered with great amazement23. As a matter of fact, it has been shown very clearly by Giancarlo Cavalleri et al.24: "Some special relativity textbooks assert, without giving a detailed history of the question of aberration, that Stokes theory is wrong [...] their argument is grounded on a misunderstanding: precisely, the aether which they consider is not irrotational". Moreover, we feel that is not even impossible to explain Bradley's aberration introducing a "model" similar to the local magnetosphere (quite compatible with the general theory of the dragging aether) discussed in the reprint of Zapffe's paper in this same volume, namely, that this question is still well open.

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This is the general conceptual frame25 in which one should fit the observations and proposals below, which represent a kind of Summa, trying to collect the "best" acquired in many years research and frequentation of "alternative physicists", to whom all (dead or alive) go the author's warmest thanks.

2 - Does RP Hold in Electromagnetism?

We begin our analysis restating the fundamental question in more specific words: does electromagnetic phenomenology really allows physicists to propose RP as one of the most fundamental Nature's "laws"?

It is obvious that, from the point of view of the "Cartesian physics" sketched in the previous section, the expected answer of Nature should be a clear and strong not, and not only in electromagnetism, but in principle even in mechanics, with the only difference that it is very likely that mankind has not been able to observe until now significant mechanical violations of RP, as men have been confined in their small planet, and in the realm of "low velocities".

It is rather instructive to quote at the opposite the words of a physicist (taken from an Internet group discussion), who claims that: The experimental evidence confirming the principle of relativity is actually overwhelming, in the sense that in no field has one ever discovered any dependence of the forms of the laws of physics on the velocity of the reference frame.

Is this an opinion, or objective science (as far as science can be objective in the limits of our present knowledge)? The fact is that exactly Maxwell's Electrodynamics (from now on ME), the supposed pillar of Einstein's SR26, provides a mathematical set-up which can have different interpretations as a physical theory (which is a mathematical theory, plus a set of more or less explicit, and formalized, assumptions, rules of codification and decodification, from the reality to the abstract intellectual "model", and conversely, which are not so rigid), some of which interpretations do not satisfy RP. To this question the author has dedicated a paper 27, in which it is shown that the phenomenon of the electromagnetic induction, the only one which Einstein choosed as a motivation for his proposal of a complete symmetry between "inertial frames", is indeed a good example (internal to ME) of a symmetrical interaction 28, but it should have been regarded as an exception (which has to do with the circumstance that we are in this case in front of closed circuits) in classically interpreted ME, and not as a rule. As a matter of fact, general Maxwell's treatment (which is "aether-based") suggests instead that we are possibly in front of an asymmetrical phenomenology, in which velocities with respect to a priviliged frame make a great difference. One must admit, of course, that SR show how it is possible to interpret ME even in a conceptually symmetrical framework, but one should admit too that we are indeed in front of two different physical theories, even if they are "sharing" the same equations. Which one is "true", we actually do not really know. Physics is believed to be above all an experimental science, but the most meaningful and widespread convictions appear to be more theoretical in essence (we do not want to say: ideological) than experimental, and it was really a surprise to realize that some endless discussions could have been put to an end with experiments that nobody has ever properly done (but almost every physicist thinks, and acts, as if they had been done!).

36

2.A The Direct and the Inverse Rowland Experiments It seems convenient, for many reasons, to start with an "experiment" which could be thought of as the possible key for understanding the nature of the eventual electromagnetic asymmetries we are talking about. The dear unforgotten friend Stefan Marinov explains the situation is his Divine Electromagnetism (1993), pp. 169-173, and we quote below some of his very clear words.

Rowland [Rowland H.A., Sitzungsberichte der K. Akademie der Wiss. zu Berlin, p. 211 (1876)] carried out in 1876 the following experiment: A disk was charged with positive (or negative) electricity. There was a magnetic needle in the neighbourhood of the disk. When the disk was set in rotation, the needle experienced a torque due to the magnetic action produced by the convection current of the charges rotating with the disk. I call this the DIRECT ROWLAND EXPERIMENT.

According to the principle of relativity, if the disk will be kept at rest and the needle will be set in rotation, the same torque has to act on it. Such an experiment is called by me the INVERSE ROWLAND EXPERIMENT.

[...] The above two experiments can be called ROTATIONAL Rowland experiments. It is easy to transform them into INERTIAL experiments. So if we charge a conveyer belt and set it in action, the motion of the charges can be considered as inertial (i.e., with a velocity constant in value and in

37

direction) over a considerable length of the belt and we shall realize thus the inertial direct Rowland experiment. [...] As far as I know nobody has carried out either the rotational nor the inertial inverse Rowland experiments.

Now I shall show that, contrary to the prediction of the princople of relativity, the inverse Rowland experiment must be null, i.e., a magnet moving with respect to charges at rest does not experience torque. [...] I carried out the rotational direct and inverse Rowland experiments. [...] Of course, because of the mechanical vibrations and the Earth's magnetism, it was pretty difficult to establish such a null effect and my experiment, naturally, needs confirmation carried out in a first class laboratory. According to me, the inverse Rowland experiment has been not carried until now not because of technical difficulties but because of a fear that the result will be null [...]

Marinov's words describe a situation which we will face later on in other conceptually similar contexts, but we wish to remark since now that, apart from possible theoretical and experimental questions arised by the "Rowland case"29, they testify our same experience: direct fundamental experiments, the only ones which should allow Einstein's enthusiasts to assert that SR is really beyond a shadow of a doubt, have never been performed30!

2.B Some Theoretical Remarks About ME Before going on, it is convenient to be more precise about ME as a mathematical theory. By this we mean the system of the four Maxwell's equations (expressed in standard differential notation, in the MKSQ unit system):

∂B ∂t

(1)

curl(E) = -

(2)

curl(B) = µ0 (ε0

(3)

div(E) =

(4)

ρ ε0 div(B) = 0 ,

∂E + j) ∂t

which can be reduced to the two D'Alembert wave equations for the electric and magnetic potentials Φ , A : (5) (6)

ρ , ε0 A = -µ0 j , Φ = -

where appear the charge density ρ(x,y,z,t) and the density current j(x,y,z,t) (which satisfy ∂ρ the charge continuity equation div(j) = ). ∂t The potentials Φ , A are connected by the Lorentz gauge condition: (7) div(A) = -c-2

∂Φ (where: c-2 = ε0µ0 ) . ∂t

38

The electric and magnetic fields E, B are expressed in terms of the potentials by the equations: (8) (9)

∂ A ∂t B = curl(A) ,

E = -∇Φ -

and the force acting on a charge q , movin with velocity v , is the Lorentz force: (10) F = q (-∇Φ -

∂ A + v×curl(A)) = q E + q v × B . ∂t

There is indeed in the theory a further assumption, which can be viewed as a restriction on the way fields originate from sources 31: we assume that for a given ρ and j, (5) and (6) have a unique solution which is physically relevant, namely the one given by the so called LiénardWiechert retarded potentials: r 1 ρ (x' , y' , z' , t - )dx ' dy ' dz ' (11) Φ(x,y,z,t) = , c 4π ε 0 ∫ ∫ ∫ r

(12)

µ A(x,y,z,t) = 0 4π

∫∫∫

r j (x' , y' , z' , t - )dx ' dy ' dz ' , c r

where r'(x,y,z;x',y',z') is the ordinary distance [(x - x' ) 2 + (y - y' ) 2 + (z - z' ) 2 , and the integration is made on the whole space (one gets smooth solutions if one starts from smooth data for ρ and j ).

The previous formulae (11) and (12) are in truth not so simple to understand. Their "physical" meaning is that the contribution of a point (x',y',z') to the integrals is not given for instance by the charge which is in this point at the time t , but only by the charge which was r in (x',y',z') at the retarded time t - , that is to say by the charge which is seen from (x,y,z) c in the point (x',y',z') at the time t .

The equations introduced above must be thought of - in ME's classical interpretation - as valid only in a set of privileged reference frames K , the so-called aether frames (in principle they are unique up to spatial rotations and translations, and up to a time homothety, but do not forget what has been said in footnote 25), where the ordinary concepts of classical mechanics can be used. In their relativistic interpretation, one must add an additional hypothesis, which ensures the validity of the theory in all inertial reference frames K' , namely the ones moving with a uniform velocity with respect to K (connected to K by means of a Lorentz-Poincaré transformation): (13)

(j,ρc) and (cA,Φ) are 4-vectors of the Minkowski space-time.

Only this assumption enables to write the Maxwell's equations in a covariant form, but one must remark that (13) is a genuine new physical assumption, which is logically independent of the previous ones, and that it is perfectly legitimate to use ME in a "classical" space-time theory without any connection at all with relativity. We shall show now some of the

39

differences which can arise between different physical interpretations of the same mathematical theory.

2.C Trouton-Noble Type Experiments Let us study more carefully the different previsions which a Cartesian and an Einsteinian physicists (from now on: C and E ), can do with the same mathematical theory.

Let K(x,y,z,t) be an inertial coordinate system of the space-time. K will mean for C a (possibly local) rest-frame in the aether (or even an aether-frame). Measures of space and time (for instance, synchronizations of remote clocks) can be made exactly as Einstein requires, so that even E can accept K as one of his inertial coordinate system. Until this moment, the only difference is that C would not accept as a "good" coordinate system any other similar system K' which would "move" with respect to K with a uniform velocity, and most of all that C would not accept the method that E could indeed use (rightly, from his point of view) in order to simplify the effort to give an answer to some theoretical questions.

Namely, to change the coordinate system, choosing another one K' more "suitable" with respect to the physical situation under discussion; make computations in K' ; then go back to K using some coordinate transformation (in the present case, Lorentz-Poincaré transformations). In other words, C cannot use sometimes of the facilities of E , but it does not really matter, since they agree at least in the choice of K , and most of all in the system of equations that they have in order to describe electromagnetic phenomenology.

Let us think of an electric charge Q moving in K with some uniform velocity v = (v,0,0) along the x-axis (let us even suppose that x = vt , y = z = 0 , are the equations of the motion of Q ), and let us ask, to both C and E : which are the electric and magnetic potentials associated with Q ?

The question is such that both C and E will give the same answer32: (14)

(15)

ΦQ =

1 4π ε

AQ =

µ0 4π

Q ( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )

0

,

Qv (x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )

(where, as usual, β =

v ). c

The coincidence of these potentials both for C and E , which could be extended to any system of a finite number of charges (since we are in front of a linear theory), could make believe that C and E would share even the same "physics", at least in the electromagnetic field, but this is not true, as we should immediately understand, now and later in the next section.

Let us in fact introduce another charge q , in the (xy)-plane, which in the instant t = 0 has coordinates (Rcos(θ),Rsin(θ),0) , as in the following picture, and let us ask which is the total electromagnetic force acting on q in virtue of Q in the case q is supposed to move with velocity w = (w,0,0) parallel to v (in particular, comoving with Q with the same velocity v , or standing still in K , case w = 0 ) :

40

∂ AQ + w×curl(AQ)) , ∂t straightforward computations give the following values for the three terms in the right hand side of the previous expression of the required force: Starting from (10), namely, in our case,

1 4π ε

-∇ΦQ =

-

∂ AQ µ = - 0 ∂t 4π

curl(AQ) =

Q

[

0

( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 ) Qv

[

µ0 4π

( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )

[

( x − vt ) + (1 − β )( y + z ) 2

1 4π ε -

1 4π ε

0

0

2

2

(x-vt,(1-β2)y, (1-β2)z)

3

v(x-vt)

3

]

(1-β2) (0,-z,y)

3

[

( x − vt ) + (1 − β )( y + z ) 2

2

2

2

[

R cos (θ ) + (1 − β ) R sin (θ ) qQ 2

[

2

2

2

2

R cos (θ ) + (1 − β ) R sin (θ ) qQ vw 2

1 4π ε 0 c 2

=

1 4π ε

[

2

2

R

2

R cos (θ ) + (1 − β 2

2

qQ

2

]

3

(1-β2) (0,-y,-z)

3

(Rcos(θ),(1-β2)Rsin(θ),0) +

3

β2 Rcos(θ) ix +

1 1 µ0 = : 4π ε 0 c 2 4π qQ

+

0

2

]

= q (-∇ΦQ -

Qvw

and so, remembering that

Fq =

]

Qv

µ w×curl(AQ)) = 0 4π

(16)

Fq

[ 1− β

2

sin (θ ) 2

]

3

2

2

] ]

) R sin (θ ) ] 2

2

3

(1-β2) (0,-Rsin(θ),0) =

(1-β2) [ (cos(θ),sin(θ),0) -

vw sin(θ) iy ] = c2

41

1 = 4π ε

qQ R2

0

(1 − β 2 )

[ 1− β

2

sin (θ ) 2

]

3

[u-

vw sin(θ) iy ] , c2

where ix , iy are the unit vectors of x and y , and u is the unit vector of the vector Qq in the instant t = 0 .

This formula gives the exact expression of the required interaction in ME , with no difference whatsoever whether we are following a classical point of view or a relativistic one.

1 It is in fact rather instructive, since it is made up of two terms. The first one, namely 4π ε 0 qQ R2

(1 − β 2 )

[ 1− β

]

3

u , does represent the complete force acting on q when the velocity of

sin (θ ) q is equal to 0 , or even when the velocity of Q is equal to 0 , no matter which is w . When both v = w = 0 , this term is equal precisely to the well known Coulomb's law for the interaction of static electric charges.

For any v , different from 0 or not, this "partial" (if w is not zero) force is "almost" equal - that is to say, up to second order in β - to Coulomb's force, and if we think of a "rigid rod" which connects the two charges Q and q , this term is annihilated by the reaction of the rod.

For our purposes, the interesting term is the other one, which in the comoving case β 2 (1 − β 2 ) 1 qQ ( w = v and not zero) becomes: 3 sin(θ) iy .

4π ε 0 R 2 1 − β 2 sin 2 (θ ) This force is not directed along u , so it is not annihilated by the reaction of the rod. Up to second order in β , the projection of this force along the vector u' = (-sin(θ),cos(θ),0) , namely the unit vector orthogonal to u such that the pair (u,u') has the same orientation as (ix,iy) , is equal to: 2

2

[

(17)

-

1 4π ε

0

]

qQ 2 β sin(θ) cos(θ) u' .

R2

The "symmetric" computation of the force acting on Q by means of q , always in the comoving case, gives a similar force, but with opposite sign, which implies that we are in the presence of a couple of forces, having linear momentum equal to: (18)

M = -

1 4π ε

0

1 qQ 2 β sin(θ) cos(θ) iz = 4π ε R

0

qQ 2 β sin(2θ) iz .

2R

A very "small" momentum indeed, but enough, from the point of view of C , to let him predict that the rod would turn clockwise (if we suppose the two charges of the same sign) with respect to z , in order to reach the equilibrium position parallel to v (for θ = 0 the π momentum vanishes, but it vanishes even if θ = ).

2 This is indeed a violation of the Newton's action-reaction principle, a violation which appears not only in classical electromagnetism, but even in SR (see footnote 29). It appears indeed quite "understandable" in an aether theory, since it would be due to the retardation due to the finite speed of propagation of the electromagnetic interaction. But why have we said: "from the point of view of C ", if we have even asserted that C and E agree with their computation? Because E , the previous formula notwithstanding, is forced to predict that the

42

rod would not rotate! As a matter of fact, C has no other means to ground his prevision of a rotation, while E could argue in the following way too. If I think of an observer X on the rigid rod, then from the point of view of X the rod is standing still, and since X is a "good" observer as I am, then the forces acting on the two charges at the extremities of the rod would be for X exactly equal and opposite, directed along the direction of the rod, as they are for me when v = w = 0 . Since this reference frame K' which I could think of, comoving with the rod, is physically quite equivalent to the one, K , in which I am standing still, and since in K' there should be no rotation (in SR, the action-reaction principle holds in the "proper frame" of the given physical situation), then a rotation should there be not even in K !

This analysis of E is in fact rather easy, but it is not so trivial to understand why E would conclude that, even if the previous momentum in K is indeed different from zero for him too, then the rod would remain nevertheless still. This is why the two forces acting on q and Q at the same instant t in K (we have supposed t = 0 , but it could be any other instant) are not acting in the same instant in K' . That is to say, E thinks that from K we see only an "apparent" momentum, due to the fact that the two forces "appear" to act simultaneously in K , while in the proper system K' , comoving with the rod , the two forces which are "really" simultaneous do not produce a momentum. In conclusion, E would claim that C's prediction is wrong, since he is trying to estimate physical quantities standing far away from the moving object. C could easily object that it is E which is wrong, because when he is thinking of an "observer" E' comoving with the rod, E' would be in motion with respect to the aether ("absolute" motion), and so the Einstein's synchronization of clocks performed by E' is uncorrect. This is the reason why E' believes that the two forces acting simultaneously with respect to him on q and Q do not produce momentum, while they do33.

We have proved that, even starting from the same equations, and making the same computations, there is not a physical agreement between C and E . But who is really right (perhaps no one of the two!)? Thought of a true rod like the previous one, uniformly moving with respect to a frame which one has some right to consider "inertial" (with a "good approximation"), does this rod rotate or not?? An experiment inspired to the situation above was indeed attempted by Trouton and Noble in 1903, and it is one of the few truly electromagnetic experiments aimed to prove the consistence of SR. Unfortunately, Trouton and Noble tried, as usual, to make in evidence a pretended motion of the Earth through the aether, which as we have said very likely does not exist34. To people who are influenced by the r么le of the famous Michelson-Morley optical experiment as one of the principal motivation for the birth of SR, we say that experiments of the previous kind, at the same manner that the one proposed in the next section, aimed to put in evidence the possible electromagnetic effects of the "aether wind" due to an absolute motion, should be regarded as electromagnetic "Michelson-Morley experiments", and that they should be performed for instance in a "train" like the one of the Buys-Ballot's test (see footnote 17).

2.D The Cardone-Mignani Experiment We have seen in section 2.C that it is not enough to share the same mathematical equations in order to have the same physics. Moreover, even if C and E have a common starting point in Maxwell's equations, to compute the same expressions for the potentials (and for the fields), is not the general rule. We have analysed before a very simple case, in which potentials are indeed equal for C and E , but this agreement does not exist anymore when they are in front of non-uniform motions, like the ones which appear for instance in the case of a circular current.

As an example of this, we suggest to compute (in a given aether-frame K as before; remember what has been said on the "agreement" of C and K about this frame) the force

43

which does act at the instant t = 0 on a test-charge q placed in the center of a circular circuit S , as the effect of a stationary current I flowing in S , when the circuit and the charge are comoving with a uniform speed v = (v,0,0) as in the previous section.

The situation is described in the following picture (the current is supposed to flow in the anticlockwise direction from x to y with respect to z), and so by the parametric motion's equations (both for C and E ): x = Rcos(θ) + vt , y = Rsin(θ) , z = 0 , 0 ≤ θ ≤ 2π , while the motion's equations of q are obviously: x = vt , y= 0 , z = 0 :

The author did extensively deal with this not simple computation (which requires a direct integration of Maxwell's equations) in the paper quoted in footnote 27, and the result is that the force acting on q , from the point of view of C , is equal to (up to second order effects in β ): (19)

F =-

µ 0 qI v iy .

4R

Thus, C would expect a force which is not equal to zero, and which does depend both on the intensity and on the direction of the current.

From the point of view of E , at the contrary, the prediction is quite different, and he will not agree at all with (19). As a matter of fact, in the proper reference frame K' , comoving with the circuit ( S will be no more circular in K' , but this does not really matter), the 3force acting on q must obviously be equal to zero ( E maintains the validity of Clausius' postulate in K' ), and this implies that it must be zero even in K .

So the important question is: in which point E , which is using the same Maxwell's equations as C , do not forget it, will differ by the formula (19) when doing his computations in K ?

Here they are, in order to answer precisely to this question, the exact expressions of the potentials of the circuit S computed by C 35 : (20)

ΦS = 0

44 2π

(21)

( − sin(θ ), cos(θ ),0) µ dθ , AS = 0 IR ∫ 4π ( x − vt − R cos(θ )) 2 + (1 − β 2 )[( y − Rsin(θ )) 2 + z 2 ] 0

and now the expressions of the same quantities as computed by E : v Ax'

(20') Φ*S =

1− β

2

(where Ax' is the first component of the magnetic vector potential in the proper frame K' of S ; we are using the simplest possible case of a Lorentz transformation) 2π ( − sin (θ ), 1 − β 2 cos(θ ),0) µ0 dθ .

(21') A*S = IR ∫ 2 2 2 2 2 4π 0 ( x − vt − R 1 − β cos(θ )) + (1 − β )[( y − Rsin(θ )) + z ]

The great difference between (20), (21) and the corresponding (20'), (21'), is that Clausius' postulate (see footnote 35) does hold in SR only in the proper frame of S , while it is no more valid in K , according to the transformation rules (which are consequences of (13)): Φ*S =

ρ*S =

Φ '+ v A x ' 1− β

2

v Ax'

=

1− β

v j v c 2 x' = 2 c 1− β 2

ρ '+

2

j x' 1− β

2

(where the apices designate quantities computed in K' ).

These equations imply that the moving circuit "appears" to have a non-zero density charge in K , and so a non-vanishing electric potential. In classically interpreted ME, at the contrary, the expression for ρS is simply given by the general formula: ρ(x,y,z,t) = ρ0(x-vt,y,z,t) = 0 , where ρ0 represents the density charge in the case v = 0 .

An analogous "classical" formula describes the relation between the density current terms 36: j(x,y,z,t) = j0(x-vt,y,z,t) + ρ0(x,y,z,t) , while the same equation, from the point of view of SR, is given instead by: jx(x,y,z,t) =

j x ' + vρ ' 1− β

2

=

j x' 1− β

2

(the other two components of j remains unchanged in the passage from K' to K ).

45

This shows37 that Maxwell's equations have relativistic solutions only when relativistic treatment of charges and currents is introduced, while they can have equally good "classical" solutions when these terms are defined in a classical way.

Let us remark too that the difference between AS and A*S is "very small", since the two potentials are indeed equal up to second order in β , but that it is not so small to be neglected (see footnote 32), since, in force of (7), one must have (and one has): div(AS) = - c-2

∂Φ S , ∂t

∂ Φ *S div(A*S) = - c-2 ∂ t , and these formulae show that the small difference becomes essential in the second case, when a small term (the divergence of the magnetic potential) is multiplied by c 2 , and thus it gives a meaningful non-zero time-variation of the electric potential, a potential which cannot vanish (in the first case, instead, the divergence of the magnetic potential is exactly equal to zero).

In conclusion, we should ask once again: who is really (that is to say: experimentally) right, C or E ? The aforesaid divergence can be elaborated in view of the proposal of a new gedankenexperiment aimed to discriminate between classical and relativistic interpretations of ME . One could either try to perform direct measures of the force acting on the charge q , or better of the electric potential difference across a thin linear conductor T placed along a radius with an extremity in the centre of C and the other one close to the current wire, as in the following picture:

We could attempt to make in evidence a possible Earth's absolute velocity (and this is why the sensor and the circuit's plane have been projected to be able to rotate, since this velocity is unknown), but, as we already said many times, the apparatus should be put in a real motion with respect to an ordinary Earth's laboratory, before saying that this test has given all possible information.

The fact that the force predicted by C does depend both on the intensity and on the direction of the current, should make it possible to separate a non-zero effect from other possible "disturbances" (due for instance to the electromagnetic fields existing in the terrestrial reference frame, and to other sources of systematic errors, or even to the possible

46

non-validity of Clausius' postulate - see footnote 35). Moreover, by increasing I and/or q , one might be able to observe an effect even if the velocity of the moving laboratory is very small, as presumably it has to be, compared with c .

We show below another picture, showing the experimental apparatus which we38 have tried to use in an amateurish way (in Foligno, near Perugia, in 1990):

An experiment of this kind has been in fact performed in a professional way by CardoneMignani39, with results which are difficult to interpret. Anyway, their apparatus was still in an Earth's laboratory, and so it could have possibly put in evidence only an unlikely "absolute" Earth's velocity.

In conclusion, we want to repeat it once again that: * - Apart the fact that the most conspicuous phenomena alleged in favour of SR (namely the increasing of the inertial mass and the mean-life of speedy particles) appear rather more compatible with an "absolute theory", than conversely (in absence of any evidence about a symmetry of these phenomena), it is possible to predict from ME physical effects which would depend from an absolute velocity, and this shows that the observation at the beginninf of section 2 - in no field has one ever discovered any dependence of the forms of the laws of physics on the velocity of the reference frame - is wrong (at least from a theoretical point of view, but the assertion appears to be theoretical, and not experimental). ** - Electrodynamical experiments (charges-and-currents) to test SR have been undeservedly neglected, to our actual knowledge, in favour of optical ones, and they moreover (of both kinds) have never (or seldom) been performed in moving laboratories with respect to the Earth.

These statements should "prove" our assertion that SR has not been tested so much as it is usual to claim, by those physicists who appear anxious to persuade their audience that Einstein was the greatest scientist of all times, and that a doubt about SR would be the same as a doubt about the Copernican system40.

3 - An (Impossible?!) Gedankenexperiment with Moving Clocks There is little doubt that one of the most impressive, and counter-intuitive, consequences of SR, is the so called time dilation, which could be roughly41 expressed as (from the same Internet group discussion quoted before, in section 2): The lengthening of the period of a moving clock in the ratio γ =

1 1− β

2

.

47

It would be quite better to say that, for any observer Ω , the time interval ∆τ which has elapsed for Ω between two events E , F in its life is equal to: F

(22)

1 2 ∆τ = ∫ − ds cE

(where ds2 is the pseudo-metrics of Minkowski space-time), and that, when expressed in any Lorentz coordinate system K(x,y,z,t) , then (22) becomes: F

(23)

F

1 1 2 2 2 2 2 ∆τ = ∫ − dS + c dt = ∫ − v + c dt = cE cE

F

∫

1 − β 2 dt ,

E

since now ds2 = dx2 + dy2 + dz2 - c2dt2 = dS2 - c2dt2 , and where v = observer Ω with respect to K , and as usual β =

dS is the speed of the dt

v . c

Of course, if this speed is a constant, for instance when Ω is an inertial observer, then we can write: F

(24)

∆τ =

1− β

2

∫ dt

=

1− β

2

[t(F) - t(E)] =

1− β

2

∆t ,

E

or even: (25)

∆t = γ ∆τ ,

which means that the coordinate time which has elapsed between the two events E , F is γ times the so-called proper time which has elapsed between the same two events with respect to Ω .

This is all, as far as the mathematical theory of "relativistic time" is concerned. Thereafter it is the moment of phenomena, which go from the observed increasing of the mean-life of speedy particles (with respect to an Earth's laboratory), to the so called twin-paradox, which seems to have been experimentally confirmed by the famous Hafele-Keating clocks' travel around the world (an effect which is more complicated by the presence of a theoretical time dilation due to the gravitational potential, which must be taken into account by people which are confident in relativity, either special or general).

Well, as far as this last experiment is concerned, we share the strong doubts which are illustrated in the very important paper by A.G. Kelly listed at the point N. 17 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme, and so we propose a similar test, remarking that, at least in principle, this "twin effect" could be checked also by comparing the time elapsed for a rotating clock (with constant speed, which makes the formula (24), or (25), applicable, even if we are not in front of an "inertial" clock) with a reference clock, which remains still in an Earth's laboratory:

48

One cannot of course hope to be able to reach very high speeds v of C' , but one could think to take advantage from the fact that C' could be rotated for a long period of time. If for instance we take for the radius R of the rotating platform R = 1 m , and an angular speed ω = 2πν which is corresponding to a frequency of ν = 50 Hz, then v is just about 300 m sec1 , which is almost exactly the Earth's rotation speed. From the formula (24) we have ∆τ = 1 − β 2 ∆t , which is almost equal (namely, once again, up to second order in β ) to: (26)

∆τ ~ (1 -

1 2 1 β ) ∆t = ∆t - β2∆t .

2 2

This last equation shows that the rotating clock C' should loose

1 2 β ∆t sec for each 2

second which is measured by the reference clock C , and since actually: β =

v 1 2 1 3x102 = = 10-6 , β = 10-12 , 8 c 2 2 3x10

then we have that in an hour time the rotating clock should theoretically (according to SR) loose 18 x 10-10 sec , which is about 2 nano-seconds, a value perhaps great enough to be detected (even in the Hafele-Keating test quoted above the "game" is played around a few nano-seconds).

Going on with our pure theoretical (pre-experimental) speculations, what could we expect, from a qualitative point of view, from such an experiment?

Well, according to SR, one should observe not only the expected time retardation, but even that all kind of clocks should show exactly the same slowing down. From an aethertheoretical point of view, instead, a time retardation is not strictly necessary; moreover, if there is one, then it should be explained by some "absolute" effect, namely a real physical effect due to the interaction of the moving clock with the aether. Along this path of thought, a Cartesian physicist should expect that different clocks (atomic, mechanical, etc.) could experience different time dilations (and, why not?, even contractions), at different rates.

The author can hear "orthodox" physicists saying: "this experiment has to do with one of the phenomena which we observe every day in our particle accelerators", but we object that the increasing of the mean-life of a particle (and let us even accept that the corresponding rate is exactly the one predicted by SR, and moreover equal for all particles) is not exactly the same thing proposed before. As an example of a physical cause (coherent with the hypothesis of a dragging aether) which one could think of, in order to explain the increasing of this mean-life, let us give the following one, which comes from an analogy (analogies are methodologically

49

fundamental in Cartesian philosophy). Let us imagine an ordinary cartesian orthogonal reference frame, with an origin O and three axes Ox, Oy, Oz , and a rain falling down along zaxis with intensity s (for instance millimeters of rain for time unity: so s has the physical dimension of a speed). This means that, if we take a container (a tea-cup!) in form of a paralleliped (suppose that it has a vertex in the origin, and the three sides coming out from this vertex along the three axes of the given reference frame being such that the length along x-axis is L , along y-axis L' , along z-axis L'' ; so the volume is V = LL'L'' ), then, after a period of time T , we will find a volume of water inside the container which is equal to LL'sT . Suppose now to rotate the cup along the y-axis of an angle θ , less than 90°, and then ask the same question: what will be the volume of water inside the cup after a time T ? It is clear that the answer will be LL'sTcos(θ) , and so far so good. Suppose now that the cup with sides parallel to the three axes - is moving along x-axis with a velocity v = (v,0,0) , and then ask once again the same question: after the same time T , what will be the volume of water inside the cup? It is rather clear that, from the point of view of an observer moving with the cup at the same velocity v , the rain will not fall anymore along the perpendicular to the "base" of the cup, since one must take in account a kind of "composition of velocities" (classical aberration, see next section!), and that the rain will fall for him along the direction s (v,0,s) , "aberrated" of an angle θ , with respect to z-axis, such that: cos(θ) = .

2 s + v2 This obviously means that the case we are studying now is exactly the same as before, as if the cup was simply rotated along y-axis of the same angle θ , and then the answer will be once again:

LL'sTcos(θ) = LL'T

1

s2 s + v 2

2

= LL'T

1+

v2 . s2

When comparing this value with the value LL'sT found at the beginning, we find, as it was obvious to expect, that the water inside the moving cup is less than the water inside the standing cup, and, pushing further our analogy, if T = U/LL's is the time required for getting a given volume U of water in the standing cup, then this same time will be equal to: (27)

T(v) =

U v2 v2 1+ 2 = T 1+ 2 LL' s s s

in the case of a moving cup, a time which is bigger than T .

Of course, we claim that we could possibly be in front of a "similar" phenomenon in the case we wished to "explain". Let us call T the mean-life, for instance of a muon, in a terrestrial laboratory: then this T will be, presumably, a function of the given particle and of its interaction with the "surrounding aether". Then we know that a speedy particle will appear to have, from the point of view of the terrestrial laboratory, a bigger mean-life, equal to: (28)

T(v) = γT =

T 1− β

2

~ T(1+

1 2 β ) (up to second order in β ), 2

which is the value predicted by SR, and which we admit agrees with the experimented value.

But let us now compare (28) and (26), by putting in the first equation, as it would be quite "natural", s = c . Then, up to second order in β , the two equations appear to be identical! In conclusion, could we be quite sure that the "true" physical reason of the discussed

50

phenomenon is not of the kind of the "moving cup" model, at least in absence of any evidence of symmetry, which would be essential for the relativistic explanation?

Coming back to the argument of different clocks, and in view of the possible objection of relativity's supporters (if the proposed experiment would fail their expectations), that the "failing" clocks are not "good" ones, the question which must receive a clear answer is: but which is a "good" clock for SR? (remember that at Einstein's times atomic clocks were not available, not even in theoretical speculations). As a matter of fact, the answer is not difficult, since the only one clock which is good for relativity is the light-clock, which is described in the following figure (which we take, with the description below, from Marinov's book: Classical Physics, Part III, High-Velocity Mechanics, 1981, p. 7):

A short light pulse (i.e., a group of photons) is generated at a given initial moment. The pulse flies ... to mirror B, ... it returns to A, where it puts a counter ... showing the number "1" and generates (after amplification) a second pulse which flies to mirror B again; after the return of the second pulse the counter will show the number "2"...

It is rather clear why this the ideal, perfect clock in SR, and it is curious to remark 42 that even from an aether-theoretical point of view a light-clock would experience some time dilation when in (absolute) motion through the aether. If we suppose that the absolute velocity is (v,0,0) along the horizontal arm of the clock 43 (say that its length is L , in such a way that 2L the period of the clock44 is T = ), then the moving period would be: c (29)

T(v) =

2L 1 L L 2 Lc + = 2 = = T , 2 2 (1 − β 2 ) c(1 − β ) c− v c+ v c − v

NT ticks with respect to T an aether-rest light-clock, then the same time interval will be measured with N' ticks with respect to the (absolutely) moving light-clock, in such a way that: which implies that, if one measures some time interval ∆t as N =

(30)

N' =

NT = N (1 - β2) .

T (v )

The previous formula can be interpreted as a time dilation effect due to the absolute velocity 1 v , and when compared with (26) one realizes that only a factor is missing (of course, the 2 same is true for (29) and (28)). If one introduces a "real" length contraction too, again due to a possible interaction with the aether, then one would get exactly the same factor of the relativistic time dilation. But since we do not have enough information whether this length contraction must be conjectured or not (see in this same Episteme's volume the first Larson's paper), we prefer to leave (30) as it is, because it gives, after all, an instructive example of other possible time dilations factors, not necessarily equal to the unique one predicted by SR.

51

In other words, if for instance from an aether-theoretical point of view, the previous tea-cup model would be able to predict a time dilation for moving atomic clocks equal to the relativistic time dilation, for light-clocks this dilation could be different, and so on, so on...

In conclusion, let us repeat it, even if it was true - at least in some measure - that absolute speed effects are such that to imply a perfect quantitative identity with SR predictions, then all the same this would not mean that we are in front of identical physical theories (or of equivalent physical theories, as many physicists like to say), since the proper time should be interpreted, from the point of view of the aether physics, only as an apparent time, while the true time would always be only the coordinate time measured in an (absolute) aether-frame45.

4 - On Relativistic Light's Aberration We end this paper by proposing at last an optical experiment, but not a test like the usual ones, aimed to measure speeds, or speeds' differences. Rather, we feel that a very important consequence of relativity is the so-called light's aberration, which could easily been explained as follows.

Think, in a coordinate system K of Minkowski space-time as above, of a photon emitted at the time t = 0 along the y-axis by a light source S standing still in K , say for instance at the L point (0,L,0) . Then, at the time , the photon will arrive in the spatial "origin" of K , the c point (0,0,0) . Suppose instead that the source is moving with respect to K with some velocity v = (v,0,0) , and suppose to introduce a proper system K'(x',y',z',t') comoving with S (with spatial axes "parallel" to x, y and z). Then the photon will go along a straight line in L K' , but not in K , which implies that, at the time γ (now it appears, as it must in SR, the c time dilation factor!), the photon will meet the x-axis in the point (βγL,0,0) , and not in the point (0,0,0) as before.

So, the aberration angle θ is given (in K ) by: (31)

tg(θ) =

βγL = βγ , L

or even, up to second order in β : (32)

tg(θ) ~ β =

v , c

which is the classical formula for astronomical aberration46.

A few mathematics would perhaps describe better the situation.

Motion's equations of the photon in K , when the source is still in K : x = 0 , y = L - ct , z = 0 ; 3-velocity of the photon in K (0,-c,0) ; speed = c .

Motion's equations of the photon in K' , source moving in K : x' = 0 , y = L - ct' , z' = 0 ; 3-velocity of the photon in K' (0,-c,0) ; speed = c .

Motion's equations of the photon in K , source moving in K : v x' = x - vt = 0 , y = L - c(t - γ 2 ) , z = 0 c

52

x = vt , y = L - γct + βγvt = L - γct(1 - β2) = L - ct 1 − β arrival of the photon at y = 0 : L - ct 1 − β 3-velocity of the photon in K : (v,-c 1 − β

2

,z=0

L c ,0) ; speed2 = v2 + c2(1 - β2) = c2 .

=0 , t=γ

2

2

This relativistic analysis of aberration shows that, if it is true, according to SR, that the light's speed c does not depend from the source's motion (in our case from v ), then the light's vector velocity can depend from v . As a matter of fact, in the 3-velocity (in K ) of the photon the quantity v does appear explicitely, even if it disappears in the formula which gives the speed.

Well, from a possibly strict aether-theoretical point of view, when supposing the independence of light's propagation from the "source's movement", we could think that the whole vector velocity would not depend from the source, and not only the speed. That is to say, there is possibly in this point a divergence between aether-grounded previsions and the corresponding relativistic previsions. So, is it possible to compare relativistic predictions with analogous aether-theoretical ones, outside from the realm of astronomical observations? In other words, is it possible to test the relativistic aberration of light in an Earth's laboratory??

We suggest to use a circular platform P like in the following picture:

First suppose that P is at rest, and place a mono-directional (the most possible point-like!) photon's source S in the rim of the platform, near to a "fixed" point p in the laboratory.

Direct the source towards the centre of P , in such a way that a "fixed" light's detector S* (once again, the most possible point-like), placed near the "antipodal" point p* of p , can detect the arrival of the photons emitted by S . Then, we can make the platform rotate, and arrange things in such a way that, in "stationary" conditions for the angular velocity of P , S does emit photons only when it is in front of p . The goal is to check whether S* will continue to detect these photons, as an aether theory would foresee, or not, as relativity would instead predict. That is to say, one could test whether light is really "dragged" by the velocity of the source, or not.

One could even think to take both detector S* and source S fixed in the laboratory, and to use as a moving source a mirror M (almost possibly point-like, as before!), placed in the rim of P . S does emit photons directed towards the centre A of P , and these photons are reflected only when M passes in front of A (that is to say, with a period equal to 2πR/v = 2π/ω - of course, from relativity's point of view, one must specify that this is the period with respect to the laboratory coordinate system). The trace of the backwards photons can be detected by a fixed screen-detector S* .

In order to avoid S and S* to be too much close one to the other, one could think to place a semi-transparent mirror M' at some inessential distance from S , orthogonal to the photon beam, and at a distance L 1 from A , in such a way that the emitted photons can pass through

53

M' . One could then place S* at some distance L 2 from A , in order to detect the backwards photons reflected by the "other" face of M' , like in the following picture:

One could even think to increase the expected effect by repeated reflections, introducing another "mirror" placed between the platform and the detector S* .

It is easy to give quantitative evaluations for this Gedankenexperiment. For a given radius R , and a given angular speed ω , then the distance between the impact point A° of the inwards non-aberrated photons, and the impact point A1 of possibly aberrated backwards photons would be equal, in force of (32), to: (33)

δx = δx' + δx" = (L1+R)tg(θ) + (L1+L2)tg(θ) = (2L1+R+L2)tg(θ) ,

which is almost equal (up to second order in β ) to: (34)

δx ~ (2L1+R+L2)β = (2L1+R+L2)

ω R . c

This identity shows, first of all, that the described test would be called to measure a first order effect in β . For 1 meter radius, a distance L1 = L2 equal to 25 meters, an angular speed ω once again corresponding to 50 Herz, then, according to SR, one should have a "shifting effect", after just one reflection, of: 76 x

3x102 = 76 x 10-6 m , 3x108

namely an effect of a few microns, which is perhaps not so small to start with. This effect could afterwards be emphasized - as we have suggested - and finally detected.

It would perhaps be even better, from practical purposes, to replace the rotating platform with a "very sly" vertical spinning rotor - as in the following picture - in order to get always an angle of 90° between the inwards beam, and the reflecting mirror M :

In such a way, the proposed "experiment" would rather be similar to the famous Fizeau cog-wheel experiment. Summing up, the light emitted by S is periodically reflected by M .

54

Then, after a new reflection by M' , the beam hits the mirror-detector S* , from which it is once again reflected to M' , and so on. If SR is correct, then one should be able to appreciate an increasing displacement of the trace of the reflected photons, compared with the original one, corresponding to photons which have not been reflected (and hence are not aberrated). At the contrary, if the aether-theoretical prevision is correct, then one should not observe any displacement. The qualitative side of this last experiment could be perhaps one of its most attractive features47.

Notes 1 - "Special" refers to the first 1905 Einstein's theory, which did not yet include a treatment of gravitation (Newtonian gravitation was irremiadably out of the requested relativistic "covariance").

After the building of general relativity (GR), we could say that SR is the theory of a flat space-time (a 4-dimensional connected time-oriented Lorentz manifold; in truth, to the property of flatness, one has to add simply connectedness and completeness in order to get the characteristic properties of Minkowski space-time), namely that part of relativity which does neglect gravitational effects due to the presence of the space-time curvature induced by matter. In this sense, SR deals only with electrodynamics in Minkowski's space-time.

2 - One should perhaps emphasize that any "relativistic space-time" in GR, must be be regarded as a purely logical admissible construction, whose only "fault" is that it does not describe the "space" and "time" thought-categories which are rooted in the human mind (a statement this one with which even relativity supporters generally agree). Hence one can just discuss whether these new space-time (or others, there is no limit to abstract mathematical constructions) do correspond in some extent to reality, or not. This remark implies that attempts to prove that relativity is "logically inconsistent" (contradictory in itself) are worst than useless as arguments against relativity (one case for all, the socalled Dingle syllogism, see section 5 in our "Most Common Misunderstandings...", quoted in footnote 18 in the quoted Letter...). This does not exclude, of course, that such attempts could teach, in any case, something interesting (see footnote 14 in that same Letter...).

3 - We say that in the conviction that some of the usual criticism against relativity is, unfortunately, ineffective (see the paper mentioned in the previous footnote).

4 - We must acknowledge that, during his many years of activity, Newton did not always push his criticism against Descartes up to the point to completely refuse the aether. Anyway, what does really matters in this discussion, is the manner in which Newton's ideas have been interpreted - and developed - by his followers, and not which was his original, authentic, thought about this, or others, argument (if there ever was such a "thought", since it could have changed from an age of life to the other, or could have been uncertain, undecided). The historical fact is that the hypothesis of the aether was dismissed after Newton in the conviction that the conception of a "plenum space" was incompatible with the gravitation's law which ruled the the movement of celestial bodies (see also footnote 10), and this is enough for our "judgement". Of course, the two conflicting options influenced the conjectures about the nature of the light too, which was thought of as made up of "corpuscules" in one case, or conceived as a "wave" (perturbation of the medium) in the other (Huyghens).

5 - Which grounds in something like an "antinomy of the pure reason". The conception of an empty space does in fact correspond to the mental space of euclidean-intuitive geometry, the "space" regarded as a "transcendental form" of the human intellect, and it should not by any means be confused with the space of physical reality.

6 - Besides, a rather old argument, expressed for instance almost in the same words by Nicholas of Cusa and Giordano Bruno (traces of its influence can be found even in Copernic). It was at that time needed in order to rebate the objection: "why the pretended Earth's movement around the Sun is not detected by Earth's inhabitants?". This shows that the chief argument which opposes relativity to the aether's physics was already fully active not only at the beginning of XVII Century, but at an earlier

55

date too. As we shall see, the most popular experiments alleged in favour of relativity show only that this pretended movement (the famous aether's wind) cannot be detected in a terrestrial laboratory.

7 - By the way, there were already important studies about the question which gave only to him an unprecedented fame, see Bjerknes' book reviewed in this same volume.

8 - Which - and this could be thought of as a "paradox" - does not include Newton's gravitation's theory itself, since, as it is well known, this was the first victim of the requirement that all physics' laws should be expressed in a covariant form. Of course, people seeing this much beloved theory disappear, together with the "classical" space-time which Newton too used in his work (as everybody else until the beginning of XXth Century!), fall in the mental trap of identifying classical physics with Newtonian physics, and do not realize the importance of the fact that the conception of "physical space" is identical in Newton's and Einstein's approach.

9 - Even the introduction of the term "inertial" (by no means an easy concept to understand: Einstein in fact did not make any attempt of explanation, and just used the language of "ordinary" Newtonian mechanics), show the asserted conservative side of SR. 10 - We feel dutiful a reference to the "unknown" Italian physicist Marco Todeschini, who studied deeply this argument, and advanced the question to investigate Newton's objections to Descartes' "gravitational theory", in order to realize whether they are, at the light of advanced physical and mathematical knowledge, still well-founded or not. See for instance some information about this scientist in: http://www.dipmat.unipg.it/~bartocci/todes.html (in Italian only).

11 - And many other "implicit" assumptions, see footnote 9.

12 - This restriction to inertial observers appears indeed a conceptual weak point of SR, since a fully relativistic approach should perhaps make no difference at all between "states of motion" with respect to nothing (see even the footnote 18 mentioned in the previous footnote 2).

13 - One should not forget that, if Maxwell's theory is "correct" (an assertion, however, which should be investigated with more care: see for instance, both in this same volume, Galeczki's article, or the "Call for papers": Has the last word been said on classical electrodynamics?), then LSP would be a direct consequence of RP, since there is nothing in that theory which connects the speed of an electromagnetic wave to the speed of its source.

14 - Not to say of their "accuracy", either theoretical or instrumental. Flaws appear sometimes unintentional, sometimes more suspicious (see for instance Kelly's paper mentioned in section 3). One of the most interesting examples of this situation, is the analysis of Michelson-Morley's experiment made in: Marco Mamone Capria, Fernanda Pambianco, "On the Michelson-Morley Experiment" (Foundations of Physics, 24, 6, 1994), or the refusal of subsequent Miller's results - obtained during many repetitions of this same experiment - which is discussed in DeMeo's paper listed at the point N. 6 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. We consider worth of attention under this point of view many papers by the (well known as a critic of relativity) Italian physicist Roberto Monti, in particular his "Theory of Relativity: A Critical Analysis", Physics Essays, Vol. 9, N. 2, 1996, pp. 238-260 (see also his papers published in Episteme N. 3 and N. 4).

15 - The Earth's revolution speed is about 30 km/sec , and it was not detected for instance by Michelson and Morley, Trouton and Noble (see section 2.C), and many others. The Earth's rotation speed in the 24 hours is a more likely candidate for this detection, and it is about 300 m/sec , so an hundred of times less than the previous one, which implies that, for experiments of-second order in β, the factor β2 = v2/c2 becomes 10.000 times less. We believe that this could be the reason for the experimental "anomalies" pointed out for instance in Van Flandern's paper about GPS (see this same volume of Episteme), but the trouble is that the "detection" of this speed (already realized by Michelson-Gale's experiment, or by variations of Sagnac-kind experiments) would easily be

56

considered uninfluential to our purposes by relativity's supporters, since it does concern non-uniform motions!

16 - See for instance Alessandro Moretti: "L'universo intellegibile, ovvero, la gravitĂ descritta da Leibniz", in Episteme N. 3 (2001) (in Italian only).

17 - One of the very rare exceptions is the experiment that the Dutch meteorologist Buys-Ballot (18171890) "conducted in order to confirm the Doppler shift. "He put a group of musicians on a train and took up his position on a station platform. He asked the train driver to rush past him as fast as he could while the musicians played and held a constant note, and was able to detect the Doppler shift (as a change in pitch) as the train passed him (D. Filkin, S. Hawking: Stephen Hawking's Universe: The Cosmos Explained, BasicBooks, New York:, 1997, p. 65)". From: http://scienceworld.wolfram.com/physics/DopplerEffect.html .

18 - From the title of the chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will, Was Einstein right?, Oxford University Press, 1988 - quoted also in the Letter... which opens this volume.

19 - See for instance Pyenson's book, quoted in the aforesaid Letter... (previous footnote).

20 - We repeat that it seems necessary to accept as a fact the failure of too many experiments aimed to detect an "appreciable" aether's wind in a terrestrial laboratory, and so we confess to have some suspicion towards those people who claim for instance to have proven the existence of an Earth's absolute movement of almost the same amount of the famous speed with respect to the background radiation (and of course these numerical evaluations have been given only a posteriori).

21 - See for instance: Giuseppe Antoni, Umberto Bartocci, "A Simple 'Classical' Interpretation of Fizeau's Experiment", Apeiron, Vol. 8, N. 3, July 2001 (available on line at: http://www.dipmat.unipg.it/~bartocci/fizhoek.html ).

22 - Robert Resnick, Introduction to Special Relativity, Wiley, New York, 1968.

23 - It is very famous the alleged Hilbert's remark: "Physics is too important to be left to physicists" (see for instance Pyenson's book quoted in footnote 19, p. 183). Unfortunately, from one side it is true that theoretical physics should always be carried on with all the logical exactitude which mathematicians display in their researches. For instance, it is surprising to see how often physicists assert that something cannot be done, giving as only proof the fact that they did not succeed in doing that, when it is well known that any assertion of this kind in mathematics is very difficult to prove (a good example: Paul Cohen's 1963 proof of the independence of the so-called "continuum's hypothesis" from the Zermelo-Fraenkel-Skolem axioms for a set theory; or perhaps, even better known, Galois' proof that it was not possible to give a "general" formula for the solutions of an algebraic equation with degree greater than 4, it would have been certainly not enough to claim this impossibility on the basis that mathematicians did try for some time to find this formula, and that they did not find it!). But from the other side, it is even true that mathematicians have in many recent circumstances shown themselves perhaps worst, with their propensity to aesthetical canons, formalistic abstractness, etc., and that these propensions are one of the not minor causes of the physical "philosophy" we are criticizing (see again Pyenson's book in footnote 19, or, of the present author: "'Cattivi maestri', ovvero, a proposito di un morbus mathematicorum (ma non solo!) recens", at the web page: http://www.dipmat.unipg.it/~bartocci/st/goedel6.htm - in Italian only).

24 - G. Cavalleri, L. Galgani, G. Spavieri, G. Spinelli, "Esperimenti di ottica classica ed etere Experiments of classical optics and aether", Scientia, Vol. 111, 1976, pp. 667-673.

25 - We should perhaps explicitely remark that in this theory could even happen that observers in effective relative motion could be both in absolute rest, a situation which implies that all aetherframes, or rest-frames, should be considered only as local ones.

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26 - "The special theory of relativity grew out of the Maxwell electromagnetic equations. So it came about that even in the derivation of the mechanical concepts and their relations the consideration of those of the electromagnetic field has played an essential role" (A. Einstein, "Elementary Derivation of the equivalence of Mass and Energy", Bulletin of the American Mathematical Society, 41, 1935). See the second Bjerknes' paper in this same volume of Episteme.

27 - "Symmetries and Asymmetries in Classical and Relativistic Electrodynamics", with Marco Mamone Capria, Foundations of Physics, 21, 7, 1991; availabe on line at: http://www.dipmat.unipg.it/~bartocci/symm.html .

28 - Einstein's source was very likely Alfred Föppl's: Einführung in die Maxwell'sche Theorie der Elektricität, 1894, but this case was well known to Maxwell himself (A Treatise on Electricity and Magnetism, 3rd edition, 1892, p. 601).

29 - See for instance: G. Cavalleri, G. Spavieri, G.Spinelli: "On the Action and Reaction Principle in Special Relativity", Nuovo Cimento B, 5, 1988; G. Spavieri: "Proposal for Experiments to Detect the Missing Torque in Special Relativity", Found. of Phys. Lett., 3, 1990.

30 - Some people question whether even Marinov did really perform all the experiments he claimed to have done, or whether they were "professionally" performed, which is perhaps true, at least to some extent. But this could be so only because Marinov, after his exile from Bulgaria, was a poor man, and did everything with his own money and enthusiasm, not having access to public funds, often not used in the best way by luckier establishment's physicists. As far as the strictly experimental situation is concerned, we should perhaps add that Marinov did not use an electric coil, or a magnetic needle, in order to try to detect the torque which was, at last, missing, and that he claims to have used an Hall detector.

31 - The solution below gives the "right" behaviour of fields E and B at infinity, and excludes the so-called advanced potentials as having no possible physical meaning. We could perhaps point out that Roberto Monti (see footnote 14) remarks that in equation (2) it should be added a term σ0E , where σ0 is the possible vacuum conductivity, and that the conventional present-day choice of putting σ0 = 0 is not experimentally so well established as it should be. Even if this observation, in case it was experimentally confirmed, would destroy all pretended covariance of Maxwell's electrodynamics, one must acknowledge that in non-cosmological contexts (such as the ones we shall be dealing with) σ0 seems to be really negligible. In other words, that this would be one of those possible violations of SR on a large scale which would not worry relativity's supporters (see also footnote 11 in the often mentioned Letter...).

32 - See for instance the celebrated Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965, "Electromagnetism and Matter". The author warns (21-5) that it is not so trivial to get (14) and (15) from (11) and (12), since at first sight "almost everyone" would claim that after integration it should appear, in the denominator of the fractions, the retarded distance (namely, the distance from the point in which the charge is seen at the time t), which is not the case. We could perhaps emphasize that the distance which appears in (14) and (15), and the "ordinary" distance , differ only up to second order in β , but their difference - which a physicist willing to uncautiously approximate computations since the beginning, and not only at the end, would risk to neglect! - is essential to further developments.

33 - One should perhaps meditate about the circumstance that this possible factual divergence between classically interpreted and relativistic Maxwell's electrodynamics is in principle meaningful even for a small length of the rod, or for a "low" absolute speed v .

34 - But see also the analysis and the experimental results mentioned in the paper listed at the point N. 17 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. As far as Trouton-Noble's type experiments is concerned, see also the paper by G. Spavieri, et al., again in this same volume.

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35 - In the calculation which leads to formula (20) we did use the fact that Φ = 0 , and then ∇Φ = 0 .

This is the so-called Clausius' postulate: "For a circuit in which is flowing a stationary current, the charge density is zero" (another electromagnetic "principle" which is not explicitely stated in ME).

Recent reports (for instance: O. Jefimenko, "Demonstration of the Electric Fields of Current-Carrying Conductors", Am. J. of Phys., 30, 1962; T. Ivezic, "The 'relativistic' electric fields produced by steady currents: comparison with experiments", Phys. Lett. A, 156, 1-2, 1991; A.K.T. Assis, W.A. Rodrigues, A.J. Mania, "The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current", Foundations of Physics, 29, 1999), both experimental and theoretical, have questioned its validity, but this would not change the essence of the present discussion. As a matter of fact, both classical and relativistic Maxwell's electrodynamics should take into account the same modification, and moreover a charge situated right in the centre of a circular circuit should not be affected by the force arising from this nonzero electric potential, apart from "asymmetries" in the circuit (not to say of the fact that the special features of the force (19) could be, at least in principle, allow its detection between other forces).

36 - It is perhaps useful to remark that the charge continuity equation does hold for these classical values of the density charge and of the density current, as well as it does hold for the corresponding relativistic values.

37 - By the way, as one should always expect: mathematics can never give explicitely at the end anything more than it had in itself implicitly, in the original assumptions one started from!

38 - Umberto Bartocci, Marco Mamone Capria, Luigi Mantovani; see Umberto Bartocci: "On a Possible Experimental Discrimination Between Classical and Relativistic Electrodynamics", Proceedings of the International Conference "What Physics for the Next Century?", Ischia, 1991, Ed. Andromeda, Bologna, pp. 88-94.

39 - Umberto Bartocci, Fabio Cardone, Roberto Mignani: "New electromagnetic test of breakdown of local Lorentz invariance: Theory and experimental results", Foundations of Physics, Vol. 14, N. 1, 2001 (see point N. 10 in: http://www.dipmat.unipg.it/~bartocci/listafis.htm, with figures).

40 - Tullio Regge, Cronache dell'Universo , Ed. Boringhieri, Torino, 1981.

41 - This is indeed a popular description of time dilation, but we find it misleading - that is to say, a source for possible misunderstandings - to speak of a "moving clock", since in Minkowski's spacetime nothing is really "moving" (space and time are "tied" together, and can be untied only in particular coordinate systems), and so the period of a clock remains always unchanged.

42 - As it is curious to remark that the ideal clock of SR (which, as far as our actual knowledge, has never been realized in practice!) cannot be thought of as point-like, since a length is necessarily required (one could object that any real clock cannot be thought of as point-like, but here the question is different, since the light-clock has even a privileged direction). This shows that, at least in principle, it is not possible to think of a light-clock in an accelerated frame (for instance in the "rotating platform" of Sagnac's experiment: see section 3 in "Most Common Misunderstandings...", quoted in footnote 2), without meeting serious conceptual troubles. This observation refers for instance to the well known difficulties of SR when one wishes to introduce in it some "simple" physical concepts, like for instance the concept of rigid body.

43 - Not fortuitously we have decided to neglect to analyse any "transversal" motion of the lightclock's behaviour from the point of view of an aether theory! It is clear that to discuss this question would be exactly as to discuss the Michelson-Morley experiment, and we have serious doubts about the correctness of its usual theoretical descriptions (see for instance the paper by Mamone Capria and Pambianco quoted in footnote 14). It is obvious that, at least in the case of high absolute speeds, a light-clock should in general simply cease to work.

44 - This period of time is quite suggestive, since it would imply that, thought of a minimum possible length (an hypothesis rather natural in the fluid-dynamical conception of space), call it for instance a

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metron, then one would have as a consequence a minimum possible time, call it for instance a cronon: 1 cronon = 1 metron / c . Just to give an idea of the possible quantitative size of these units, if we conjecture that a metron has something to do with the so-called Planck length, whose magnitude is about 10-35 m , then the cronon would be about 10-43 sec .

45 - About the supposed equivalence of different physical theories (would the pretended equivalence mean that all possibly conceivable experiments should give the same result? Or that this would be true for only some of them??), it is rather instructive the reading of: Gianfranco Spavieri, "Nonequivalence of Ether Theories and Special Relativity", Physical Review A, 34, 1986.

46 - This light's relativistic aberration was studied by Einstein since his first 1905 paper, since he had to explain the known phenomenon of the annual stellar aberration, discovered by James Bradley in 1728. As a matter of fact, this phenomenon could have thought of, at first sight at least, a physical fact contrary to relativity's principle. We have to admit that Einstein seems to have succeeded in his purpose, and that annual stellar aberration has a good relativistic explanation too - that is to say, one must even admit that this phenomenon has - and it had before Einstein - other "classical" explanations.

In truth, this is a rather controversial argument, and are numerous the Einstein's critics which assert instead that SR cannot provide a good explanation for astronomical aberration (see for instance: Thomas E. Phipps Jr., "Relativity and Aberration", Am. J. Phys., 57 (6), June 1989). The point is that, according to SR, only the relative speed between the Earth and the moving star should be the reason for the observed phenomenon, while all stars appear equipped with the same aberration, which does depend only from the Earth's revolution speed v around the Sun. This is of course wholly correct, but the point is that, always according to SR, the phenomenon does depend from a comparison between two positions of the same star in a 6 months interval, when the Earth should be thought of in an (approximatively) inertial frame K' different from the one K in which it was 6 months early ( K' is then moving with respect to K with a speed 2v ). If this argument appears able to "save" SR, at least on this question, and in general, one could object that the indispensable hypothesis for the relativistic explanation of stellar annual aberration is that the relative speed Earth-star does not change significatively in this 6 months time, and that this could not be always the case, for instance when dealing with binary stars, which have a revolution period comparable with that of the Earth, but show the same aberration of all other stars. At this point, relativity's supporters find another ad hoc explanation for these stars, etc., and the question does not appear settled once for all (but see the chapter dedicated to aberration in Reflections on Relativity, http://www.mathpages.com/rr/s2-05/205.htm).

47 - For instance one could think to invert the rotation of the platform, or of the wheel, and to see what happens: that is to say, whether there is "symmetry" in the observed patterns (the case in favour of the aether hypothesis), or not (which would be the case in favour of SR). Needless to say, one should discuss many more practical details of this "experiment", such as the necessity to provide for a suitable photon source, since a "real" laser beam is much more similar to a divergent cone, rather than to a cylinder, as one should instead need in the actual case. These practical imperfections notwithstanding, a SR supporter should yet predict that one would truly find an asymmetry in the trace of the photons in S* , depending on the direction of rotation.

----[A presentation of the author can be found in Episteme N. 1] bartocci@dipmat.unipg.it

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S. Tolver Preston's Explosive Idea E = mc and the Huyghens-Leibnitz Mass/Energy Identity as a Heuristic Principle in the Nineteenth Century 2

(Christopher Jon Bjerknes) Abstract. In 1875, S. Tolver Preston published a prophetic treatise, which set forth his arguments for the existence of an aethereal medium in space. The title of this work is Physics of the Ether. Its purpose is to discredit the spiritualistic concept of "action at a distance" and to evince the irrationality of the principle of "potential energy", and replace these mythologies with "physical causes capable of rational appreciation." Among the many achievements of this heuristic masterpiece are Preston's arguments for atomic energy, the atomic bomb, a luminal speed for the propagation of gravity, and the heuristic principle that E = mc2.

Introduction Samuel Tolver Preston [b. 1844, was the son of Daniel Bloom Preston (b. 1807) and Mary Susannah Tolver] set forth arguments in the nineteenth century, which were to condition life in the twentieth century, and beyond. In an early attempt to apply Herbert Spencer's "Social Darwinism" in a constructive way (as opposed to the horrific racism it furthered), Preston argued for the collegiate education of females, on the grounds that it would strengthen the genetic stock of males and generally increase the intelligence of human beings.[1] This opposed the longstanding tradition that the Church is the bride of Christ, and is obedient; and, therefore, a woman must obey her husband and shun professional work. In a letter to Darwin, Preston professed rationalistic words to the effect of, "self-interest as a motive for conduct is a thing to be commended - and it certainly [is] I think ... the only conceivable rational motive of conduct: and always is the tacitly recognized motive in all rational actions."[2] Preston's equally pragmatic aether theories led him into diverse fields. For example, Preston speculated on the nature of "Free Will" and brain dynamics - another of his scientific challenges to the religious ontology and traditions pervasive in his time.[3] Preston's profound physical insights were the result of a rational analysis of phenomena he conducted in the refined language and images of the eighteenth century homme d'esprit George-Louis Le Sage. Preston's work was in part a self-described scientific reaction to contemporary "theories of a vague nature" which proposed "phantom agencies" to account for known phenomena. His Physics of the Ether [4] is a scientific synthesis derived from the hypotheses that aether is rarified mass, mass, concentrated aether; and that aether particles must be in motion and this motion is conserved. For Preston, as for many of his contemporaries, all things are modes of motion. These premises evolve subtly into a definition of terms, identities, and mathematical expressions described in compelling prose, which assert, among other things, that energy is proportional to mass times the speed of light squared, yielding incredibly potent kinetic effects, "165. To give an idea, first, of the enormous intensity of the store of energy attainable by means of that extensive state of subdivision of matter which renders a high normal speed practicable, it may be computed that a quantity of matter representing a total mass of only one grain, and possessing the normal velocity of the ether particles (that of a wave of light), encloses a store of energy represented by upwards of one thousand millions of foot-tons, or the mass of one single grain contains an energy not less than that possessed by a mass of forty thousand tons, moving at the speed of a cannon ball (1200 feet per second); or other wise, a quantity of matter representing a mass of one

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grain endued with the velocity of the ether particles, encloses an amount of energy which, if entirely utilized, would be competent to project a weight of one hundred thousand tons to a height of nearly two miles (1.9 miles)."

Towards a Comprehensive Theory of Dynamics Based on Motion as a Unifying and Vivifying Cause Preston set a high standard for his work, which many today would consider na誰ve, "there can exist but one correct method of viewing any subject or question whatever." Before we can come to understand Preston and evaluate the nature of his conclusions and determine his method for arriving at them, we should first explore the historical context, which led him to question the mythologies prevalent in his day, and to propose alternative points of view based on a Le Sagian materialism, which originally arose as a materialistic exposition on the Epicurean theory of "universal attraction".[5] Le Sage argued that if space were to contain an extremely fine particulate aether of "ultramundane particles" moving at light speed in all directions, these particles would bombard bodies. In the case of a comparatively isolated body, the bombardment would, statistically, be even on all sides, and a sort of equilibrium pressure would result. However, bodies would cast "shadows" on other bodies by blocking out those "ultramundane" aether particles which strike them. This proposed shadowing effect would cause a net force of attraction between bodies, in conformity with Newton's inverse square law.

In Preston's day, as today, there was a lingering religious opposition to any such mechanistic exposition on the cause of gravity, which would obviate the governance and active intervention of God as the cause of gravity. Many, Roger Cotes, Richard Bentley and Voltaire, among them, considered the idea of "universal attraction" to be a scientific proof of the existence and active governance of God. Just as the Church had opposed any refutation of Aristotle's Physics and Metaphysics, religious extremists opposed and oppose any mechanistic exposition on a proposed cause of "mutual attraction". This corrupt attitude toward pure science, which is an offense against religious freedom, not an expression of it (Descartes, Huyghens and Leibnitz, who were vocal advocates of aethereal gravitational theories, were deeply religious men), is exemplified by Bentley's A Confutation of Atheism from the Origin and Frame of the World, written pursuant to Newton's letters,[6] "And first as to that ordinary Cant of illiterate and puny Atheists [***] That such a mutual Gravitation or spontaneous Attraction can neither be inherent and essential to Matter; nor even supervene to it, unless impress'd and infused into it by a Divine Power. (3.) That though we should allow such attraction to be natural and essential to all Matter; yet the Atoms of Chaos could never so convene by it, as to form the present System: or if they could form it, it could neither acquire such motions, nor continue permanent in this state, without the power and Providence of a Divine Being."[7] This religious persecution had a chilling effect on research into the physical causes of gravity and magnetism. The subject became and remained largely taboo, with a few notable exceptions. Colin Maclaurin's writings evince how lightly one had (has) to tread when proposing a physical theory of gravity. He was a diplomatic apologist for such an approach: "14. As we cannot but conceive the universe, as depending on the first cause and chief mover, whom it would be absurd, not to say impious, to exclude from acting in it; so we have some hints of the manner in which he operates in nature, from the laws which we find established in it. Tho' he is the source of all efficacy, yet we find that place is left for second causes to act in subordination to him; and mechanism has its share in carrying on the great scheme of nature. The establishing the equality of action and reaction, even in those powers which seem to surpass mechanism, and to be more immediately derived from him, seems to be an indication that those powers, while they derive their

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efficacy from him, are however, in a certain degree, circumscribed and regulated in their operations by mechanical principles; and that they are not to be considered as mere immediate volitions of his (as they are often represented) but rather as instruments made by him, to perform the purposes for which he intended them. If, for example, the most noble phaenomena in nature be produced by a rare elastic aetherial medium, as Sir Isaac Newton conjectured, the whole efficacy of this medium must be resolved into his power and will, who is the supreme cause. This, however, does not hinder, but that the same medium may be subject to the like laws as other elastic fluids, in its actions and vibrations; and that, if its nature was better known to us, we might make curious and useful discoveries concerning its effects, from those laws. It is easy to see that this conjecture no way derogates from the government and influences of the Deity; while it leaves us at liberty to pursue our enquires concerning the nature and operations of such a medium. Whereas they who hastily resolve those powers into immediate volitions of the supreme cause, without admitting any intermediate instruments, put an end to our enquires at once; and deprive us of what is probably the most sublime part of philosophy, by representing it as imaginary and fictitious: by which means, as we observed above, they hurt those very interests which they appear so sanguine to promote; for the higher we rise in the scale of nature, towards the supreme cause, the views we have from philosophy appear more beautiful and extensive.

Nor is there any thing extraordinary in what is here represented concerning the manner in which the Supreme Cause acts in the universe, by employing subordinate instruments and agents, which are allowed to have their proper force and efficacy; for this we know is the case in the common course of nature; where we find gravity, attraction, repulsion, &c. constantly combined and compounded with the principles of mechanism: and we see no reason why it should not likewise take place in the more subtile and abstruse phaenomena and motions of the system. "[8]

Preston courageously and unapologetically confronted the religious bias and dogma against mechanistic theories of gravitation. He cautions us to not "attach two ideas to [a] fundamental conception[.]" Motion is the sole cause, for Preston. He also notes, regarding theories of a vague nature, "that their very vagueness, in which their real weakness consists, is employed as a defence against argument: hence the long life of such theories." This is a reaction against the vague and "spiritualistic" notion of "action at a distance" as a "cause".

The cause of gravity is to this day considered by some a divine mystery not meant to be understood by humankind.

Consider Cotes' preface to Newton's Principia, where he intimates that the search for a physical cause for gravity, as opposed to a blind faith in (mythological and numerological) theological forces, is heresy. Cotes, seemingly together with Newton, asserts that induction resolves gravity to the will of God as the ultimate cause of the phenomenon, "Without all doubt this World, so diversified with that variety of forms and motions we find in it, could arise from nothing but the perfectly free will of God directing and presiding over all. [***] All sound and true philosophy is founded on the appearance of things; which if they draw us never so much against our wills, to such principles as most clearly manifest to us the most excellent counsel and supreme dominion of the All-wise and Almighty Being; those principles are not therefore to be laid aside, because some men may perhaps dislike them. They may call them, if they please, miracles or occult qualities; but names maliciously given ought not to be a disadvantage to the things themselves; unless they will say at last, that all philosophy ought to be founded in atheism. [***] He must be blind who from the most wise and excellent contrivances of things cannot see the infinite Wisdom and Goodness of their Almighty Creator, and he must be mad and senseless who refuses to acknowledge them.[9] Newton's distinguished work will be the safest protection against the attacks of atheists, and nowhere more surely than from this quiver can one draw forth missiles against a band of godless men."[10] Voltaire, also, threatened those who would attempt a Cartesian exposition on gravity, "The cause of this cause is among the Arcana of the Almighty. 'Procedes huc, et non amplius.'

(Thus far shalt thou go, and no farther.)"[11]

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Preston's fundamental conception is that all things transform as modes of motion through the impact of particles. These hypothetical particles bear the measurable properties of inertia, momentum and energy, and "fill" an otherwise void cosmic "empty space". There is a tacit monadism lurking in Preston's ideas, which he leaves largely unexplored. He argues through induction that the gaseous nature of his aether filling "space" is self-evident and need not be explained in terms of frames of reference, or contained volumes, other than as ontological absolutes. It is this absolutism, which ultimately leads him to predict that E = mc2, as an absolute store of energy contained in material bodies, which can be put to work.

For Preston, as for Huyghens and Leibnitz, the identity between mass and energy is the mode of motion. He argues that "action at a distance" is an impossibility, which requires the "absurd postulate of an infinite velocity[.]" He further argues that the concept of "potential energy" is devoid of meaning, because it asserts energy without motion, and confuses terms by equating, in name only, one state with a completely different state. A living person can potentially die, and become a dead person, but such a fact does not render a living person, dead. The state of a mass in a field of force is not the same as the state of a mass in motion, in terms of the ability to do work. Should a field of force composed of a shower of aether particles impart motion to a body, then it is this conserved motion which is cause, not spiritual "potential" which is cause.

Preston substitutes the action of an intervening medium for the two myths of "action at a distance" and "potential energy", which he finds feed off of one another, the fall of one necessarily toppling the other. He attempts to logically prove that the conservation of energy is only satisfied by supposing that the aether is a gas of particles in linear motion, which expand to fill any contained volume. The "forces" of Nature result from contact with these moving particles of aether. The velocity of these particles cannot be infinite, for if it were, then the aether particle which causes the phenomena of gravity and magnetism would have to concurrently occupy the beginning, middle and end of its journey, an impossibility.

Preston induces the elasticity and speed of aether particles, which of logical and experimental necessity (by analogy to an aeriform medium) must be in motion, from the speed of light. He does not delve into the metaphysics of why his proposed aether particles move at light speed, but instead infers this speed as a logical necessity, his necessary singular exposition of the known phenomena, his ultimate generalization arrived at through induction from known experimental results.

We see here many of the elements of the theory of relativity, stated in scientific terms, as opposed to the metaphysics, which later replaced the scientific hypotheses of this aether theory. "Action at a distance" must occupy time, due to the fact it is through the action of an intervening medium that the effects known as "action at a distance" arise. This speed is the normal speed of aether particles, known through induction to approximate the speed of light gravity propagates at the speed of light, a speed which nothing can exceed, for speed depends upon the size of a particle and an aether particle is perhaps the smallest fathomable subdivision of matter, and the fastest motion. Preston induces these Le Sagian ideas from the properties of light propagation. Le Sage simply wrote, "we assume for the [gravitational] corpuscles the velocity of light[.]"

From these basic inductions to general principles, Preston begins to synthesize these generalizations into fantastic and useful conclusions, "The above deduction, as to the high speed of the ether particles in their normal state, throws at once a light upon the existence of a vast store of energy in space of a very intense character, competent to produce the most forcible observed molecular motions, such as the phenomena of chemical action, combustion, the explosion of gunpowder, and other remarkable cases of the development of motion or work, all such effects finding their explanation in an interchange of motion between the ether and the molecules of matter under special conditions[.] "

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The bombardment of aether particles flying about in space, each with great energy due to their high velocity, produces an enormous pressure in space. Taking note of the fact that the tensile strength of steel wire is enormous and again appealing to reason, Preston holds that matter cannot cohere with the immense force it does if it is simply composed of isolated masses suspended in empty space. There must be a "material agent" which causes this effect, which effect Preston attributes to a pressure differential, as a logical necessity, "As to the precise physical process by which a reduction of the pressure of the intervening medium can take place in the presence of vibrating matter, we shall reserve the consideration of this point for the present; but it may be noted that the inference is none the less essential, that a reduction of the ether pressure does take place in the presence of the opposed vibrating molecules of the wire, since there remains no other conceivable means of explaining in a realizable manner why these portions of matter (molecules), already completely disconnected from each other in the normal state of the wire, should require this enormous force to shift their positions in the act of breaking the wire, unless in this act there were something further to be accomplished than merely to change the positions of molecules in space. [A change in position of the wire itself, without breaking it, requires no such powerful force.]"

Preston goes on to attribute the pressure differential to a rarefaction of the aether between vibrating bodies caused by "stationary waves" between them, "We have observed that a vibratory movement of matter, under such conditions that the waves are reflected and thereby stationary vibrations are formed in the medium, is well qualified to disturb the equilibrium of pressure of the medium," and makes clear that he does not see cohesion as the ultimate pressure differential between normal volume elements of aether and of vacuum; and he gives the example of chemical bonds as a state of pressure differential far exceeding the force of cohesion. His inferences again and again produce an increase in force commensurate with a reduction in scale. The subdivision results in the attenuation of matter into aether particles, as a limit. He sets a figure of, "500 tons per square inch as a limiting value for the ether pressure".

Again, there is no metaphysical attempt to delve into the cause of the normal velocity of aether particles, but Preston does tacitly and ontologically assume a quite vaguely defined frame of reference for this velocity. This ontological belief, and Preston's attitudes toward mechanics, truth, and his epistemological agenda, would today be considered by many to be naĂŻve and circularly reasoned; but they nevertheless produced predictions which have been borne out by technological advances in the twentieth century; and one seriously doubts that these predictions would have arisen in relativity theory, other than as a thinly veiled repetition (without attribution) of the conclusions drawn by Preston, Olinto De Pretto [Editor's note: see for instance Umberto Bartocci, Albert Einstein e Olinto De Pretto: la vera storia della formula piĂš famosa del mondo, Ed. Andromeda, Bologna, 1999; information on line: http://www.dipmat.unipg.it/~bartocci/listast.htm, points 9 and C] and others, through relativity theory's more complicated ontological fictions, which have no inductive justification, and which reify purely abstract conceptualizations of dimension. In contrast to relativity theory, Preston's ideas are based on quantifiable measurements, on measurable relations, ultimately resolved into the most scientific expressions of our empirical sensual experience, the sense of resistance to touch, which is "pressure" and "matter", as a measurable thing; and the separation of distance through time, which velocity constitutes a measurable relation. Preston proposes a dynamic "material agency", the aether.

Preston derives the density of the aether. This is quite significant to his later derivations of the store of energy contained in the density of matter, and the powerful effects which he predicts will occur should matter be subdivided into aether particles, "In connection with this subject, it may be of great interest to contemplate the possibility of the following as a physical problem. If we suppose a given mass of matter and a given volume of

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space, the volume of the space being supposed vastly greater than that of the mass of matter. Then it becomes possible, by the subdivision of the this mass of matter (which may be readily conceived to carried out to any extent), to pervade the entire volume of the space with matter, or there is no limit to the degree of close proximity into which the particles of matter pervading this space may be brought by continuous subdivision, the approach of the particles going on continuously without limit as the subdivision progresses. Thus, with a given mass of matter there is no limit to the extent of space that may be pervaded by matter by continued subdivision, or there may be no appreciable portion of the vast volume of space but what contains myriads of particles of matter. The normal state of this finely subdivided matter may be conceived to be a state of motion or a state of rest; if a state of motion, then we may observe the physical possibility of the existence of a store of energy of an extreme intensity, and which, from the minuteness and small length of path of the moving particles, must be concealed; this motion being also necessarily attended by the production of an intense and at the same time evenly balanced pressure, the smoothness and uniformity of the pressure, and the consequent concealment of its existence from the senses, being more and more complete as the subdivision progresses."

Preston concludes that the aether is made up of subdivided particles of matter, which conclusion is happily in agreement with the velocity and properties of light propagation. He infers a posteriori a relation between the subdivision of matter and an increase in the speed of particles, which ultimately results through the subdivision of mass in aether particles moving at or slightly above light speed. In a statement of the working principle of the atomic bomb, Preston avows, "If now we imagine, merely for illustration, each of these air molecules to be subdivided into a million parts, and that the speed of each component part has been increased a thousand times. The presence of the ether within the receiver may be left out of account for the present. Then by this imaginary process of subdivision, the mean distance of these parts of matter (which we shall term 'particles') would be so reduced as to bring these particles into closer proximity than the molecules of air outside the receiver (the mean distance of the particles of the subdivided matter being inversely as the cube root of the their number). The pressure against the interior of the receiver, which is as the square of the speed of the particles, would now be increased a million-fold; and yet this result is attained without any increase in the absolute value of the energy of each particle, for the energy has, by the reduction of mass, remained precisely the same for each particle as before, although the total energy has become vastly greater, this energy being now subdivided among a large number of particles, and the pressure maintained by a greatly increased number of moving particles.

We might imagine this process of subdivision, or this reduction of mass combined with increase of speed, to go on progressively, and thus the total energy would be continually increasing, and the mean distance and mean length of path of these small moving masses or particles would be continually diminishing, and therefore the concealment of this motion from the senses would be more and more complete. The pressure would continually rise in intensity, and at the same time become more even and perfectly balanced as the number of particles increased.

We might thus imagine this process to go on progressively, until at length the dimensions, mean distance, and speed of the ether particles themselves had been reached; or its possible thus step by step to arrive at a just conception of the wonderful intensity of the store of energy that is rendered physically practicable, and the high static value of the pressure that may be reached, under the simple mechanical conditions of an extensive subdivision of matter combined with a high speed. " The "speed of the ether particles" is that of a wave of light, and the "absolute value of the energy of each particle" when reduced to aether is mc2, which is described in Preston's prose in section 165 of his book, as quoted here above in the introduction. S. Tolver Preston provided a qualitative and quantitative theory, which set in motion the search for atomic energy and weaponry, a search which was ultimately successful. His contributions to science deserve far greater mention. Preston was indeed a man of science, who did not flinch when opposing the religious zealotry he confronted. We would do well to follow his example and

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oppose "theories of a vague nature" which propose "phantom agencies" like "space-time" and replace them with "physical causes capable of rational appreciation."

Notes [1] S. T. Preston, "Evolution and Female Education", Nature, (23 September 1880), pp. 485-486; Revised, Original essays. I. On the social relations of the sexes. II. Science and sectarian religion. III. On the scientific basis of personal responsibility, with a reprint from an essay on "Evolution and female education," revised from Nature, September 23, 1880, Williams and Norgate, London, Edinburgh, (1884).

[2] S. T. Preston paraphrased in F. Darwin & A.C. Seward, Editors, More letters of Charles Darwin, Volume 2, Chapter 8, John Murray, London, (1903), p. 52, Letter 421.

[3] S. T. Preston, "On a Point Relating to Brain Dynamics", Nature, (13 May 1880), pp. 29-30; Responses by G. Romanes, Nature, Volume 22, p. 75, and W. C. Ley, Nature, Volume 22, (10 June 1880), p. 121; Reply by Preston, Nature, (10 June 1880), p. 121.

[4] S. T. Preston, Physics of the Ether, E. & F. N. Spon, London, (1875).

[5] G. L. Le Sage, read by P. Prevost to the Berlin Academy in 1782, "Lucrèce Neutonien", Nouveaux Mémoires de l'Académie royale des Sciences et Belles-Lettres de Berlin,Year 1782, (Berlin, 1784), pp.

404-427; reprinted in Notice de la Vie et des Écrits de George-Louis Le Sage, Chez J. J. Paschoud, Genève, (1805), pp. 561-604; English translation by C. G. Abbot with an introduction by S. P. Langley appears in: "The Le Sage Theory of Gravitation", Annual Report of the Board of Regents of the Smithsonian Institution Showing the Operations, Expenditures, and Condition of the Institution for the Year Ending June 30, 1898,(U.S.) Government Printing Office, Washington, (1899), pp. 139-160.

W. Thomson, S. Tolver Preston, H. A. Lorentz, and J. J. Thomson, among many others, pursued Le Sage's shadow theory of ultramundane particles. Maxwell and Poincaré opposed it, on the basis that it would result in excessive heat accumulation.

[6] I. Newton, Four Letters from Sir Isaac Newton to Doctor Bentley containing Some Arguments in Proof of a Deity, London, (1756) [Editor's note: see also Episteme N. 5, March 2002]. Edward B. Davis has presented significant scholarship on Newton's religious views: "Newton's Rejection of the 'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy", Fides et Historia, Volume 22, Number 2, (Summer 1990), pp. 6-20; reprinted Science and Christian Belief, Volume 3, Number 1, (1991), pp. 103-117; reprinted with additions Facets of Faith and Science, Volume 3, University Press of America, Lanham, Maryland, (1996), pp. 75-96.

[7] R. Bentley, A Confutation of Atheism from the Origin and Frame of the World, Part 3, Phoenix, London, (1693), pp. 4, 20-21.

[8] C. Maclaurin, "Of the Supreme Author and Governor of the universe, the True and Living God", An Account of Sir Isaac Newton's Philosophical Discoveries, Book 4, Chapter 9, Patrick Murdoch, London, (1748), pp. 388-390.

[9] R. Cotes, in I. Newton, The Mathematical Principles of Natural Philosophy, London, (1729), from "THE PREFACE OF Mr. Roger Cotes", not paginated.

[10] R. Cotes, Cote's preface to the second edition of Newton's Principia. Sir Isaac Newton's Mathematical Principles of Natural Philosophy and his System of the World, University of California Press, Berkeley, Los Angeles, London, (1962), p. XXXIII. [11] F. M. A. Voltaire, "On Attraction", Letters on England, Letter 15.

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[We believe it worthwhile to add an ending section about the important question: vis viva versus kinetic energy] Clash of Leibnitz and Newton Space as Meta-Aether There was in Preston's day an emerging rejection of the Newtonian ideas of mystical "force" as a cause of phenomena among "empty space". Fechner stated, "All that is given is what can be seen and felt, movement and the laws of movement. How then can we speak of force here? For physics, force is nothing but an auxiliary expression for presenting the laws of equilibrium and of motion; and every clear interpretation of physical force brings us back to this. We speak of laws of force; but when we look at the matter more closely, we find that they are merely laws of equilibrium and movement which hold for matter in the presence of matter. To say that the sun and the earth exercise an attraction upon one another, simply means that the sun and earth behave in relation to one another in accordance with definite laws. To the physicist, force is but a law, and in no other way does he know how to describe it. . . All that the physicist deduces from his forces is merely an inference from laws, through the instrumentality of the auxiliary word 'force'." [12]

T. H. Pasley, in 1835, averred, "Of the nature of matter the knowledge is limited to the principle of inertia. Matter being inert it can do nothing and bodies formed of inert matter are incapable of acting in any manner: the want of power cannot originate power: hence cause must consist in means independent of action by matter.

Matter consisting in unorganized molecules, it appeared nothing out of reason to conclude that the whole and all things they go to form are inert. For if a body be broken its parts are inactive, and the body itself to be in an acting state requires to be impelled by means such as itself does not possess.

The inertia of matter therefore is evident. Matter being inert it cannot either attract or repel. But then, how is universal gravitation, acknowledged by all the most learned of the world and demonstrated mathematically, to be set aside, and wherein is cause of it and attraction be rejected. The difficulty is as great as the Authorities who make no difficulty of supporting these principles and causes are exalted in fame. The greatest difficulty however lies in reconciling them with the Inert nature of Matter. Matter has no acting properties as it is essentially inert. Acting implies being in motion; motion requires physical impulse foreign to that which is made to act, and from the atoms of matter being unalterable, by nothing but physical impulse can they be affected, nor can the effect be other than motion. Wherefore, gravitating, and repelling are not properties of either matter or bodies. [***] In moral philosophy inertia means inferior ability and ability sluggishly exerted; in Physics it signifies no ability or power whatever. Making inertia a 'passive power' amounts to no power; power implies acting, passive power not acting or that can act, but power is never passive. Inertia being an 'inert force' is the same as force without force: 'vis inertiae' is the force of inactivity, the power of inability.

All bodies are convertible into powers, but are such only while being made to act. To say a body 'resists' by means of its inertia, is making nothing a physical force. Who can conceive force at rest.

Inertia causing 'an endeavour and perserverance in a body to continue in motion or at rest' is a contradiction in terms [***] Inertia is no cause, it is nothing active or passive. The resistance of a ponderable body at rest is caused by that which makes it ponderable. Inertia being nothing is productive of nothing; it may be said to be the zero of cause. " [13] Pasley identified many of the fatal flaws in the Epicurean mythologies, for example, "[W]itness the Newtonian Theory of Gravitation, Attraction and Repulsion, which, it is said 'Newton has proved to the whole world direct and regulate the System.' But as gravitating, attracting and repelling cannot belong to inert bodies, formed as all are of inert matter, the adopted theory, in these respects, is utterly fallacious and untrue. Gravitating by the Planets of their own accord is as

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movement in the lifeless; attraction as the will of the dead; and repulsion as antipathy possessed by a stone. The whole of these and all such monstrocities have origin solely in the theory of Perception being rejected where most applicable, and in coupling Activity with Inertia. " [14]

Preston wanted to replace these myths with a physical agent, which obeyed the principle of the conservation of energy. Perhaps the most famous name associated with the principle of the conservation of energy, the foundation of Preston's natural philosophy, is Julius Robert Mayer. He sought a meaningful definition of the concept of "force" and this is likely why Preston, in working out the energy store in bodies through Joule's and Clausius' methods, deduced Leibnitz' vis viva, as opposed to kinetic energy,[16] as the absolute store of energy contained in mass. In 1807, Thomas Young defined "energy" in English as, "The term energy may be applied, with great propriety, to the product of the mass or weight of a body, into the square of the number expressing its velocity. "[17] Mayer stated, in 1852, in an effort to provide a "generic conception of 'force,'" "On the other hand, the product of the pressure into the space through which it acts, or, again, the product - or half-product - of the mass into the square of the velocity, is named 'force.' In order that motion may actually occur, it is in fact necessary that the mass, whatever it may be, should under the influence of a pressure, and, in the direction of that pressure, traverse a certain space, 'the effective space' (Wirkungsraum): and in this case a magnitude which is proportional to the 'pushing force' and to the effective space, likewise receives the name 'force;' but to distinguish it from the mere pushing force, by which alone motion is never actually brought about, it is also called the 'vis viva of motion,' or 'moving force.' With the generic conception of 'force,' the higher mechanics, as an essentially analytic science, is not concerned. In order to arrive at it, we must, according to the general rule, collect together the characters possessed in common by the several species. As is well known, the definition so obtained runs thus - 'Force is every thing which brings about or tends to bring about, alters or tends to alter motion'. This definition, however, it is easy to see, is tautological; for the last fourteen words of it might be omitted, and the sense would be still the same. [***] If a mass M, originally at rest, while traversing the effective space s, under the influence and in the direction of the pressure p, acquires the velocity c, we have ps = Mc2. Since, however, every production of motion implies the existence of a pressure (or of a pull) and an effective space, and also the exhaustion of one at least of these factors, the effective space, it follows that motion can never come into existence except at the cost of this product, ps = Mc2. And this it is which for shortness I call 'force.' "[18] Preston focused on the notion of aethereal pressure (as opposed to mystical "forces" of gravitation and magnetism exerted upon a mass by a mass via "action at a distance") again and again in opting for the formulation of the absolute store of energy as E = mc2 , as opposed to E = ½ mv2. This is perhaps due to the fact that most of the writings on the principle of the conservation of force from the 1840's focused on Galilean-Leibnitzian style experiments with falling masses. Leibnitz' arguments for a conserved vis viva against Descartes' momentum were initially a posteriori and depended upon experiments of gravitation on the Earth.

However, by 1875 it was an anomaly for Preston to not see the "transference of work" done by a body thrown upwards against the "resistance" of "gravity" as ½ mv2. Preston wrote, "26. In considering the high normal velocity of the ether particles, it is to be expected beforehand that this agent must exert an extremely forcible pressure upon the molecules of matter, even if every allowance be made for the extreme low density of the agent; for it is important to note that the pressure exerted is as the square of the speed of the particles of the agent, and therefore the pressure rises in a very rapid ratio as the speed increases; so that taking into account this fact, in conjunction with the high velocity of the particles, we must be prepared to find this pressure will have a very high value. In looking to physical phenomena for an indication of this pressure, and also with the object, if possible, of arriving at a limiting value for its intensity, or the value which this pressure

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must at least attain on the lowest computation, we will consider one observed fact. [***] 53. Secondly, it may be shown that an excess of energy is imparted to the surrounding medium by a vibrating mass or molecule, due to a second separate physical cause, which we shall now consider. We have observed that the speciality of a vibrating movement is to affect the normal velocity of the component particles of the medium in such a way that equal increments and decrements of velocity are experienced. But it is an important principle to observe, that when masses of matter experience equal increments and decrements of velocity so that the mean velocity remains unaltered, that, nevertheless, the energy being as the square of the velocity, the value for the energy does not remain unaltered. Thus, if we take the case of two equal masses having equal velocities, which we may express by V, the energy in each case being expressed by V 2, and the total energy therefore by 2V 2. If now we suppose one of the masses to receive an increment of velocity v, its velocity therefore becoming V + v, the other mass experiencing an equal decrement of velocity, its velocity becoming V - v; then although the mean value for velocity has remained unchanged, yet the value for energy has by no means remained unchanged, for the energy of each mass being as the square of its velocity, the total energy now becomes (V + v)2 + (V - v)2 = 2V2 + 2 v2. Now the value for the total energy before this change of velocity took place was only 2V2. The total energy has therefore, by merely changing the velocities by equal amounts (so as not to affect the mean velocity), received a notable increase represented by the amount 2v2. This is an important point, on account of the direct and practical bearing which it has on the phenomena of vibratory motion; the above indicating that the change of the velocities of the component particles of the medium by equal amounts, which it is the special function of a vibratory motion of matter to effect, is itself a direct cause whereby a certain excess or surplus of energy is communicated to the medium. [***] 98. Important Influence of Subdivision. - One of the most important practical consequences following from the extensive state of subdivision, which is the characteristic of the molecular condition of matter, is the vast extent of surface which is thereby brought under the action of the ether pressure. This is a fact of importance, by a due appreciation of which the great energy of the action of the ether upon molecules will appear no longer discordant or inconsistent, but the fact may be brought into harmony with ordinary mechanical principles, this vast extent of surface being the fitting mechanical condition for the production of static and dynamic effects of extreme intensity. [***] [114] III. High Normal Speed of Component Particles. - This physical quality is absolutely essential to constitute a powerful dynamic agent, for without this high speed dynamic effects of a high intensity cannot be produced. Second, this high normal speed of the particles is the sole condition on which the loss of motion sustained by the ether can be replenished with that degree of speed which is essential to render a continuous dynamic effect of a high intensity possible to the ether. Third, this high speed of the component particles is the sole quality by which the loss of motion sustained by the ether in producing a given dynamic effect can be subdivided or distributed over a large volume of the ether, whereby a notable local disturbance of the equilibrium of the ether is prevented. Fourth, this quality is essential for the rapid interchange of motion between masses and molecules of matter at a distance from each other, the rapidity of intercommunication or exchange of motion being strictly limited by the normal speed of the particles of the intervening agent.

Fifth, this high speed of the component particles is necessary to render possible the existence of a store of energy of a high value, without the encumbrance of a large quantity of matter in space. Sixth, the high normal velocity of the ether particles is the necessary mechanical condition to enable an intense pressure to be exerted by the ether upon the molecules of matter, without the movements of these molecules and masses being obstructed by the agent exerting the pressure. For, in the first place, by this high speed of the component particles an intense pressure is attainable (more especially as the pressure rises as the square of the speed) without the necessity for the agent being dense, by which the free passage of masses of matter through the agent would be obstructed. In the second place, the high speed of the component particles enables masses of matter to pass through the agent with the least disturbance of its equilibrium, or with a minimum of resistance from this cause, the agent becoming almost impalpable; the exertion of an intense pressure by the agent being itself the necessary condition to render the agent adapted to control forcibly the molecules of matter in stable equilibrium, as exhibited in the general phenomena of 'cohesion,' or the aggregation of the molecules of matter generally. The above may serve as a general summary of the special physical qualities of the ether; and it may be noted that if the attempt were made beforehand, as a mechanical problem or speculation, to devise or scheme out what special physical qualities an agent should possess in order to be mechanically fitted to produce the varied physical effects of the character observed, then the scheme of the ether would be found to constitute the only possible solution of which the mechanical problem

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admits; or the ether may be contemplated as a piece of mechanism specially adapted to its work. [***] 128. We shall now proceed to consider more closely the mode or general principle upon which physical processes effect themselves, and it will be our endeavour to show that these processes resemble one another in a second fundamental aspect, viz. that all these processes are cyclical, i. e. consist in a transference of motion from the ether through matter to the ether, or consist in a transference of motion from and to the same source; and therefore that all physical processes, however diverse and varied, are identical in this fundamental respect; or that every observed motion whatever came from the ether at one time, and will return to the ether at some subsequent time. This theorem may be shown to be a necessary consequence resulting from the fundamental principle of conservation. The normal state of the ether is a state of motion, or the component particles of the ether transfer their motions among themselves, and this motion is of necessity permanently maintained. The ether, therefore, constitutes a source of motion. A mass or molecule of matter, on the other hand, cannot possibly be in motion without continually giving up some of its motion to the surrounding ether, which motion is rapidly carried off to a distance in the form of waves; so that matter cannot possibly remain in motion, unless the motion be renewed by the ether as rapidly as it is being dissipated in the ether, which would constitute a cyclical process. Since, therefore, the motion of matter is being continually dissipated in the ether, the ether constitutes the receptacle of all the motions of matter. The ether therefore must, in accordance with the principle of conservation, be the source of all the motions of matter, for matter cannot evolve motion out of itself. Also, since matter cannot retain its motion, but must be always dependent on the ether for any supply of motion, matter therefore cannot in any case constitute a source of motion. The ether therefore constitutes both the source and the receptacle of all the motions of matter, or this would constitute the theorem that all physical processes are cyclical, or consist in a transference of motion from and to the same source, and accordingly that all physical processes are correlated in this fundamental respect. [***] 135. Amount of energy being dependent on the quantity of matter in motion and on the square of the velocity of motion, and since motion cannot come into existence spontaneously, or go out of existence spontaneously, but in accordance with the principle of conservation, the sum of energy must remain constant; it follows, therefore, that whenever there is a loss of motion by matter, there must be a simultaneous gain of motion by matter, or the loss and gain of motion must be simultaneous, for a loss of motion without a simultaneous gain of motion would involve for an interval of time an annihilation of energy. It follows, therefore, as a necessary consequence from this, that the energy expended in any physical process whatever can be solely dependent on and due to motion simultaneously imparted, i. e. imparted at the time of the expenditure of the energy; for unless motion be imparted at the time, energy cannot be expended at all, for to expend motion without imparting motion would be to annihilate energy; indeed, the motion imparted is itself the measure of that expended, and is the sole cause of its expenditure, i. e. motion can only be expended in the communication of motion, and in that fact lies apparent the principle of the Indestructibility of Motion. [***] 163. Absolute Quantity of Energy in the Unit Volume of Space. - We shall now consider more particularly the energy enclosed by the ether, with the endeavour to give some idea of the absolute value of the energy represented by the motion of the ether particles contained within a given portion of space, with the object, if possible, to fix upon a limiting value for this energy, or the lowest value consistent with what physical facts would require. The conditions required in order to determine the amount of energy enclosed in the unit volume of space are clearly, first, a knowledge of the quantity of matter in the form of ether contained in the unit volume of space (i. e. the density of the ether); and secondly, the normal velocity of the ether particles. Now, although we do not know the density of the ether independently, nevertheless since density is determined by pressure and velocity of component particles, if, therefore, by a known limiting value for the velocity of the ether particles, a limiting value for the ether pressure can also be fixed upon, then a limiting value for the ether density is thereby given. The limiting value for the velocity of the ether particles is given by the measured velocity of a wave of light. As regards the value for pressure, we take the estimate already fixed upon: that this amounts to 500 tons per square inch as the lowest limiting value. There are valid grounds for inferring that this value for pressure has been under-estimated; for we assumed the total ether pressure as a small multiple of the observed difference of pressure in the case of 'cohesion,' whereas, as before remarked, it is a known fact that the force required to separate chemically combined molecules must be many times greater, this indicating the high intensity of the controlling ether pressure, and showing that an estimate of this pressure from the case of 'cohesion' must be but an inadequate representation of the reality. The tremendous energy developed in explosives, which is the very energy of the ether itself, is a direct indication of the

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intensity of the ether pressure, which is the necessary accompaniment of this energy. That this value for pressure has been under-estimated, a bare consideration of the dependent value for density would almost show, for the ether density corresponding to this pressure (1/5264800 of the atmospheric density) represents a density so insignificant as to be less than that of the best gaseous vacua. "

Additional Notes [12] Fechner quoted in H. Vaihinger's, Philosophy of the 'As if', Barnes & Noble, Inc., New York, (1966), p. 215; translated by C. K. Ogden.

[13] T.H. Pasley, A Theory of Natural Philosophy, on Mechanical Principles, Divested of All Immaterial Chymical Properties, Showing for the First Time the Physical Cause of Continuous Motion, Whittaker & Co., London, (1836), Preface and pp. 145-146.

[14] Pasley, ibid. xcii.

[15] See for example the many works of Marc Seguin and M. F. de Boucheporn, Cf. The Correlation and Conservation of Forces, D. Appleton, New York, (1867), pp. 4, 76-82; W. B. Taylor, "Kinetic Theories of Gravitation", Annual Report of the Board of Regents of the Smithsonian Institution, U. S. Government Printing Office, Washington, (1877), pp. 205-282. Another good example is A. Anderssohn, Die Mechanik der Gravitation, Breslau, (1874); and Zur Loesung des Problems ueber Sitz und Wesen der Anziehung, Breslau, (1874); and Physikalische Prinzipien der Naturlehre, G. Schwetschke, Halle, (1894). See also: G. Hoffmann, Die Anderssohn'sche Drucktheorie und ihre Bedeutung für die einheitliche Erklärung der physischen Erscheinung, G. Schwetschke, Halle, (1892).

For some, the aether become their embodiment of the Tertullian-Newtonian pantheistic God and Holy Wind. See, for instance, Philipp Spiller, Die Urkraft des Weltalls nach ihrem Wesen und Wirken auf allen Naturgebieten, Verlag der Stuhr'schen Buchhandlung (S. Gerstmann), Berlin, (1876).

[16] G. G. Coriolis, Du calcul de l'effet des machines, ou Considérations sur l'emploi des moteurs, Paris, (1829). Coriolis used the term "force vive". First use of the term "kinetic energy" in English is perhaps by Thomson and Tait, Good Words, (October, 1862).

[17] T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, Volume 1,Taylor and Walton, London, (1845), p. 59.

[18] J. R. Mayer, translated by J. C. Foster, "Remarks on the Mechanical Equivalent of Heat", The Correlation and Conservation of Forces, D. Appleton, New York, (1867), pp. 331, 336.

----Christopher Jon Bjerknes is an American historian of science, who has authored six books and numerous articles on the theory of relativity and on Albert Einstein. His most recent book, Albert Einstein - The Incorrigible Plagiarist, is reviewed in this same volume of Episteme. cbjerknes@attbi.com

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Einstein's Irrational Ontology of Redundancy The Special Theory of Relativity and Its Many Fallacies of Petitio Principii (Christopher Jon Bjerknes) Abstract. Albert Einstein's arguments were almost always fallacies of Petitio Principii. He argued well-known experimental results as if a priori first principles. Einstein would then induce, as if deducing, the well-known hypotheses of others, and deduce from these plagiarized hypotheses the same experimental results as conclusions, which he had first stated as premises. This was Einstein's modus operandi for plagiarism. In the special theory of relativity, Einstein argued light speed invariance, a well-known (supposed) experimental result at the time, as if an a priori first principle, which an empirical measurement cannot be, to then induce through analysis, as if deducing in synthesis, the "Lorentz Transformation" hypotheses. Einstein then used the "Lorentz Transformation", the true set of hypotheses of the special theory of relativity, to deduce light speed invariance as a conclusion, a conclusion which Einstein had already presumed as a premise. Einstein employed the same fallacious method in the general theory of relativity. Einstein irrationally asserted the wellknown experimental gravitational-inertial mass equivalence of Bessel and Eรถtvรถs as if an "a priori" postulate, which an experimental result cannot be, only to arrive at it as an ultimate conclusion, a conclusion redundant to the premise. The quasi-postivistic analyses Einstein presented by turning the synthetic scientific theories of his predecessors on their heads have been applauded, ridiculed and often misrepresented as synthetic, which they are not.

Method In 1905, Mileva Einstein-Marity and Albert Einstein [1] coauthored a paper on the "electrodynamics of moving bodies". Fallacies of begging the question emerge even in the very introduction to the work. The Einsteins acknowledge in their introduction, that light speed invariance and the symmetry of electrodynamic phenomena were well-established phenomena. Well-known specific phenomena are not, by definition, "a priori" general concepts. However, the Einsteins asked us to abandon reason and assert specific experimental results and empirical observations, as if a priori general principles. In other words, the Einsteins engaged in an analysis of the problems of invariant light speed, and of the symmetry of electrodynamic phenomena in alleged violation of Maxwell's theory, which problems faced physicists at the end of the nineteenth century; and the Einsteins irrationally pretended that these two problems were solutions of themselves.

1 Henry August Rowland stated the two main problems facing the physicists of his day, on October 28th, 1899, and I have italicized that which the Einsteins would later call "two assumptions", or "postulates": "And yet, however wonderful [the ether] may be, its laws are far more simple than those of matter. Every wave in it, whatever its length or intensity, proceeds onwards in it according to well known laws, all with the same speed, unaltered in direction, from its source in electrified matter to the confines of the Universe, unimpaired in energy unless it is disturbed by the presence of matter.

However the waves may cross each other, each proceeds by itself without interference with the others. [***] To detect something dependent on the relative motion of the ether and matter has been and is the great desire of physicists. But we always find that, with one possible exception, there is always some compensating feature which renders our efforts useless. This one experiment is the aberration of light, but even here Stokes has shown that it may be explained in either of two ways: first, that the earth moves through the ether of space without disturbing it, and second, if it carries the ether with it by a kind of motion called irrotational. Even here, however, the amount of action probably depends

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upon relative motion of the luminous source to the recipient telescope. So the principle of Doppler depends also on this relative motion and is independent of the ether. The result of the experiments of Foucault on the passage of light through moving water can no longer be interpreted as due to the partial movement of the ether with the moving water, an inference due to imperfect theory alone. The experiment of Lodge, who attempted to set the ether in motion by a rapidly rotating disc, showed no such result. The experiment of Michelson to detect the ethereal wind, although carried to the extreme of accuracy, also failed to detect any relative motion of the matter and the ether [Emphasis Added]."[2]

The Einsteins turned reason on its head and called these two a posteriori problems, a priori "postulates". The Einsteins phrased their two "postulates", as follows: 1"1 (a). Examples of a similar kind, as well as the failed attempts to find a motion of the earth relative to the 'light medium', lead to the supposition, that the concept of absolute rest corresponds to no characteristic properties of the phenomena not just in mechanics, but also in electrodynamics, on the contrary, for all systems of coordinates, for which the equations of mechanics are valid, the same electrodynamic and optical laws are also valid, as has already been proven for the magnitudes of the first order.

1 (b). The laws according to which the states of physical systems change do not depend upon to which of two systems of coordinates, in uniform translatory motion relative to each other, this change of state is referred.

12 (a). [L]ight in empty space always propagates with a determinate velocity c irrespective of the state of motion of the emitting body.

2 (b). Every ray of light moves in the 'resting' system of coordinates with the determinate velocity c, irrespective of whether this ray of light is emitted from a resting or moving body. Such that velocity = (path of light) / (interval of time) , where 'interval of time' is to be construed in the sense of the definition of § 1."

Note that the first "postulate", the principle of relativity, refers only to "moving systems" and the second "postulate", the light "postulate", refers only to a proposed "resting system". Note further, that the light "postulate" refers only to a proposed source independence of light speed, but not to an observer independence, because this "postulate" assumes a prior privileged frame and medium in the 1905 paper, the "resting system". The paper later presumes that c' = c +/- v, relative to the "resting system".

1Many assert that the Einsteins employed only these two "a priori postulates" in their theorization, as opposed to FitzGerald, Larmor, Lorentz, and PoincarĂŠ, who required the additional hypotheses of length contraction and time dilatation to arrive at the same formulation - long before the Einsteins. Ad hoc hypotheses were frowned upon at the time, due to Newton's admonitions against them, such that the removal of hypotheses was seen as an improvement. The two postulate myth is substantially and demonstrably false. The two postulates are not postulates, but rather are the deduced conclusions of the theory summations of the supposedly observed phenomena of the day.

After asserting the two "postulates", the Einsteins raised a straw man argument based a non sequitur. They asserted that the two "postulates" appeared irreconcilable with each other.

If light speed is constant in the "resting system", then how can it also be isotropic in a "moving system"? This is a (manufactured) dilemma, because, in some inexplicable way, the Einsteins argue that the first postulate, the principle of relativity, compels that light speed from a given light signal be isotropic for all systems in uniform motion with each other.

However, this is clearly a non sequitur, because the principle of relativity no more compels light speed isotropy for all "moving systems", then the principle of relativity requires that a body resting relative to one "moving system" k also rest relative to another "moving system" K, which is in motion relative to the first. Einstein also raised the opposing problem. How can light speed be isotropic in the "resting system" and also be isotropic in a "moving system"? Of course, these questions presume the conclusion before it has been proven, the conclusion being that light speed from any given signal is isotropic in the "resting system" and all

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"moving systems", which are in uniform translatory motion with respect to the "resting system". To knock down these straw men, the Einsteins turned the "two postulates" into one "postulate", the conclusion which is sought. 1The Einsteins asserted that it is the combination of the two postulates, not either postulate by itself, which "deduces" c' = c between the moving system and the resting system, by simply asserting that c' = c, before it has in any way been proven: "It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one expresses by means of these equations, that light (as the principle of the constancy of the velocity of light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as measured in the moving system."

After irrationally presuming this conclusion, the Einsteins proceeded to pretend that they had not presumed it: "Now, we have to prove that every ray of light propagates with the velocity c as measured in the moving system, in case this is, as we have taken for granted, the case in the resting system, because we still have not offered up the proof that the principle of the constancy of the velocity of light is reconcilable with the principle of relativity."

However, the combination of the two postulates induces c' = c +/- v, not c' = c. One must take the supposed empirical phenomenon of c' = c as a point of departure for an inductive analysis, not a deductive synthesis, to induce a fundamental geometry, which fundamental geometry then deduces the identity c' = c and the covariance of the laws of physics, as a synthetic theory. The Einsteins averred, before any proof was offered: "It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one expresses by means of these equations, that light (as the principle of the constancy of the velocity of light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as measured in the moving system. For a ray of light emitted in the direction of increasing ξ at the time τ = 0, the following equations are valid: ξ = cτ. . ."

Note the non sequitur, which begs the question: That allegedly if the speed of light is c in the "resting system" the principle of relativity compels that it also be c in the "moving system"; which, without the prior hypotheses of the Lorentz Transformation, clearly is not a rational conclusion, for if I rest in the resting system, the principle of relativity does not compel that I also rest in the moving system. Rather, the Einsteins simply confused their conclusion as an additional premise, which renders the two "postulates" redundant, or renders one postulate deducible from the other, and in no sense a postulate.

As Einstein, himself, avowed, "the real basis of the special relativity theory" is not the conclusion of light speed invariance and the covariance of the laws of physics in Lange's "inertial systems". As Albert Einstein later admitted, the real set of a priori postulates is the "Lorentz Transformation", replete with its dreaded ad hoc hypotheses. The Lorentz Transformation deduces all velocity comparisons, not just invariant light speed, which is a specific speed, and a derived unit, not a general geometry.

Later formulations of the special theory of relativity change the 1905 light postulate, from the Einsteins constant speed of light exclusively in the "resting system", into the invariance of light speed in all of Lange's inertial systems. But this renders the principle of relativity redundant to, or deducible from, the light "postulate", and, therefore, not a "postulate", per se, because the light "postulate" then asserts the identity of Lange's inertial systems as light speed invariance, and the principle of relativity is already proven in the light "postulate". On the other hand, if we pretend that the principle of relativity is the covariance

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of the laws of physics embracing Maxwell's theory, given the "Lorentz Transformation" as a premise, then the second "postulate" is already incorporated in the first "postulate".

If we are to assume that the Einsteins, in their 1905 paper, deduced, not induced, the Lorentz Transformation from invariant light speed; we would further have to fallaciously assume that empirically observed Lorentz Transformation metrics provoked the Einsteins to induce an unobserved invariant light speed and the unobserved symmetry of phenomena, as self-evident general truths induced a posteriori from empirically observed and reciprocally measured: length contraction, time dilatation and relative simultaneity. Such is obviously not what happened, and such is not what is argued in the 1905 paper.

On the contrary, supposedly observed invariant light speed and the supposedly observed symmetry of electrodynamic phenomena led Voigt [3], FitzGerald [4] and Larmor [5] to scientifically induce, a posteriori, the general geometry of the (misnamed) "Lorentz Transformation", which general set of hypotheses supposedly deduced all "known" phenomena in non-existent hypothetical "inertial systems". The Einsteins pseudoMetaphysics, their ontology of redundancy, simply disguised the more scientific, though likewise irrational, work of their predecessors, in a way which attempted to make it appear that the Einsteins had deduced that which must be induced, and had avoided hypotheses, which they had not avoided, but rather induced, through fallacy of Petitio Principii.

Most of the post-1905 statements of the special theory of relativity substitute a completely different proposition for the "two postulates". Einstein, himself, substituted one light theorem, in 1907, for the "two postulates" of 1905: "the 'principle of the constancy of the velocity of light' [***] for a system of coordinates in a definite state of motion [as opposed to solely in the 'resting system' as in 1905.]" [6]

which presumes the Lorentz Transformation from which this "postulate" is deduced, and which presumes the tacit hypotheses of an isotropic and homogenous absolute space [7] and "a definite state of motion" relative to that absolute space. This new light "postulate" represents, therefore, not a postulate, but a deduction, a theorem, and a phenomenon. Einstein admitted, in 1907, that this "postulate" could not be a priori, but must, instead, be a posteriori: 1"That the supposition made here, which we want to call the 'principle of the constancy of the velocity of light', is actually met in Nature, is by no means self-evident, nevertheless, it is - at least for a system of coordinates in a definite state of motion - rendered probable through its verification, which Lorentz' theory based upon an absolutely resting aether has ascertained through experiment." [8]

1The so-called "postulates" are simply a restatement of supposed experimental facts, and are not postulates, but empirical facts generalized as "laws" and "theorems". As Robert Daniel Carmichael stated: "The experiments which we have described (and others related to them) are fundamental in the theory of relativity. The postulates in the next chapter are based on them. These postulates are in the nature of generalizations of the facts established by experiment. [***] In the next chapter we shall begin the systematic development of the theory of relativity. It will be seen that its fundamental postulates, or laws, are based on the experiments of which we have given a brief account and on others related to them. [***] The postulates, as we shall see, are simply generalizations of experimental facts; and, unless an experiment can be devised to show that these generalizations are not legitimate, it is natural and in accordance with the usual procedure in science to accept them as 'laws of nature.'" [9]

H. A. Lorentz questioned Albert Einstein's "method" of pretending that induction is deduction:

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1"Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. [***] I have not availed myself of his substitutions, only because the formulae are rather complicated and look somewhat artificial". [10]

1We soon discover in the introduction of the Einsteins' 1905 paper a clear statement of the fallacious objective of their entire paper: "These two assumptions are sufficient in order to arrive at a simple and consistent electrodynamics of moving bodies, taking as a basis Maxwell's theory for resting bodies."

Is Maxwell's theory for resting bodies a third postulate? One of the "two assumptions", the first "postulate", is that the laws electrodynamics of moving bodies be consistent among systems of reference in uniform translatory motion with respect to the "resting system". Of course, the reasoning presented is circular, first assuming via the first "postulate" that the laws of electrodynamics are consistent, then arguing that this mandated consistency, as a premise, causes consistency as an effect. It is the first of many circular arguments found in the Einsteins' 1905 paper. How do we determine that which constitutes an "inertial system", other than circularly, as in: An inertial system is one in which there is no net force acting on the system; there is no net force acting on a system, when it is inertial?

Maxwell's theory for resting bodies is Maxwell's theory of the medium, a privileged frame, the aether. However, the Einsteins alleged that the aether was "superfluous" to their theory. The Einsteins irrationally wrote with the same pen that the aether was superfluous, while asserting it as a basis for their theory.

In the introduction to the 1905 paper, we are being primed to venture forth from Maxwell's theorems for bodies resting in the aether, so that we can return to them, Petitio Principii, as the covariant laws of moving bodies, while being asked to pretend that the aether is superfluous, so that we aren't too shocked when simultaneity is claimed to be relative, again, Petitio Principii, via an impossible light synchronization assumption of light speed invariance, or c' = c, which premise is also the conclusion of the theory.

For example, Albert 1Einstein stated in 1949: "[T]he following postulate is [***] sufficient for a solution [***] L-principle holds for all inertial systems (application of the special principle of relativity to the L-principle) [***] With the help of the Lorentz transformations the special principle of relativity can be expressed thus: The laws of nature are invariant with respect to Lorentz-transformations". [11]

Compare Albert Einstein's later statement to Willem de Sitter's statement of 1911: "The principle of relativity can be enunciated as the postulate that the transformations, with respect to which the laws of nature shall be invariant, are 'Lorentz-transformations.'*" [12]

Einstein, ever the plagiarist, stated in 1952: "The whole content of the special theory of relativity is included in the postulate: The laws of Nature are invariant with respect to the Lorentz transformations."[13]

Modus Operandi for Plagiarism 1 Einstein disclosed his modus operandi for manipulating credit for the synthetic theories of others, when he stated in 1936:

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"There is no inductive method which could lead to the fundamental concepts of physics.

Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century. [***] Logical thinking is necessarily deductive; it is based upon hypothetical concepts and axioms. How can we expect to choose the latter so that we might hope for a confirmation of the consequences derived from them? The most satisfactory situation is evidently to be found in cases where the new fundamental hypotheses are suggested by the world of experience itself."[14]

This is a clear statement by Einstein that he would have science deduce a thing from itself, taking the world of experience as a hypothesis, only to deduce the world of experience as an effect, of itself. Of course, Mileva and Albert were forced to present the real hypotheses, which they stuck in the middle of their arguments by way of induction, or an attempt at induction, which analyses they attempted to disguise as deductions from a priori principles, but which "a priori principles" were well-known summations of phenomena.

Einstein wanted people to believe that it is irrelevant that his predecessors induced the theories he later copied, because Einstein just invented them, sua sponte, irrationally, after he had read them, and therefore deserved credit for them: "Invention is not the product of logical thought, even though the final product is tied to a logical structure."[15]

Conclusion Einstein stated, together with Infeld: "Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world."[16]

Certainly, the two "postulates" of the theory of relativity were not, "free creations of the human mind," but were, instead, summations of the empirical observations of the wellknown phenomena of the day framed with the familiar concepts of the day. What Infeld and Einstein meant by "free" is difficult to fathom, and it is simply repetitive to say that creations of the mind are creations of the mind. Einstein's vague notions are perhaps the result of his plagiarizing Newton, Mach, Pearson, and others, on the principle of logical economy and watering down what they had written with Einstein's simplistic and na誰ve talk. If "free" is to mean unrestricted in any sense, no human mind is "free". We are limited in our concepts, experience, and scope, and we are socialized, indoctrinated and inculcated into certain beliefs.

Despite Einstein's assertions, there is no mutual exclusion between being creative and being logical. One can create logical hypotheses through creative induction.

It is the Lorentz Transformation which is the product of creative inductive logic, with its hypotheses of length contraction, time dilatation and relative simultaneity, and which is the fundamental postulate of the special theory of relativity. Invariant light speed and the covariance of the laws of physics are deducible from the Lorentz Transformation, the laws of physics, and the definition of inertial motion, which are more fundamental in the special theory of relativity, than invariant light speed. Speed must be composed of the more fundamental elements of distance and duration. Speed is a derived unit. Therefore, the synthesis of the special theory of relativity comes in deducing invariant light speed from the hypotheses of an isotropic and homogenous space, Maxwell's theory of the medium, the theory of inertial motion, and the hypotheses of length contraction, time dilation and relative simultaneity. This is precisely the conclusion Einstein was obliged to admit, in 1935: "The special theory of relativity grew out of the Maxwell electromagnetic equations. So it came about that even in the derivation of the mechanical concepts and their relations the consideration of those of the electromagnetic field has played an essential role. The question as to the independence

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of those relations is a natural one because the Lorentz transformation, the real basis of the special relativity theory[. . .]"[17]

To argue, as the Einsteins did argue in 1905, that invariant light speed and the mandated identity of Lange's inertial systems deduces invariant light speed and the mandated identity of Lange's inertial systems, is to argue in fallacies of Petitio Principii, which the Einsteins did do, in an attempt to hide their plagiarism of the induced hypotheses of Boscovich, Voigt, FitzGerald and Larmor.[18]

Notes 1 - M. Einstein-Marity and A. Einstein, "Zur Elektrodynamik bewegter Körper", Annalen der Physik, Series 4, Volume 17, (1905), pp. 891-921.

2 - H. A. Rowland, The Physical Papers of Henry August Rowland, The Johns Hopkins Press, Baltimore, Maryland, (1902), pp. 673-674.

3 - W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in 1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39, Number 3, (June, 2001), pp. 211-230; URL < http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf> Lorentz acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the "Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig, (1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica, Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars, (1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity, Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1, 1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122.

4 - G. F. FitzGerald, "The Ether and Earth's Atmosphere (Letter to the Editor)", Science, Volume 13, Number 328, (1889), p. 390.

5 - J. Larmor, "A Dynamical Theory of the Electric and Luminiferous Medium", Philosophical Transactions of the Royal Society of London A, Volume 185, (1894), pp. 719-822; Volume 186, (1895), pp. 695-743; Volume 188, (1897), pp. 205-300; and Aether and Matter, CUP, (1900).

6 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416.

7 - See: A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, (1982), p. 142; where Pais refers to Einstein's so-called "Morgan manuscript" of 1921. Einstein plagiarized this from: N. R. Campbell, "The Common Sense of Relativity", Philosophical Magazine, Series 6, Volume 21, Number 124, (April, 1911), pp. 502-517, at 505. See also: R. D. Carmichael, "On the Theory of Relativity: Analysis of the Postulates", The Physical Review, First Series, Volume 35, (September, 1912), pp. 153-176; and "On the Theory of Relativity: Mass, Force and Energy", The Physical Review, Series 2, Volume 1, (February, 1913), pp. 161-197.

8 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416.

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9 - R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley & Sons, Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14.

10 - H. A. Lorentz, The Theory of Electrons, Dover, New York, (1952), p. 230.

11 - A. Einstein, The Theory of Relativity and other Essays, Carol Publishing Group, (1996), pp. 6-8.

12 - W. de Sitter, "On the Bearing of the Principle of Relativity on Gravitational Astronomy", Monthly Notices of the Royal Astronomical Society, Volume 71, (March, 1911), pp. 388-415, at 388-389.

13 - A. Einstein, Relativity, the Special and the General Theory, Crown Publishing, Inc., New York, (1961), p. 148.

14 - A. Einstein, Ideas and Opinions, Crown Publishers, Inc., New York, (1954), p. 307.

15 - A. Einstein, quoted in A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, (1982), p. 131.

16 - A. Einstein and I. Infeld, The Evolution of Physics, Simon & Schuster, New York, London, Toronto, Sydney, Tokyo, Singapore, (1966), p. 31. Compare to the more lucid, prior statements of: W. K. Clifford, The Common Sense of the Exact Sciences, Dover, New York, (1955), pp. 193-194. E. Mach, "The Economy of Science", The Science of Mechanics, Open Court, LaSalle, Illinois, (1960), pp. 577-595. K. Pearson, The Grammar of Science, Second Revised and Enlarged Edition, Adam and Charles Black, London, (1900), pp. 30-37. H. Poincaré, Dernières Pensées, Flammarion, Paris, (1913); English translation Mathematics and Science: Last Essays, Dover, New York, (1963), pp. 22-23.

Einstein often plagiarized these works.

17 - A. Einstein, "Elementary Derivation of the equivalence of Mass and Energy", Bulletin of the American Mathematical Society, Series 2, Volume 41, (1935), pp. 223-230, at 223.

18 - Cf. C. J. Bjerknes, Albert Einstein: The Incorrigible Plagiarist, XTX Inc., Downers Grove, Illinois, USA, (2002), ISBN 0971962987.

Selected Bibliography R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley & Sons, Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14.

H. Dingler, Die Grundlagen der Physik, synthetische Prinzipien der mathematischen Naturphilosphie, Verlag der Vereinigung wissenschaftlicher Verleger, Leipzig, (1919).

S. H. Guggenheimer, The Einstein Theory Explained and Analyzed, The Macmillan Company, New York, (1925).

J. Mackaye, The Dynamic Universe, Charles Scribner's Sons, New York, (1931).

W. Kantor, Relativistic Propagation of Light, Coronado Press, Lawrence, Kansas, (1976).

S. Goldberg, Understanding Relativity, Birkhäuser, Boston, Basel, Stuttgart, (1984).

----[A presentation of the author is given at the end of his previous paper published in this same issue of Episteme] cbjerknes@attbi.com

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La nuova teoria del cielo La cosmologia osservativa di Halton Arp (Alberto Bolognesi)

Questo articolo cerca di comunicare informazioni e interpretazioni alternative dell'universo che sono state a lungo ostacolate e, in qualche caso, perfino soppresse. Sono tutte di natura osservativa e si basano essenzialmente sui risultati ottenuti al telescopio dall'astronomo americano Halton Arp, a cui sono legato da lunga e profonda amicizia.

La ragione per cui questi dati stentano tanto a circolare è che la loro accettazione determinerebbe automaticamente uno sconvolgimento scientifico e culturale paragonabile almeno a quello che si produsse con la falsificazione del Sistema Tolemaico. "L'astronomia e l'intera fisica - è stato autorevolmente sancito - dipendono totalmente dalla fisica delle particelle la quale a sua volta proviene direttamente dal Big Bang. Con il Big Bang e l'espansione dell'universo - concordano Murray Gell Mann, David Schramm e Stephen Hawking - astronomia e fisica hanno cessato per sempre di esistere come discipline autonome".

Amen. E se i biologi molecolari inaugurano le loro indagini sul funzionamento del cervello umano con riferimenti espliciti alla nucleosintesi prodottasi nella "fornace primordiale", si dovrebbe aggiungere che non solo fisica, astrofisica e costanti universali, ma chimica, biochimica, botanica, zoologia, storia e filosofia si trovavano in qualche modo già iscritte nella prodigiosa formula dell'Inizio, intesa come un tutto creato dal nulla.

L'alternativa kantiana che il tutto sia inaccessibile all'esperienza è una concezione in disuso: oltre al sottoscritto - che è un dilettante - non conosco più di una dozzina di astrofisici che dichiarano apertamente che l'unico universo di cui abbia senso parlare è quello osservabile o potenzialmente osservabile, e che l'espressione "tutto l'universo", "condizioni iniziali" e "fine dell'universo" sono prive di qualsiasi contenuto scientifico.

Poiché un protone, un neutrone o un elettrone non possono mai essere creati o distrutti isolatamente in un'interazione di particelle, i cosmologi deducono che il loro numero totale è stato fissato rigorosamente al momento del "Fireball". Non un fermione di più e non un fermione di meno. Dio - o chi per esso - ha parlato una volta sola. Dalla massa delle galassie alle singole stelle, dalla balenottera azzurra al giaguaro, alla zanzara tigre, tutto dipende interamente e unicamente dalle condizioni iniziali. Tutto. Ma proprio tutto. All'obiezione di Leibniz - perché c'è qualcosa al posto di nulla? - i teorici della Palla di Fuoco oppongono l'esistenza del falso vuoto, il magico tappeto delle fluttuazioni virtuali, i formicolii del nulla, "l'aperto del puro compossibile". Basta associare al mondo fisico un'energia positiva e alla gravitazione un'energia "negativa" per avere l'universo a costo zero, tutto e nulla contemporaneamente. Più uno meno uno uguale zero, "poiché nulla era - come già scriveva Edgar Poe nel 1848 - tutto è". Eureka!

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Una testimonianza a tarallucci e vino di questo trionfo moderno ci è fornita dal bellissimo libro di Dennis Overbye ("Cuori solitari del cosmo"), che descrive i canti e i lazzi di famosi astronomi che ridiscendono in pulmann dall'osservatorio Keck, sulla cima del Mauna Kea: "Sai qual fu la conclusion, dopo molte ore di osservazion? - cantavano festanti - L'universo è in espansion, sempre in espansion, sempre in espansion …".

Ma qualcosa è andato storto, e nei dispositivi ad accoppiamento di carica applicati ai telescopi sono apparsi sempre più numerosi enigmatici ponti, filamenti luminosi di materia e sinistre connessioni che collegano oggetti che dovrebbero essere invece lontanissimi fra loro. Allora?

"La festa appena cominciata … è già finita?.

DILETTANTI DENIGRATORI E RIVOLUZIONI SENZA PROVE Il preambolo mi consente di fissare drasticamente i termini della questione. Che cosa succede alla cosmologia, alla fisica delle particelle, ma anche alla fisica ordinaria e all'epistemologia, se le connessioni fra oggetti di diverso spostamento spettrale sono reali?

L'assunzione fondamentale su cui è costruita tutta la conoscenza attuale dell'universo è che lo spostamento verso il rosso deve rappresentare una velocità. Non basterebbe infatti che rappresentasse una mera misura delle distanze come nell'originario "effetto Hubble": per avere un universo in espansione, velocità e distanza devono in qualche modo coincidere. Uno spostamento verso il rosso in relazione lineare con la sola distanza eliminerebbe il Big Bang, darebbe di nuovo un universo statico, togliendo di mano ai cosmologi la sospirata "età dell'universo" e ai fisici delle particelle la mitica "era di Planck". E perfino ovvio che il sistema del mondo contemporaneo deve fare quadrato attorno alla recessione delle galassie.

Non ci sono alternative: questo effetto deve essere "universale" e aumentare in proporzione diretta alla distanza che ci separa da esse. Più elevato è il redshift più lontane sono le galassie, più lontane sono le galassie più velocemente devono allontanarsi. Anche il profano capisce facilmente che è una questione di vita o di morte: le velocità devono essere reali.

Ma rispetto a cosa? Se prendiamo tre galassie A, B e C fra loro molto lontane e le disponiamo su una retta immaginaria, quella che sta in mezzo deve allontanarsi radialmente rispetto alle altre due che recedono più rapidamente. Come è possibile? Se A e C si allontanano reciprocamente e proporzionalmente alla loro distanza, come fa B a recedere verso C se C vede B recedere verso A?

A

B

C

∗←→ ∗ ←→ ∗ ←→ Il solo modo di intendere la recessione universale non è evidentemente di assegnare una velocità alle galassie, ma di attribuire una velocità alle distanze. Non è la fuga delle galassie, ma la fuga delle distanze! Per aver dichiarato e scritto questo una trentina di anni fa, sono stato incolpato di "infangare l'immagine pubblica del mondo scientifico" e inserito nella lista dei proscritti dalla divulgazione scientifica.

In un clima più liberal, oggi i cosmologi ammettono che non sono le galassie a fuggire attraverso lo spazio separandosi le une dalle altre, ma che è lo spazio stesso a dilatarsi e ad espandersi trascinando con sé gli oggetti cosmici. Si fa ossessivamente riferimento all'uvetta di un panettone che cresce nel forno, e così tutto va a posto se si è disposti ad assegnare al vuoto e alla metrica le qualità di una pasta che lievita col tempo. (Chiedersi poi chi alimenta il

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forno sarebbe "altamente provocatorio"). Ma questa precisazione ha un costo drammatico e i cosmologi ammettono adesso, con scarso entusiasmo, che lo spostamento verso il rosso delle galassie "non è dovuto all'effetto Doppler" (J. Gribbin, Enciclopedia di Astronomia e Cosmologia). Cioè, a rigore non è dovuto alle loro velocità.

Se però vi iscrivete alla Facoltà di Astronomia il redshift cosmologico vi verrà spiegato sistematicamente in questo modo: "Consideriamo due fotoni che partono dalla sorgente con un ritardo ∆ t l'uno rispetto all'altro. Poiché in quel ∆t l'universo si espande, la sorgente si allontana di una quantità vx∆t e il secondo fotone deve percorrere una distanza più lunga per giungere fino a noi: il ritardo ∆t' con cui lo riceviamo è perciò maggiore". Ma questo è l'effetto Doppler canonico, e gli educatori sanno bene che c'è qualcosa che non va, perché è ovvio che la dilatazione deve avvenire nel tempo attraverso lo spazio che lievita mentre i fotoni sono in viaggio, non quando "il primo e poi il secondo fotone si stacca dalla sorgente" per intraprendere il suo lungo percorso fino ai nostri strumenti! Come faccia allora una lunghezza d'onda a "stirarsi" nello spazio che cresce in misura uguale e contraria alla direzione di propagazione della radiazione elettromagnetica, è un inquietante capitolo di spettroscopia che attende ancora di essere scritto.

Altri trent'anni di proscrizione? Sarebbe un bel traguardo per un cinquantasettenne.

Prima di passare ad alcune confutazioni osservative raccolte da Halton Arp vorrei chiudere il greve argomento riportando la lettera di un dilettante pubblicata di recente da una rivista specializzata. "Che cos'è che veramente si espande? - si chiede con passione il signor Ariberto Papini di Siena - Perché si fa presto a far dilatare la superficie di un palloncino: è di gomma!

Oppure un lenzuolo: è di stoffa! Ma come si fa a fare espandere, oppure ad incurvare qualcosa di non materiale: il vuoto, il nulla?". La profonda risposta fu che "gli aspetti della cosmologia non sono intuitivi, e che alla comprensione dell'espansione dell'universo si arriva solo per via matematica poiché l'estrema astrazione di alcuni concetti rende ardua una spiegazione divulgativa. Comunque tenga presente che la gravità frena la materia - rispetto a cosa?! - ed è la materia ad espandersi. Essa con tale espansione crea lo spazio. Ovvero, le galassie non si espandono in uno spazio circostante, ma lo spazio stesso è creato dall'espansione dell'Universo" (Nuovo Orione n. 123, agosto 2002).

Cioè lo spazio è creato dall'espansione dello spazio. Soddisfatti o rimborsati.

RIVOLUZIONI SENZA PROVE? O gli oggetti di Arp sono tutte illusioni ottiche o i cosmologi difendono un'espansione dell'universo smentita dall'osservazione astronomica. Non è possibile una soluzione "salomonica" o di compromesso e questo rende la controversia ancora più aspra e drammatica. Poiché galassie interagenti con redshift discorde non possono essere contemporaneamente vicine e lontane, connesse e disconnesse, lente e veloci, il punto di vista convenzionale è costretto ad invocare sistematicamente effetti di prospettiva, allineamenti e accavallamenti accidentali nella profondità del cielo.

Né potrebbe accontentarsi di attribuire all'oggetto con redshift eccedente uno spostamento non cosmologico assegnando a quello con minore spostamento verso il rosso un redshift sicuramente e interamente cosmologico.

Giudicate voi.

La prima immagine (Fig. 1) che ho selezionato da un gran numero di casi esistenti, mostra un quasar che cade davanti a una galassia ellittica, la NGC 1199. L'oggetto compatto indicato con una freccia ha uno spostamento verso il rosso abbastanza elevato (z = 0,044) mentre quello della galassia è modesto (z = 0,009). Per la legge di Hubble e per la buona sorte della cosmologia del Big Bang l'oggetto di tipo quasar dovrebbe invece trovarsi dietro (cioè molto più lontano della galassia ellittica).

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Fig. 1

L'immagine successiva (Fig. 2) rappresenta la galassia NGC 4319 e il quasar Markarian 205 connesso da un visibile ponte di materia. Ma lo spostamento verso il rosso della galassia è z = 0,006 mentre quello del quasar è di 0,07, cioè dovrebbe trovarsi undici volte più distante secondo la "legge" che tutela l'espansione dell'universo.

Fig. 2

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La fotografia seguente (Fig. 3) rappresenta il Sestetto di Seyfert, un gruppo di galassie in interazioni che hanno all'incirca la stessa magnitudine apparente. Cinque di esse hanno pi첫 o meno lo stesso redshift (z = 0,015) ma quella indicata con la freccia presenta uno spostamento quasi cinque volte maggiore, il che la renderebbe cinque volte pi첫 lontana e di enormi dimensioni.

Fig. 3

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La quarta immagine (Fig. 4) mostra la suggestiva catena di galassie blu VV 172. Quattro di queste galassie hanno un valore di redshift che oscilla intorno a z = 0,05 mentre quella indicata con una freccia presenta uno spostamento verso il rosso estremamente elevato: z = 0,12. Chi crede davvero che questa galassia non faccia parte della configurazione e che si tratti di un lontanissimo oggetto blu che si è andato ad incastrare accidentalmente fra quattro compagne blu lungo la nostra linea di vista, alzi la mano: e chi alza la mano sostiene implicitamente che si tratta della galassia blu piĂš grande di tutto l'universo â&#x20AC;Ś

Fig. 4

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La quinta immagine (Fig. 5) presenta tre quasar nei bracci a spirale di NGC 1073. C'è una probabilità su cinquantamila che si tratti di un allineamento accidentale.

Fig. 5

E ancora, in Figura 6, una fotografia profonda di tre quasar intorno a NGC 3842. Qui c'è una possibilità su un milione di trovare per caso questa associazione.

Fig. 6

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La settima immagine mostra la spirale barrata a due bracci NGC 1097 con i suoi quattro getti luminosi. Ci sono almeno cinquanta quasar attorno a questa galassia straordinariamente attiva.

Fig. 7

Fig. 8 (Grafico dei quasar individuati attorno a NGC 1097 da Arp, Wolstencroft e He nel 1979).

Concludo questa "rivoluzione senza prove" con la foto (Fig. 9) ottenuta da N. Sharp della coppia di galassie NGC 7603 A e B, foto che i lettori di Episteme giĂ conoscono per via della recentissima e sensazionale scoperta effettuata dagli astronomi M.L. Corredoira e C.M. Gutierrez. Rappresenta il coronamento di cinquant'anni di ricerche che hanno fruttato ad Arp soltanto l'allontanamento dall'Osservatorio di Monte Palomar. Sebbene siano stati pubblicati sulla celebre rivista "Astronomy and Astrophysics", i risultati continuano a circolare nella comunitĂ astronomica come l'ennesimo, imbarazzante X file.

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Le due galassie collegate da un evidentissimo ponte di materia hanno rispettivamente uno z: 0,029 per l'oggetto più grande e z: 0,057 per la compagna più piccola. Al momento della scoperta della clamorosa discordanza (1971) Arp notò subito due condensazioni di aspetto stellare immerse nel braccio, e auspicò che i futuri spettrografi potessero analizzarne i dettagli e determinarne gli spostamenti verso il rosso. Impresa riuscita a Corredoira e Gutierrez trent'anni dopo col N.O.T. di La Palma, e con tecnologia progredita: le due condensazioni hanno mostrato gli spettri tipici dei quasar con z = 0,391 per l'oggetto più vicino alla galassia principale e z = 0,243 per quello prossimo alla compagna! Così abbiamo due galassie interagenti con diverso spostamento verso il rosso e due quasar ad alto redshift nel filamento che le connette: il mondo avrebbe dovuto fermarsi per questo, almeno per un giorno, ma i grandi media non ne hanno nemmeno parlato.

Fig. 9

Che dire? C'è una terza condensazione che emerge dal nucleo della NGC 7603A: e basterebbe un'occhiata dell'Hubble Space Telescope o del Keck per affossare il Sistema del Mondo.

Richiesta di ulteriori osservazioni con il telescopio orbitale a raggi X Chandra e con l'8 metri del VLT dell'ESO al Cerro Paranal sono state prontamente respinte.

LA NUOVA TEORIA DEL CIELO Le discordanze di redshift constatate, richiedono che le condizioni di emissione della radiazione da parte di oggetti interagenti o posti alla stessa distanza mutino da un sistema all'altro. Si tratta dunque di comprendere un fenomeno fisico in grado di operare su interi insiemi estesi di stelle, gas e polveri, generando spostamenti intrinseci che non hanno a che vedere né con la velocità né con la distanza. Un meccanismo che opera ancora più vistosamente nei quasar, che lungi dall'essere gli astri favolosi più energetici e lontani di tutto l'universo, svelano la loro natura di oggetti piccoli e poco luminosi, connessi alle galassie.

Questo cambio - val la pena sottolinearlo - non è invocato da una nuova stravagante teoria dell'universo ma, se non avete già dimenticato le precedenti immagini, dalle osservazioni stesse.

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Dunque nuova fisica, nuova informazione che dovrebbe esaltare - e non deprimere! - chi tende ad approfondire la conoscenza della struttura cosmica. Anche se questo sembra aumentare la nostra ignoranza, allontanandoci da certezze gelosamente custodite.

L'evidenza osservativa dello spostamento verso il rosso intrinseco chiama in causa direttamente la fisica quantistica e l'azione interparticellare che devono giustificare l'esistenza del mondo collegandolo al microcosmo. Per gli scopi divulgativi che si propone questo articolo dirò semplicemente che la varietà dei redshift intrinseci osservati richiede che le transizioni energetiche di un atomo di idrogeno, di elio, di ossigeno, di magnesio … devono trovarsi a frequenze e a lunghezze d'onda diverse da quelle che sperimentiamo in laboratorio.

E questo dà già un'idea della immensa posta in gioco. A qualsiasi livello di conoscenza si trovi il lettore (e lo scrivente!) la falsificazione dell'universo in espansione impone che le righe degli elementi e le serie spettrali che compongono l'intero spettro elettromagnetico si trovino realmente alle frequenze osservate.

Si può ben comprendere lo shock stemperato dall'ironia che ha fatto esclamare a un eminente fisico che "i dati di Arp implicano costanti personalizzate!": Ma questa è esattamente la sfida osservativa, questa è esattamente la vita sulla frontiera.

"Che cosa determina l'energia di transizione tra due stati atomici dell'idrogeno? - si chiede Arp - Un fattore è rappresentato dalla carica relativa tra l'elettrone e il nucleo, l'altro fattore è la massa dell'elettrone che subisce una transizione tra i due possibili stati orbitali. Se le misure della costante di struttura fine eliminano la possibilità che le cariche elettriche possono essere diverse, resta solo la massa dell'elettrone"1.

Poiché lo spostamento verso il rosso intrinseco è documentato dalle osservazioni, una delle poche interpretazioni in grado di spiegarlo efficacemente è di attribuire massa minore a tutte le particelle che costituiscono la materia dell'oggetto con più alto spostamento verso il rosso.

Ciò darebbe immediatamente frequenze più basse e fotoni più spostati verso il rosso, orbite elettroniche "allargate" e, in pratica, isotopi più leggeri. Se dunque quasar e galassie compagne risultano associate a oggetti più massici, come nipotini a spasso coi nonni, una delle differenze più qualificanti sta nel loro tempo di formazione. E' pensabile - si chiede Arp - che oggetti connessi da ponti di materia, mobilizzati nei bracci di spirali o immersi in filamenti luminosi e in gas caldi ad alta e ad altissima energia (X e gamma) abbiano la medesima età del sistema a cui appartengono?

La soluzione cosmogonica è immediata: gli oggetti cosmici con più alto spostamento verso il rosso devono essere stati "creati" (espulsi o condensati) in un tempo successivo rispetto a quelli con basso redshift. "Non appena la materia appare - scrive Arp - essa risulta altamente spostata verso il rosso. Col passare del tempo diventa più pesante, più grande e più luminosa e il suo altissimo spostamento decade verso valori più contenuti. Abbiamo in pratica la rappresentazione empirica di un piccolo quasar con altissimo redshift che evolve in una galassia compatta con spostamento verso il rosso inferiore e infine in una galassia compagna con leggera eccedenza nello spostamento verso il rosso" rispetto all'oggetto che l'ha generata. ("Quasar, redshifts and controversies", 1987)2.

E' dunque nei fatti, per Arp, un'evoluzione delle costanti. Ed è ironico - rileva - che il punto di vista convenzionale ne difenda ad ogni costo l'immutabilità invocando il Secondo Principio della Termodinamica. La materia creata tutta in una volta dal Big Bang con proprietà immutabili non rappresenta una violazione, ma le masse delle particelle variabili col tempo lo sono …. "Mi rendo conto che il mio universo si restringe paurosamente all'universo delle osservazioni - mi disse una volta - un universo locale dove la materia vi compare continuamente ricreata, o riciclata. I tuttologi non potrebbero accontentarsi ma ciò è esattamente quel che osserviamo!". Evidentemente a partire da uno stato particellare estremamente diffuso - ipotizza Arp - Da un "apeiron" sconosciuto e onnipervasivo che accende i nuclei delle galassie e che le moltiplica attraverso espulsioni secondarie come una gragnola ininterrotta di fuochi d'artificio. O come una pianta che germoglia.

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E' un immagine locale ma grandiosa, che non può (né si vede come potrebbe) pretendere di fissare tutto l'universo. La sola definizione sensata del Mondo - insiste - è: "tutta la materia osservabile o potenzialmente osservabile che siamo in grado di sperimentare".

I limiti kantiani vengono immediatamente ristabiliti: siamo all'interno di un perimetro o di una bolla i cui orizzonti si allargano per mezzo di strumenti sempre più progrediti, ma continuiamo a permanere confinati al centro del mistero. Più che una condizione umana sembra una condizione della fisica.

CHE COS'È H ?

O

Ma all'interno della "bolla delle osservazioni", come sull'isola di Kant battuta dai marosi dell'inconoscibile, possiamo ancora fare scienza. Se la creazione di materia prende posto nell'universo come un processo continuato, e se i redshift esprimono semplicemente l'età degli oggetti cosmici e non più la loro velocità e la loro distanza dal mitico Inizio del Mondo, può ancora avere un significato la determinazione della "costante Ho"?

Sorprendentemente la risposta è sì. La costante di Hubble che nella cosmologia del Big Bang non è che un numero che quantifica la rapidità con cui l'universo si va espandendo, diventa nella relazione age-redshift di Arp la chiave di volta per misurare la variabilità della massa in funzione dello spostamento verso il rosso. L'integrazione che lega lo spostamento spettrale alla scala delle magnitudini apparenti è immediata, e con essa l'annosa questione dei "redshift anomali".

La trasformazione della convenzionale legge di Hubble "velocity-distance" in "age-distance law" e in "age-luminosity law" è fissata nelle equazioni della massa variabile: m = mo

t2 t0

2

(1)

sul redshift: 2

1+ z =

t0 t2

(2) 2

1 + z1 t 0 = (3) 1 + z 0 t1 2 e sulla trasformazione delle scale temporali τ = tempo locale e t = tempo cosmico:

τ =

t3 3t 0

2

(4)

in cui la soluzione di Friedmann (Big Bang) viene ricondotta a uno spaziotempo piatto (euclideo) e a un universo statico.

Il diagramma sottostante (Fig. 10) visualizza le due soluzioni, che a sinistra forniscono il Big Bang e a destra l'universo di Narlikar-Arp. Ma, ben conscio di perdere in tal modo i contatti con i lettori che non hanno specifiche esperienze di cosmologia, dirò subito che non intendo cavarmela con la mera esposizione del formalismo matematico.

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Fig. 10 (da Arp, 1997)

E non è una passeggiata. Limitandomi all'essenziale, è evidente che non tutte le galassie sono grandi galassie: al contrario, queste ultime sono abbastanza rare. Nella cosmologia del Big Bang tutte le galassie hanno però all'incirca la stessa età mentre in quella di Arp devono avere età assai variegate, e dalla loro età deve dipendere la massa, lo splendore e soprattutto lo spostamento spettrale, mentre nell'ipotesi convenzionale i redshift misurano essenzialmente le velocità e le distanze prodotte dall'espansione dello spazio.

E' ovvio che anche le galassie "in carriera" di Arp non sono destinate a raggiungere tutte la medesima massa e luminosità (le differenze morfologiche sono un fatto osservativo), ma in questo quadro non si presenta il rischio di mescolare sistematicamente oggetti di magnitudini assolute molto diverse. Che è poi un vantaggio che ha una terribile contropartita, perché in tal modo non possiamo più dire gran che sulle loro distanze.

Anche una semplificazione così estrema riesce a mettere a nudo la prima cruciale questione: meglio una distanza sbagliata o una distanza incerta? E' l'eterno tallone d'Achille della scienza astronomica, che non può misurare nelle due dimensioni disponibili un mondo fisico che ne ha almeno tre: misure sbagliate non hanno contenuto scientifico, misure incerte non producono risultati scientifici. Basta questo preliminare per capire perché, a dispetto delle confutazioni osservative, l'espansione dell'universo è così strenuamente difesa. E' solo in base all'interpretazione cinematica del redshift che si è potuta sviluppare una tecnica in grado di scandagliare l'universo e di produrre spettacolari mappe tridimensionali della struttura cosmica. Che producono mostri, si potrebbe aggiungere, come le grandi muraglie, le "dita di Dio", le spropositate luminosità dei quasar, le velocità superluminali e le masse dei buchi neri che aumentano con la distanza.

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Fig. 11 Interpretazioni a confronto - Nella figura precedente appaiono cinque oggetti di debole luminosità molto vicini fra loro. I dettagli della composizione spettrale sono qualitativamente molto simili per tutti i componenti ma l'aspetto non puntiforme dei primi tre a sinistra li definisce come "galassie" mentre i due oggetti di forma sferica (puntiformi) appaiati sono riconosciuti come "quasar". Il redshift medio è z = 0,435 il che li collocherebbe a più di cinque miliardi di anni luce di distanza da noi, ma il quasar a destra ha un redshift quasi cinque volte più alto (che anche dopo le correzioni relativistiche dovrebbe essere spostato a una distanza almeno doppia). L'interpretazione cosmologica richiede che tre galassie e un quasar si trovino tutti alla stessa distanza mentre il quasar di destra viene a cadere solo accidentalmente vicino al gruppo per un effetto di prospettiva. Per Arp gli oggetti sono tutti alla stessa distanza, molto giovani, molto più vicini e molto meno luminosi, e il quasar di destra rappresenta l'ultimo nato della formazione. Si noti che il quasar più luminoso non mostra alcuna nebulosità circostante, che dovrebbe invece essere rivelata sul versante del compagno ritenuto più lontano. Non appare nessuna galassia "ospite" in 1548+144a e il quasar appare "nudo".

(Cortesia di E.M. Burbidge).

Come si fa a distinguere una galassia debole da una galassia lontana?

E' l'eterno dilemma della "distanza secondo luminosità": quando la luminosità apparente di una sorgente luminosa è pari a un quarto della luminosità apparente di un'altra sorgente di medesima luminosità assoluta, la prima si trova a distanza doppia. Nella teoria del Big Bang quando il redshift di un oggetto è doppio, questi deve recedere a velocità doppia, quando il redshift è quadruplo l'oggetto si allontana quattro volte più velocemente e deve trovarsi quattro volte più lontano. La circolarità è in agguato: se i rapporti di luminosità apparenti non tornano, o coincidono sopra valori di redshift differenti, basta aumentare (o diminuire) le luminosità assolute. E se due galassie morfologicamente identiche e del medesimo splendore apparente, ma individuate in posizioni contrapposte del cielo presentano spostamenti verso il rosso discordi, si chiamano in causa "espansioni asimmetriche dell'universo". Non si può … sbagliare.

L'alternativa di Arp è il crollo dell'espansione dell'universo, e questo implica che le distanze siano sbagliate di un fattore che può superare 100, le masse e le luminosità di un fattore 10.000, le età assegnate in base al "look back time" di un fattore fino a 10 10: un'alternativa da

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Sant'Uffizio, si potrebbe dire, quando i detentori del potere temporale per colpa di un piccolo cannocchiale si trovavano a dover riconsiderare l'inviolabile architettura del Cielo.

Ma il "look back time", cioè l'effetto di osservare gli oggetti cosmici allo stato non attuale per via della velocità finita delle propagazioni elettromagnetiche, ha importantissime e decisive conseguenze su entrambi i modelli di universo. Nello schema immaginario del Big Bang come in un film girato alla rovescia, l'età delle galassie si abbassa progressivamente e uniformemente con la distanza, svelando oggetti primordiali, in cui la "metallicità" (cioè la formazione degli elementi più pesanti all'interno delle prime stelle) tende a scomparire. Le galassie svaniscono per far posto a singole palle di gas di massa grandissima e di vita brevissima (l'ipotetica popolazione III). Più in là c'è solo "l'era della radiazione". Nella cosmologia osservativa di Arp, la scalata verso epoche più antiche dipende invece da un unico parametro, l'età della nostra galassia. Tecnicamente, quindi, la cosiddetta costante di Hubble rappresenta l'inverso dell'età delle nostre stelle più antiche! Per esprimermi nei termini più semplici: come ci apparirebbe la nostra galassia alla distanza di un megaparsec (3,261 milioni di anni luce)? Se la nostra galassia ha quindici miliardi di anni ci apparirebbe a un'età di circa 14 miliardi novecentonovantaseimilioni di anni. Alla distanza stimata dell'ammasso della Vergine (circa 16-17 megaparsec), ci apparirebbe di una cinquantina di milioni di anni più giovane, mentre a 5 miliardi di anni luce si mostrerebbe all'età apparente di 10 miliardi di anni.

Gli specialisti perdoneranno l'ovvietà della rappresentazione, ma a buon profitto dei non iniziati dirò che a 10 miliardi di anni luce la Via Lattea ne dimostrerebbe cinque e che a 15 miliardi di anni luce (che è distanza spaziale), la nostra galassia - che pure sta là in tempo reale - sparirebbe come non fosse mai nata, perché la prima luce partita dalle nostre stelle più antiche non ha ancora potuto colmare quella distanza. E anche una buona risposta al problema del cielo buio in un universo statico (paradosso di Olbers) che qui non esamineremo. Come dovrebbero apparirci galassie molto vicine a noi e della medesima età della nostra?

Ovviamente con uno spostamento verso il rosso molto basso, sul quale graverebbero i moti peculiari di avvicinamento o di allontanamento sulla nostra linea di vista (effetti Doppler) dovuti all'interazione gravitazionale. Che è poi, in pratica, ciò che constatiamo nel Gruppo Locale e nei sistemi a noi più prossimi. Ne parleremo fra un attimo.

Apparentemente non resta che chiederci a quale spostamento spettrale dovrebbero trovarsi oggetti vicini molto giovani e - se esistono - oggetti vicini più antichi della Via Lattea. La risposta è molto semplice anche se sorprendente: gli oggetti giovani mostrerebbero un redshift molto alto che tenderebbe ad aumentare con la distanza. L'"orizzonte" degli oggetti intrinsecamente giovani diventa piuttosto angusto a causa del look back time. La risposta a come si presenterebbero sistemi vicini più vecchi nella soluzione di Arp è ancora più facile essendo intuitiva: galassie più antiche della Via Lattea mostrerebbero un redshift negativo, cioè in pratica esibirebbero un blueshift rispetto al nostro spettro elettromagnetico.

Nelle parole dello stesso Arp: "M 31(la grande galassia in Andromeda di cui la nostra Via Lattea è una compagna) anche dopo la correzione per la rotazione galattica continua a esibire un elevato spostamento verso il blu. In questo caso la nostra galassia apparirebbe spostata verso il rosso se vista da M 31 così come M 31 risulta spostata verso il blu vista da noi. Questa è la sfida".

PROFONDO ROSSO O ROSSO POCO PROFONDO ?

Resterebbe da chiedersi a quali frequenze e a quale spostamento spettrale dovrebbero presentarsi sistemi più antichi del nostro e della stessa M 31 se posti a grandi distanze. Ma è una risposta difficile anche per uno stregone. Nessuno è in grado di dire quanto "durino" le più grandi galassie: certo non possono essere eterne, e già questo determinerebbe dei grandi "buchi di buio", immense interruzioni temporali nella propagazione delle radiazioni; e poi si renderebbero necessarie conoscenze inaccessibili sull'omogeneità o la disomogeneità della

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materia cosmica su scale tendenti all'infinito (cfr. K.V.L. Charlier, "How Infinite can be built up", 1922). Ricompaiono tutte le grandi e insolute questioni ottocentesche sul cielo buio o su come potrebbe mai raggiungerci una sorgente luminosa posta a distanza infinita. La scelta di Arp è ancora di natura empirica: poiché le galassie che presentano blueshift nell'universo osservabile sono pochissime, noi ci troviamo evidentemente a vivere in uno dei sistemi più antichi. Galassie un po' più vecchie della nostra alle più grandi distanze tornerebbero ad apparirci spostate verso il rosso a causa del look back time, e per il lettore che rischia di smarrirsi nelle proprietà dell'universo statico farò l'esempio grossolano di un sistema dell'età di 25 miliardi di anni (cioè di circa 10 miliardi di anni più antico della Via Lattea) alla distanza di 15 miliardi di anni luce. Se fosse ancora osservabile a quella distanza, ci apparirebbe più giovane delle nostre stelle più vecchie di circa 5 miliardi di anni, quindi non spostato verso il blu ma di nuovo verso il rosso.

L'interpretazione cosmogonica di Arp dell'universo osservabile richiede che Andromeda (M 31) sia il capostipite e in pratica l'oggetto più antico di tutto il Gruppo Locale; e ciò risolve anche un rompicapo di lunga data che resta inspiegato nella cornice convenzionale. E' un problema che mi ha coinvolto personalmente e riguarda l'enigmatica distribuzione dei redshift della nostra congregazione di galassie che sono tutte positive rispetto a M 31! Io segnalai questo risultato all'Astronomia professionale sin dal 1971, all'indomani della pubblicazione degli spostamenti spettrali allora disponibili dei componenti il Gruppo Locale: ma all'epoca propagandavo epatoprotettori e antinfluenzali e non venni preso sul serio. Scrissi a Paolo Maffei e a Livio Gratton che "o il Gruppo Locale si sta disperdendo o gli spostamenti verso il rosso non c'entrano con l'effetto Doppler".

Il fenomeno tuttavia è stato confermato e ampliato con nuovi dati anche per l'altro gruppo di galassie a noi più vicino, in Ursa Major, dominato dalla grande spirale M 81, e poi esteso a un gran numero di ammassi dove la galassia più massiccia risulta possedere sistematicamente il redshift più basso.

Fig. 12 e 13 Distribuzione degli spostamenti verso il rosso-relativi di tutte le più importanti compagne rispetto alla loro galassia dominante nei gruppi di M 31 e M 81. (Cortesia di H. Arp)

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E' aperta la caccia alle galassie "madri" e alle più antiche progenitrici? Un buon metodo potrebbe essere quello di utilizzare i quasar come indicatori delle distanze, ma bisognerebbe passare sul cadavere del Big Bang.

Nella loro nuova "veste" di oggetti piccoli connessi alle galassie, giovani e poco luminosi, i quasar non potrebbero essere osservati intorno a galassie attive molto lontane, per le quali, in base alla sola relazione "age-redshift" è oltretutto molto difficile stimare la distanza.

L'"estinzione" degli oggetti giovani (quasar, BL Lac, etc.) è una funzione che cresce assai rapidamente nel modello di universo di Narlikar e Arp cosicché i "progenitori" sono identificabili con sicurezza solo nel nostro vicinato e tuttalpiù alle medie distanze.

Poiché la creazione di oggetti cosmici è osservativamente un fenomeno continuo, l'integrazione delle due scale temporali (t = tempo cosmico e τ = tempo locale) comporta notevoli complicazioni che qui risparmieremo al lettore. Mi limiterò a rilevare che si potrebbero anche osservare oggetti con il medesimo redshift (cioè con la medesima etàapparente) a distanze molto diverse e quindi con età intrinsecamente diverse sulla scala t del tempo cosmico.

IL NUOVO SCENARIO Un quesito ricorrente tra i pochi esploratori di questa nuova formulazione del mondo è il seguente: se i quasar vengono processati e poi espulsi dalle galassie per dar forma a nuove galassie che a loro volta semineranno nuovi quasar in un processo a cascata, come è apparsa, come si è formata la prima galassia? Ovviamente, in un universo indefinitamente grande e antico la domanda è priva di senso: è un po' come cercare l'albero che avrebbe dato origine a una foresta di dimensioni illimitate: Arp non ha la soluzione complessiva della Natura e non ne fa mistero.

"Da ciò che possiamo vedere le cose si formano continuamente, e continuamente cambiano scomparendo e riapparendo: eppure ogni cosa sembra essere in comunicazione con tutte le altre cose. Se la materia cosmica dispone di un tempo illimitato è possibile che sperimenti ogni possibilità" (Comunicazione privata, 1993).

E' tuttavia estremamente interessante indagare come avrebbe potuto avere origine la parte visibile del mondo, l'universo locale delle osservazioni al tempo cosmico t = 0. Essa comincerebbe con un'esplosione di formazioni di tipo quasaroide di bassa luminosità, circa 15 miliardi di anni fa. Forse a partire da singoli oggetti al centro del Superammasso Locale (che è oggi la più grande aggregazione di galassie conosciuta) vennero proiettate formazioni successive poi evolutesi in brillanti galassie della seconda generazione, come M 31 che occupa il centro del Gruppo Locale. Le analogie con l'Inizio degli Inizi della teoria del Big Bang sono ingannevoli, perché questa è una creazione continua, continuata e intermittente e quindi, temporalmente, l'esatto opposto del Big Bang che è invece per definizione un evento unico a partire dal nulla.

Circa 8 milioni di anni dopo che una galassia come M 31 ha preso a formarsi, essa espelle una famiglia di compagne di cui la Via Lattea è uno dei componenti: è la foto di gruppo del cortile di casa, dove le compagne più giovani devono essere generalmente più attive ed aver espulso molto di recente i quasar del Gruppo Locale (come ad esempio, 3C 120 e i 7 quasar che la circondano, PKS 0123 + 25, 3C 48 e il BL Lac che si trova nelle vicinanze).

Questo scenario empirico di creazione continua ha celebri eponimi in Fred Hoyle, Hermann Bondi e Thomas Gold con la Teoria dello Stato Stazionario, e anche nel suggerimento dell'illustre fisico Paul Dirac che ipotizzò la creazione di materia nell'universo come un processo "moltiplicativo" preferibilmente in prossimità di precedenti concentrazioni di materia più vecchia.

Va detto però con chiarezza - ed è lo stesso Arp a farlo - che qui non abbiano nuovo spazio che sloggia le vecchie formazioni per dar forma a quelle nuove attraverso una metrica in

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espansione, perché gli spostamenti spettrali "anomali" e la relazione age-redshift eliminano l'espansione dell'universo.

Così le ipotizzate "superfici di massa nulla" di Hoyle e le equazioni della materia di Narlikar a partire da m = 0 diventano quasi nulle e quasi zero. "Per quanti sforzi si possano fare ammette Arp - non è scientificamente possibile ridurre qualcosa al nulla". O si fa intervenire un falso vuoto, una radiazione di punto zero, uno stato iperdiffuso di materia-energia o si sfocia nel misticismo. Anche lui alla fine ha bisogno di un apeiron che accende i nuclei delle galassie primordiali: "Quale possa essere la connessione fra l'osservata creazione locale e l'universo in generale pone una questione affascinante ma smisurata. Nei termini delle forme di vita che stanno lottando con questi concetti, tuttavia è rilevante domandarsi se pure loro, oltre ad essere continuamente create e ricreate in forme leggermente diverse, possano anche trovarsi nei loro costituenti più microcospici in continuo contatto informativo con il resto dell'universo".

IL MISTERO DELLA VERGINE Se è palesemente retorico chiedersi in quale pozzanghera si sviluppò la prima cellula, è però del tutto legittimo domandarsi chi fu la madre di M 31. La madre della nostra galassia deve pure avere una madre, e poiché stiamo parlando del nostro universo locale e non di tutto l'universo, la "nonna" - se esiste da qualche parte - non dovrebbe poi essere tanto lontana.

Feci questa domanda ad Arp quasi per scherzo una decina di anni fa e lui ammise che gli sarebbe piaciuto avere una risposta a tutto: aggiunse subito che "sarebbe assai più fruttuoso conoscere il destino finale delle galassie e della materia che si condensa in stelle piuttosto che rintracciare una foto dell'antenato da incorniciare". "Hai una risposta anche per questo?

- incalzai malizioso - Ma è molto interessante - fece ignorando la mia provocazione - che le uniche galassie non locali che presentano spostamenti verso il blu si trovano tutte al centro del vicino ammasso della Vergine. Sono sei, spirali Sa e Sb, molto simili alle galassie più vecchie che conosciamo. Se ti fidi della mia relazione age-redshift, è facile calcolare che si tratta di sistemi più vecchi di una ventina di milioni di anni delle galassie del Gruppo Locale: il problema è che questo corrisponde solo ad un incremento dello 0,1% rispetto alle nostre stelle più antiche, così se ti occorre anche la bisnonna dovresti forse trasferirti lassù per continuare la tua ricerca genealogica …".

Gli spostamenti verso il blu delle galassie della Vergine non trovano spiegazioni soddisfacenti nella cornice dell'universo in espansione: alla distanza stimata di 16-17 Mpc le galassie più massicce hanno redshift equivalenti a velocità di recessione di circa un migliaio di chilometri al secondo, ma c'è una "dispersione" in eccesso enorme e un gran numero di altri membri che dovrebbero così recedere a velocità doppie, triple, quadruple e oltre. L'effetto viene di solito "calmierato" sommando a queste galassie "super veloci" un gran numero di nane a basso spostamento verso il rosso fino a farlo sparire, salvando così l'integrità temporale dei gruppi.

Ma le sei galassie con blueshift vicine al centro dell'ammasso (che altro definisce un "cluster"?) dovrebbero possedere un moto retrogrado spettacolarmente alto rispetto al flusso "quieter" dell'espansione cosmica: viene giustificato con movimenti peculiari verso la nostra linea di vista che si sommano alla direzione di rotazione della nostra galassia, e/o con altre ipotesi "esotiche" e "oscure", inaccessibili all'osservazione, che qui non menzioneremo. "E' tuttavia un fenomeno davvero straordinario" ammette il Professor Giuseppe Galletta dell'Università di Padova. Ma che significa? A tutti gli effetti gli spostamenti verso il blu accertati al centro della Vergine sono anch'essi da annoverare fra i "redshift anomali" e costituiscono un'altra formidabile confutazione sperimentale dell'assioma che gli spostamenti delle righe spettrali delle galassie significano sempre e soltanto velocità.

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LE DITA DI DIO Il Palladio, la mitica pietra della sapienza caduta dal cielo, non si trova più ad Atene o a Troia.

E' oggi custodito nei penetrali dello Smithsonian Center for Astrophysic ad Harvard, montato su un rozzo piedistallo in uno dei corridoi dell'ala nuova ricoperta di una smorta moquette grigia. E' un cubo di plexiglass di circa un metro di lato, all'interno del quale si trovano migliaia e migliaia di palline colorate in apparente sospensione: sono rosse e azzurre, palline rosse per le galassie ellittiche e palline azzurre per le galassie a spirale.

Al centro del "diorama" una sferetta bianca marca la posizione della Via Lattea, molto prossima a un nugolo di palline e più in là a un'altra concentrazione che nelle intenzione del costruttore dovrebbero rappresentare rispettivamente l'ammasso della Vergine e il più distante assembramento della Chioma di Berenice. E' la cartografia tridimensionale della struttura cosmica ottenuta attraverso la misurazione dello spostamento verso il rosso di 2.400 galassie (palline) in base all'"indubitabile" assunzione che il redshift rappresenta comunque una distanza e una velocità.

Un'altra di queste mappe di profondità è mostrata nella Fig. 14 che compendia ulteriori surveys spettroscopiche di una gran numero di galassie.

Fig. 14

Appaiono stupefacenti strutture come "grandi muraglie", filamenti e immense bolle di vuoto.

Presenti in tutti questi diagrammi sono le cosiddette "dita di Dio", smisurati e inspiegabili allineamenti di galassie che puntano direttamente alla Via Lattea e che vengono giustificati come "dispersioni di effetti Doppler conseguenti a moti peculiari all'interno degli ammassi" … (vedi Fig. 15).

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Fig. 15 (Le dita di Dio)

Ma se i cartografi delle tre dimensioni avessero preso la precauzione di annotare la posizione in base alle luminosità e alle "taglie" delle galassie, avrebbero potuto constatare ad un'occhiata che le più luminose cadono sistematicamente vicino all'apice delle "dita di Dio": qualsiasi dilettante puntiglioso potrebbe facilmente dimostrarlo provando una volta per tutte che quei redshift non possono rappresentare velocità e distanze, e che queste "mappe" sono prive di significato come indicatori della distribuzione in profondità delle galassie.

CROCI DI EINSTEIN, TOLOMEO E QUANTIZZAZIONE L'evidenza che i quasar cadono vicini alle galassie non è contestata dai cosmologi di credo convenzionale: viene attribuita per lo più a "vizi di selezione", a "stastistiche a posteriori" e a "effetti lente gravitazionali" previsti dalla teoria della Relatività. Anche la presenza di "materia oscura" - la cui presunta concentrazione al centro e ai bordi degli ammassi amplificherebbe la visibilità degli oggetti di fondo - è chiamata in causa; e quando si trovano coppie, tripletti, quartetti di quasar molti vicini e con analogo spostamento verso il rosso, questi diventano automaticamente "candidati lenti".

"E' anche un buon modo di sfoltire i quasar- feci notare a un influente astrofisico nel corso di un dibattito - e sarebbe istruttivo per la platea comprendere perché la loro concentrazione intorno alle galassie attive è una statistica a posteriori, mentre le lenti gravitazionali non lo sono".

"Naturalmente lei è libero di non crederci - fu la risposta - ma l'ha detto un certo Einstein!

Vada a guardarsi la «croce» che porta il suo nome, e poi mi sappia dire …".

L'immagine della "Croce di Einstein" è riportata qui sotto (Fig. 16), e mostra quattro quasar centrati nel nucleo di una galassia a spirale che si trova a una distanza stimata di circa 500 milioni di anni luce.

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Fig. 16 (Einstein Cross)

Poiché i quasar sono ritenuti gli astri più distanti dell'universo e poiché l'osservazione di un simile raggruppamento profondo (dentro un secondo d'arco) sarebbe per lo meno improbabile, i cosmologi ne deducono che si tratta dell'allineamento accidentale di un unico oggetto distante nove miliardi di anni luce "spaccato" in quattro dalla massa della galassia molto più vicina a noi, che gli cade di fronte sulla nostra linea di vista.

Oppure i quasar sono quattro, e stanno emergendo ortogonalmente dal grembo della galassia con l'altissimo spostamento intrinseco dovuto alla loro giovane età. Ma così vien giù tutto, la Croce, il Big Bang e settant'anni di cosmologia.

Improbabile. L'allineamento, tuttavia, dovrebbe essere così esatto che la chance prospettica è calcolabile in 2 x 10-6, mentre la massa richiesta per il nucleo della galassia che fa da "lente" dovrebbe essere almeno 1.1 x 1010 masse solari!!

Questo valore eccede quello dei nuclei delle più massicce galassie dell'universo, mentre qualsiasi astronomo d'osservazione, potrebbe confermare ad un'occhiata che "l'oggetto lente" in questione è in realtà una galassia nana! Il lettore che cerca affannosamente di decidere dove stanno i quasar nell'universo, può tornare alla Figura 9, se crede; ma questa non è ancora tutta la storia della Croce di Einstein, perché Arp e Philip Crane, riprocessando le immagini ottenute dall'Hubble Space Telescope evidenziarono una linea Lyman alpha che connetteva il quasar di destra e quello sottostante al materiale di bassa densità della galassia "lente". La rivista "Nature" si rifiutò di pubblicare il risultato, che tuttavia apparve su "Physics Letters" (A, 168, 6) nel 1992.

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Fig. 16 bis Contorni di immagine che mostrano elongazioni e connessioni di materiale con il nucleo della galassia centrale (da Arp e Crane, 1992).

La reazione finale fu che Arp e i suoi subalterni non credono nemmeno alla Relatività Generale, ma anche qui la sottile distinzione è che essi semplicemente non credono che la "Croce di Einstein" sia davvero un effetto lente gravitazionale.

QUANTIZZAZIONE Ma esiste un'altra conferma (del tutto indipendente dai dati di Arp) che i redshift delle galassie e dei quasar non possono essere attribuiti all'espansione dell'universo. Si tratta della quantizzazione che emerge dall'analisi dell'intera distribuzione spettrale degli oggetti cosmici, veri e propri numeri magici ricorrenti, per i quali non si può evitare di darne almeno un cenno.

Uno dei risultati più raccapriccianti dell'interpretazione ortodossa è che l'affollamento dei quasar attorno alle galassie attive comporterebbe immensi coni allungati i cui vertici puntano invariabilmente verso la Terra. Abbiamo visto che un problema analogo sorge quando si tende a rappresentare in sezioni profonde la distribuzione delle galassie in base alla relazione distanza-velocità: appaiono inspiegabili incolonnamenti in fila indiana ("le dita di Dio") intervallati da enormi "pareti" e zone di vuoto ("struttura a bolle") con la terra ancora al centro (Figure 14-15).

Un'équipe di ricercatori esaminò i dati disponibili per galassie appartenenti a zone di cielo contrapposte (T. Broadhurst et alt., Nature, 343, 72, 1990) trovando fronti e muraglie di oggetti che ricorrevano in mezzo a zone quasi completamente vuote a intervalli regolari di 130 megaparsec! (Fig. 17). Questi dati inattesi provocarono enorme stupore, ma quando fu chiaro che essi contraddicevano qualsiasi teoria di formazione delle galassie in accordo col Big Bang, si obbiettò che le porzioni di cielo indagate erano troppo piccole per essere "rappresentative", e che si imponevano quindi ulteriori investigazioni su sezioni di cielo più estese e profonde, con telescopi più potenti. Che è poi un'impresa titanica, perché i telescopi di maggiore apertura hanno un campo d'osservazione ridottissimo (il 10 metri del Keck I spazia ad esempio 1/250 della grandezza della luna piena) e non è mai chiaro dove si sta guardando.

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Fig. 17

Tuttavia le numerose surveys successive hanno "confermato" l'esistenza di muraglie e di bolle di vuoto o, equivalentemente, che i picchi di redshift risultano sistematicamente quantizzati a valori preferiti. L'ortodossia rimane "abbottonata" nei confronti della periodicità, perché la presenza a intervalli discreti di muraglie e gusci concentrici di galassie riporterebbe trionfalmente Tolomeo al centro dell'universo; le "bolle di vuoto" tuttavia sono in alcuni casi così grandi che nella cornice del Big Bang non ci sarebbe tempo sufficiente per formarle.

Come ha dichiarato a più riprese l'astronoma Judith Coehn, le grandi strutture avrebbero potuto formarsi solo accordando un tempo di gran lunga superiore "alla presunta età dell'universo", cosicché non è più chiaro nemmeno all'ortodossia quale significato accordare alle molte reclamizzate "mappe di profondità" (vedi Figure 15-16).

L'evidenza che i redshift delle galassie compaiono a valori discreti era tuttavia disponibile da molto tempo. Nel 1976 l'astronomo del Caltech William Tifft rilevò da un campione numeroso di galassie binarie che le differenze di redshift cadono costantemente nell'intervallo di 72-144-216 km/sec. e multipli: il risultato venne subito ridicolizzato in quanto nessuno sarebbe stato disposto ad accordare velocità di recessioni quantizzate alle galassie binarie.

Inoltre i moti reciproci di interazione avrebbero dovuto cancellare qualsiasi periodicità anche nel caso che l'effetto fosse stato reale: Arp ricorda che si ironizzò a lungo sulla possibilità di un annullamento retroattivo del titolo accademico di Tifft. Ma tutte le rilevazioni successive su coppie di galassie confermarono costantemente questo risultato, che fu nuovamente evidenziato con misure radio dell'idrogeno neutro, che sono in grado di determinare i redshift nel modo più accurato. Dove siano andati a finire i moti gravitazionali relativi resta un mistero insoluto sul tavolo degli astrofisici (e dello stesso Arp!): nel frattempo però è diventata schiacciante l'evidenza che anche i redshift dei quasar sono fortemente quantizzati su valori preferiti.

L'astronomo svedese Karl Karlsson trovò che i picchi ricorrenti potevano essere riprodotti da una formula ∆log(1-z) = costante, che nella tabella riportata qui sotto z = 0,30 z = 0,60 z = 0,96 z = 1,41

z = 1,96 z = 2,64 z = 3,47 z = 4,49

assume il valore cost. = 0,089.

Il punto di vista tradizionale non è mai intervenuto a smentire la periodicità degli spostamenti verso il rosso dei quasar perché nella cornice cosmologica del Big Bang la loro collocazione a

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grandi distanze ha pur sempre un significato che è in stretta relazione con l'evoluzione dell'universo. Ma non c'è dubbio che qualunque possa essere il meccanismo che impartisce valori discreti allo spostamento delle righe delle galassie e dei quasar, questa è un'altra prova decisiva che il redshift non può essere attribuito a velocità.

Val la pena concludere questo blitz nella quantizzazione ricordando che nel sistema cosmologico a creazione continua di Arp e di Narlikar i redshift degli oggetti cosmici esprimono le loro età di formazione, ma non necessariamente le loro distanze. Così le loro età (apparenti) dovrebbero essere miscelate dal look back time in quantità intermedie e cancellare così ogni traccia della periodicità. La proposta di Arp e che la quantizzazione sia in relazione diretta a passaggi evolutivi "permessi" che eludono stati intermedi nella "progressione" della massa variabile, rendendo così la sua evoluzione osservabile solo a certi stati discreti. Questo riporta l'astrofisica nell'alveo della meccanica quantistica e costituisce una formidabile sfida per la ricerca e per la scienza del futuro.

LA RIVOLUZIONE PUÒ ATTENDERE? L'osservazione delle fasi di Venere e di Mercurio non produsse immediatamente l'Illuminismo, ma una lenta agonia. E' storia nota: grandi differenze nella percezione della realtà provocano inevitabilmente lacerazioni e conflitti profondi prima di riconciliarsi in un nuovo paradigma. Ma la rivoluzione di Copernico, la genialità di Keplero o l'evidenza empirica di Galileo non rappresentarono la vittoria degli illuminati sugli ottusi, dei sapienti sugli incolti, degli "eretici" sui "collaborazionisti". Al contrario, gli oppositori che all'inizio erano il mondo intero, furono spesso persone di grande intelligenza.

Il progresso scientifico si realizza però quasi sempre quando qualcuno, nella bonaccia dell'unanimità, esclama: "E' sbagliato!". O grida, come nella favola di Andersen, che il Re è nudo. Naturalmente questo non significa che la scienza abbia sempre torto, ma che l'Autorità istituzionalizzata della conoscenza deve essere perennemente in discussione: è vero che nessuna futura razionalità potrà mai riportare la terra al centro dell'universo o restituirle una forma piatta, ma è presumibile che tutte le teorie, compresa quella di Narlikar e Arp, siano destinate col tempo a essere riformulate. Ciò che non può essere cambiato, o modificato, o soppresso, sono i bracci, i filamenti, le connessioni osservative di materia che legano oggetti di diverso spostamento spettrale e che impongono la falsificazione dell'assunzione fondamentale della cosmologia.

Paradossalmente, è proprio l'accettazione dell'evidenza che si rivela l'ostacolo più difficile.

L'astronomo Massimo Capaccioli ha dichiarato (sottovoce) che "Forse Arp ha ragione, ma fra cento, o mille anni", e se ciò è vero questo stesso articolo è in anticipo di cento o mille anni, destinato ad essere fatto a pezzi dalla Contemporaneità in attesa di una eventuale riabilitazione postuma.

Chi allontana i dati di Arp e ne sospende il giudizio rinviando la questione all'infinito ragiona più o meno così: "Nonostante queste «scomode» osservazioni non sembra che ce la caviamo tanto male; abbiamo una teoria della creazione cosmica che è matematicamente corretta fino all'istante 10-43, un modello della struttura della materia che funziona e un emergente teoria delle Supercorde che promette di unificare il tutto e il nulla nel rispetto delle leggi della fisica. E' vero che la predizione di Stephen Hawking di trovare una master equation che spieghi tutto entro il duemila («da stampare su teeshirts»)non si è avverata, ma chi può dire cosa troveremo tra dieci anni? Perché l'universo deve essere per forza complesso quando può essere invece semplicissimo? Non è colpa della scienza se gli eventi sono caotici e impredicibili, non è colpa della scienza se la natura è competitiva e non cooperativa, o se la società è sempre più cinica e violenta: mica si può incolpare le GUT (Great Unified Theories) per la fondamentale irrazionalità dell'esistenza!.

E non c'è dubbio. Se si evita di considerare le confutazioni e le falsificazioni eliminandole dalla discussione nessuno si chiederà più se la scienza possa avere ottenuto le risposte

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sbagliate da tutte le più importanti questioni cosmologiche. E se sono sbagliate, anche il Big Bang, le GUT, le Supercorde e forse "la fondamentale irrazionalità dell'esistenza" sono da riscrivere. Come sempre in tutte le grandi rivoluzioni, il fatto è più culturale che scientifico.

Vorrei concludere questa mia esposizione della controversia con due aneddoti di natura sociologico-osservativa, se così si può dire. Il primo è a lieto fine, e riguarda il braccio che collega le due galassie con redshift altamente discorde NGC 7603 A e B e i due quasar che vi sono immersi, di cui ho già parlato in precedenza (vedi Fig. 9). Appena mi fu nota, comunicai questa decisiva scoperta anche a un insigne fisico relativista di Bologna, invitandolo senza mezzi termini a prendere una posizione.

La cortese risposta fu: "Non rifiuto di guardare nel cannocchiale di Galileo, e, delle due, di fronte all'immagine trasmessa sono incline a dar ragione a lei. Ma non posso giurarci. Qui vident sciunt? Mah … nel cannocchiale si vedevano le stelle medicee, ma anche Saturno tricorporeo … Aspettiamo. Il tempo farà (forse) giustizia".

Avrei dovuto accontentarmi? "Aspettiamo … che cosa? - replicai prontamente - Io guardo galassie da quarant'anni e a meno di dubitare delle fasi dei pianeti interni, giurerei che le due galassie in questione sono connesse da un visibile ponte di materia. Lei no? Può anche tenere i due quasar nello sfondo, se crede, confidando in una possibilità su un milione, ma non può allontanare le due galassie senza sopprimere l'astronomia osservativa. Il tempo servirà solo a mantenere lo status quo. Dobbiamo convenire che la storia che si ripete non ci insegna nulla?".

Dopo qualche tempo ricevetti una comunicazione che mi preannunciava l'inserimento dei dati di Arp in un'importante Seminario sulla Cosmologia per il dottorato in fisica, e sarò eternamente grato a quel Professore per il suo atteggiamento costruttivo.

Il secondo episodio è assai meno incoraggiante ed è un esempio tipico di come l'establishment cosmologico reagisce di fronte a osservazioni di segno opposto.

La Figura 18 mostra una mappa in raggi X ottenuta da W. Pietsch nel 1994 con il telescopio orbitale tedesco ROSAT centrato sulla galassia attiva ed espulsiva di tipo Seyfert NGC 4258.

Fig. 18

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Si notano immediatamente due intense emissioni X allineate ai due lati della galassia che è a sua volta una forte emittente di raggi X. Due sorgenti così perfettamente speculari avrebbero meno di una probabilità su mille di appaiarsi accidentalmente nello sfondo e in modo così esatto ai due bordi della galassia su una linea che passa per il nucleo. Era dunque di straordinario interesse astrofisico approfondire subito la natura di queste due sorgenti: ma un radioastronomo dichiarò preventivamente che le due emissioni erano in realtà "echi elettronici dovuti al sistema di rivelazione quando si gira lo strumento, ben noti a chi conosce la tecnica nel dettaglio"!

Disgraziatamente per lui le due emissioni avevano controparti ottiche che Pietsch, Vogler, Kahabaka, Jain e Klein ("Astronomy and Astrophysics Letters, 1995) confermarono subito come candidati quasar. Io non ebbi più notizie del radioastronomo e commentai la cosa su un giornaletto amatoriale, rammaricandomi che "dopo trent'anni di allineamenti prospettici nel visibile, abbiamo adesso false eco nei raggi X che possiedono controparti ottiche che poi risultano essere quasar …".

Ma la storia era ancora ben lontana dalla conclusione, perché nessuno voleva prendere gli spostamenti verso il rosso dei candidati quasar. Arp riferisce nel suo recente ultimo libro "Seeing Red" che numerose Istituzioni richiesero l'analisi spettroscopica degli oggetti, senza alcun esito. Ci riuscì alla fine, due anni dopo, Margaret Burbidge, che con il riflettore di tre metri di Monte Hamilton rilevò z = 0,65 per il quasar a sinistra e z = 0,40 per quello di destra. Gli spettri ottenuti sono riprodotti nei grafici che mostro qui sotto, e non è senza emozione che il lettore può vedere ancora una volta le righe di elementi noti come l'ossigeno, il magnesio, l'idrogeno, etc. posizionate su lunghezze d'onda lontanissime da quelle che si formano in laboratorio.

Fig. 19 e 19 bis

E' un'altra decisiva testimonianza di differenti stati della materia cosmica e un'altra cruciale osservazione a favore della natura riproduttiva delle galassie.

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La Rivoluzione può attendere? Con commenti indipendenti sopra quel risultato, Arp ed io adoperammo termini analoghi di "tumulazione della cosmologia corrente": solo che io parlai di "ultimo chiodo nella bara del Big Bang" e lui di "ultimo fiore". Anche questo, credo, fa la differenza fra un piccolo dilettante e un grande scienziato.

Note 1

Recenti misurazioni della struttura fine su un campione di quasar effettuato da J. Webb e J. Prohaska (Physical Review, Sept. 2001) sembrano riproporre la possibilità di variazioni intrinseche nella carica dell'elettrone. Integrando questi risultati nella cornice cosmologica che colloca i quasar ai confini dell'universo, Paul Davies e altri hanno suggerito la possibilità che al momento del Big Bang la velocità della luce tendesse all'infinito! (Nature, agosto 2002). Qui il commento potrebbe essere: che duro prezzo sono disposti a pagare i sostenitori della Palla di Fuoco per tenere i quasar alle loro distanze di redshift.

2

L'induzione ricavata da Arp su base osservativa ha una formulazione matematica completa e rigorosa nella "teoria della massa variabile" sviluppata da Hoyle e Narlikar già agli inizi degli anni Settanta ("Action at Distance in Physics and Cosmology", S. Francisco, 1974). E' chiamata anche teoria generale della gravità conforme e descrive la massa delle particelle come funzione della posizione e del tempo. Informazioni dettagliate sono reperibili anche nel nuovo libro di Arp "Seeing Red", Apeiron, 1998, sull'Astrophysical Journal, Narlikar e Arp, 405:51-56, 1993, in "Origini", Autori vari, Il Poligrafo, 1994 e nel volume dell'autore di questo articolo, "Eppur non si muove!", - La controversia sull'espansione dell'universo - Studio Stampa, 1996.

----[Una presentazione dell'autore si trova nel numero 2 di Episteme - si veda anche il suo contributo nella sezione "Commenti Ricevuti" della I Parte di questo stesso fascicolo della rivista] "virgilio" <guervitt@virgilio.it>

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Beyond Maxwell-Lorentz Electrodynamics (George Galeczki) I. Maxwell's Equations Freeman Dyson published twelve years ago [1] "Feynman's proof of the Maxwell equations".

He recalls that in 1948 Feynman showed him this "proof assuming only Newton's law of motion and the commutation relation between position and velocity for a single particle."

Although formally obtaining the two "vacuum equations" (i.e. those without source terms), the claimed "proof" of the full Maxwell equations is wrong mathematically, physically and conceptually. On top of all this, it expresses the - nowadays common - arrogance of mathematical physicists giving priority to formalism against empirical facts.

As a matter of fact, Maxwell's equations (ME) represent the mathematical expression of the experimentally discovered laws of Gauss, Ampère and Faraday and are widely used in physics and engineering. Several remarks and comments are in order, each of them being subsequently discussed in more detail: 1/ The basic formulation of ME - as derived from experiments - is in integral form pertaining to a finite, closed area or volume.

2/ The ME are formulated for continuous fields and are called, therefore, field equations.

3/ ME hold for closed circuits only.

4/ The sources of the fields are continuous charges and continuous current densities.

The discrete, quantized charges introduced in Maxwell's theory are foreign elements.

5/ ME are tautological in the sense that they merely represent relationships between fields and their sources. One has to provide the initial charge distribution in order to be able to calculate the field distribution, or vice versa.

6/ ME is unable to describe the interaction between two discrete charges.

7/ ME is unable to supply the equation of motion of one charge in the field produced by all others.

8/ ME are not suited for the description of open circuits like antennas.

9/ ME are unable to prescribe the exact conditions under which a system will radiate, or not.

The notorious example is Bohr's planetary model of the hydrogen atom.

10/ ME are unable to provide a stable model for the elementary charge.

11/ ME are generally covariant and do not single out the Lorentz transformation (LT) of the "special" theory of relativity (STR).

12/ ME are formulated in terms of independent, Eulerian coordinates x, y, z, t and partial derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t .

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ME in their original, integral form and in modern notation are:

∫

E.ds = - ∫ ∫ (∂B/∂t).da

∫∫

D.da =

∫∫∫

∫∫ ∫

ρ dV

B.da = 0

H.ds =

∫∫

(1) (j + ∂D/∂t).da

(2)

Contained in the above is the equation of continuity:

∫∫

j.da = - ∫ ∫ ∫ ρdV

(3)

where ρ and j denote charge and current density, respectively.

In all cases the regions of integration are assumed to be stationary and mechanically rigid.

ME in differential form , as derived from (1), (2) and (3) by means of Stokes' and Gauss' theorem, are: ∇ × H = j + ∂D/∂t

∇ × E = -∂B/∂t

(4)

∇.D = ρ

∇.B = 0

(5)

and the corresponding equation of continuity: ∇ . j = -∂ρ/∂t

(6)

ME in differential form express the relationship that must exist between the four field vectors E, D, H and B at any point within a continuous medium (?). In this form, because they involve space derivatives, they cannot be expected to yield information at points of discontinuity in the medium. However, the integral form can always be used to determine what happpens at the boundary surface between different media. It follows then, that the tangential components of E and H (except perfect conductors) and the normal components of B and D (if no surface charges are present) have to be continuous at the interface.

II. Maxwell's Equations and "Special" Relativity As already said, besides generalizing Ampère's circuital law by introducing the "displacement current", Maxwell's achievment was to express the experimental laws of Coulomb, Gauss, Ampère, Faraday in mathematical terms. The modern, vector form of ME was introduced by Gibbs. Einstein's "special" relativity of 1905 has built heavily upon electromagnetism and, assuming the validity of ME in all inertial frames of reference (IFR's) introduced the incomprehensible "postulate of light velocity invariance". This constancy is not that refering to the light source - a wellknown fact in classical wave theory - but to the independence of the velocity of light from the uniform velocity of the observer/detector relative to the source.

Since in the special case of vacuum-as-continuous-medium the ME displayed covariance (not invariance!) under the so called Lorentz transformations (LT), ME and STR became indissolubly tied together, one implying so to say the other. This strategy proved itself very useful, since every criticism of STR was authomatically seen as criticism of ME, thus contributing to the survival of the contradiction ridden STR. The said bi-univocal correspondence between ME and STR is manifested, however, only if one has in mind the differential form of ME. The reason is that STR is a local, point-event theory, with local simultaneity and position and velocity dependent time! Due to this feature of STR, only local conservation laws of energy and momentum are compatible with

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STR. While valid in the hydrodynamic approximation - a continuum theory - the local, differential conservation laws fail in the case of discrete, extended systems. The global time required in this case, independent of position and velocity, is anathema to STR. Farady's law of induction assumes tacitely such a global time and distant simultaneity, thus allowing the definition of inductance and self-inductance for macroscopic, closed circuits. Since the stationary circuits appearing in the integral form of ME are incompatible with STR, it is quite understandable why the STR "philosophy" gave almost exclusive prominence to ME in differential form and eliminated the integral form from physics textbooks and monographies.

As a matter of fact, this form - more rich in physical information - is actively in use in engineering books on electromagnetism [2].

III. General covariance of Maxwell's equations It was repeatedly and forcefully pointed out by Post [3] that Maxwell's equations are general covariant. Post quotes that Kottler, Cartan and van Dantzig (KCD), quite independently of one another concluded on the natural invariance of ME, independent of any metric or linear connection. Post strongly emphasized the clean functional separation obtainable between the constitutive equations { D(E), B(H), J(E) } and the field equations.

In this approach the constitutive equations instead of ME carry all the metric information, while the field equations (4) and (5) are covariant under all possible space and time coordinate transformations: Galilean, Lorentzian, conform and so on. The use of (E, D, B, H) rather than two field vectors eliminates the cgs free-space field identification. The latter tied the cgs situation irrevocably to an inertial reference frame. A free-space inertial situation is defined by an explicit constitutive relation: D = Îľ0E

,

B = Âľ0H

(7)

Which can be proven to be invariant under the Lorentz group, as well as under scale changes of the conformal group. Here is the place to mention the qualitative difference between invariance and covariance: a physical law is said to be invariant under a coordinate transformation when the vectors/tensors entering the law remain unchanged, while in the case of covariance the components of the vectors/tensors are transformed, or in Thomas Phipps' words "scrambled", according to the same rules as the coordinates,. Only after performing this scrambling the equations in question remain form invariant.

The superiority of the KCD approach is that the field equations retain their form when a transition is made from an inertial to a non-inertial frame, in particular a rotating frame.

(N.B. Jan Evert Post was the chief theoretician of the ring laser gyro project, which produced the most sensible detector of rotation, i.e. of the degree of non-inertiality). Moreover, the form invariance of ME is independent of whether the fields exist in free space or in matter. The information about the reference frame and the state of motion of the matter therein is conveyed exclusively by the nature of the constitutive equations. The general form of these equations is tensorial and the applications to specific problems was intensively investigated

by Post.

IV. The force of Lorentz and Maxwell's equations It is clear from what has been said till now that the Maxwell field equations (4) and (5) expresses a law of nature and will retain their validity so long their limitation to closed circuits is assured. The tautological nature of ME follows from the absence of "detector charges" in the rhs, since only the source charges and their distribution is considered. It means that the ME are intrinsically unable to provide either a force law between discrete charges, or an equation of motion for individual charge within a system of charges. Here I can

109

mention another fundamental difficulty connected with the discrete vs. continuum dichotomy, reflected in the use of two different kinds of coordinates: the already mentioned four independent, Eulerian x, y, z, t and the three time dependent Lagrangean coordinates x(t), y(t), z(t). The former are suited for field theories, while the later for particle dynamics. Fields are functions of x, y, z, t, meaning that they have different values at the points of a 4D continuum. They don't "propagate" in the 4D continuum. The solutions x(t), y(t), z(t) of the dynamical equations of motion, on the other hand, are 3D vectors and the coordinates "move so to say - with the particle". This already shows that STR is at least formally compatible with pure field theories, but incompatible with (discrete) particle dynamics [4]. Anyway, quite independently of STR, in order to brake the tautology, ME have to be completed by a force law and an equation of motion for discrete charges, the very program of Lorentz who introduced the quantized electrical charges into Maxwell's field theory. The ME supplemented by the Lorentz force-law (LF) is called Maxwell-Lorentz electrodynamics (MLE). Lorentz himself remained unsatisfied with his force-law: FL = q (E + v × B)

(8)

In his own words [5]: "It is got by generalizing the results of electromagnetic experiments.

The first term represents the force acting on an electron in an electrostatic field [F1=qE] . On the other hand, the part of the force expressed by the second term may be derived from the law according to which an element of a wire carrying a currect is acted on by a magnetic field [dF2 = (qv x B , assuming Jds = qv ] . After having been led in one particular case to the existence of the force [F1 = qE] and in another to that of the force [F2 = qv x B ] , we now combine the two in the way shown in the equation, going beyond the direct result of experiments by the assumption that in general the two forces exist at the same time." (a) The two 'particular cases' here 'combined' are, however, quite incompatible. In one case we have a charge at rest, in the other the charges are moving. (b) Experiments with 'a wire carrying current' have to do with neutral currents, yet the derivation contradicts this neutrality. The discovery of the Hall effect, formally described as a "modified Ohm's law": j = σE + k(E × B)

(9)

where σ is the conductivity and k a constant, seemingly supports (8), but everybody familiar with the experimental set-up used in the Hall effect studies will agree that E and B above belong to different systems: a dc - or ac - source for E and a completely separated permanent or electro-magnet for B. Maxwell's theory requires, however that E and B belong to the same system of charges and currents. As shown elsewhere [6], the Lorentz force should have been written as: FL = q (E(1) + v × B(2))

(10)

i.e. a phenomenological external force, rather than fundamental force acting on a charge belonging to the same system, as implied by ME. The upper indexes (1) and (2) indicate that the electric, respective magnetic field belong to different systems, therefore ME and LF do not form a coherent Maxwell-Lorentz theory as claimed in present day textbooks and monographies! The reason for this persisting mess is the seeming compliance with SRT's LT. This belief is, however, totally wrong, since: (a) The LT apply only to E and B belonging to the same system and (b) The velocity v in most applications is a non-uniform velocity between magnets an current carrying wires, while the velocity entering the LT is the

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uniform relative velocity between two inertial frames of reference. This confusion goes back to Einstein's failure to distinguish between his theory involving schesic velocities referred to abstract "reference frames" and relative velocities between moving masses, as implied by Mach's program. For this reason STR is not a true relativity theory! Using a somewhat different terminology - 'principle of relativity vs. 'principle of relative motion' this point was discussed in a paper by Bartocci and Capria [7], too. This explains also why the aged Ernst Mach unmistakable declined the rôle of spiritual father of the "special" (very special, indeed!) theory of the young Einstein.

V. Magnetic field, vector potential and induction In the spirit of the ME in their integral form, B(2) in (10) has always to be produced by a closed current loop: B(2)(r) = I'

∫

(ds' × R)/R3

(11)

where R = r - r' and the integral is performed around the closed current loop. Attempts to generalize the Biot-Savart law for time-variable magnetic fields have been made by Jefimenco [8] in the form: B = (µ0/4π) ∫ ∫ ∫ {[j]/r² + (1/rc)∂[j]/∂t} × (r/r) dV'

(12)

where [..] denotes the retardation symbol indicating that the quantities between the square brackets are to be evaluated for t' = t - r/c , where t is the moment for which B is calculated. It is interesting to note that that Eq. (12) does not contain displacement currents, thus indicating that although time-dependent magnetic fields and displacement currents are coupled together, displacement currents are not sources of magnetic fields in the conventional sense.

Definition (11) of the magnetic field B - rightly called magnetic flux density in older books is incompatible with the "Lorentz transformed E field" definition of B in "special" relativistic electromagnetism: B = V×E

(13)

valid for uniform velocity V only! This incompatibility brings us to the most important issue of (electromagnetic) induction and the status of Faraday's "flux rule". According to textbook (and also monography) knowledge, electromagnetic induction were always due to a time variable magnetic flux crossing a closed conducting loop. Although Faraday discovered both this so called transformer induction as well as the motional induction, only the first is embedded in the integral form of ME formulated for stationary integration regions. This deficiency of the integral ME is, of course, transferred to the differential form of the Maxwellian law of induction: ∇ × E = -∂B/∂t

(4)

The correct expression for the induced electromotive force (emf), in terms of the vector potential A, follows from the integral form: emf =

∫

E.ds - (d/dt) ∫ ∫ B.da = -(d/dt) ∫ ∫ (∇ × A).da = -(d/dt) ∫ A.ds

which provides the formula:

(14)

111

Eind = -dA/dt

(15)

for the induced electric field Eind. Keeping the integration region stationary, one gets the 'transformer field': Eind = -∂A/∂t

(16)

The difference between Eq. (15) containing the total time derivative d/dt and Eq. (16) containing the partial time derivative ∂/∂t is huge and has fatal consequences for "special" relativity! This is obvious, since in ME the four partial derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t are on equal footing (see, for example, Eq.(6)) and obey the LT. The presence of the total time derivative, by giving to the time derivative a distinct status, destroys the Lorentz covariance of ME! Here is the place to mention the incompleteness of the traditional formula for the total derivative of a vector field: dA/dt = ∂A/∂t + (v.∇)A

(17)

and the time rate of change "seen" by a point moving with velocity v in a vector field A [9]: dA/dt = ∂A/∂t + (v.∇)A + (A.∇)v

(18)

Although the vector identity: (v.∇)A + (A.∇)v + A × (∇ × v) - ∇(v.A) = -v × (∇× A) = -v × B

(19)

for v.A = const. and ∇ × v = 0 leads to the 150 years old formula of Neumann: Eind = -∂A/∂t + v × B

(20)

equation (18) covers all known situation of electromagnetic induction, including those where Eq. (19) fails. Eq. (20) is still in exclusive use, although it has never been rigorously justified.

Neumann - just like later Lorentz with his force law (8) - just juxtaposed Faraday's and Maxwell's transformer field and the empirical field found in the unipolar induction experiments of Faraday and in the (then) recently discovered Hall effect, called motional induction field. Wesley derived for the first time (!) the most general law of induction which includes (20) as a particular case. The surprising result is that the law based upon (18) is able to describe phenomena governed by the term (v.∇)A like the Aharonov-Bohm (AB) effect and the Marinov motor [10]. The demystification of the "strange quantum-mechanical (AB) effect" [10] and its explanation in the framework of electrodynamics has been a real tour de force. The term (A.∇)v is presently insufficiently investigated, but preliminary results seem to support its explaining the interaction between two toroidal magnets (closed magnetic field configurations) [11], which, according to Maxwell's electromagnetism should not interact.

The local form of the correct law of induction, involving the total derivative (18), puts an end to the perennial disputes between the supporters of fields and potentials, respectively. It has to be clear that the description by means of A is more general than the usual by means of B, since it provides an induced electric field even if ∇Φ = 0 (Φ denotes here the scalar potential), ∂A/∂t = 0 and B = ∇ × A = 0 .

One is tempted to say that Maxwellian electrodynamics overcame all difficulties and retained its original form since, after all, the use of the truncated form (17) for the total derivative was not Maxwell's fault. The painful fact for STR-supporters is, however, that Eqs. (4) and (5) do

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not cover all experimental situation and - acutely painful - that they do not remain Lorentz covariant if one replaces the partial time derivative with the total one!!

VI. Beyond the Lorentz force law The force law of Lorentz (8) applies only in situations where the fields E and B are static, or quasistatic, when radiation could safely be neglected. In such situations, however, Eqs. (4) and (5) decouple in two pairs of electrostatic and magnetostatic equations, respectively: ∇×E = 0

;

∇D = ρ

(21)

∇×B = j

;

∇B = 0

(22)

and

This explains the upper indexes appearing in Eq. (10), indicating that the sources of E(1) and B(2) are different. Moreover, as already pointed out, the field B has to be produced by a closed current loop. It follows then, that the force of Lorentz can by no means be applied to a system of two charges, so that charge (1) moves in the field B(2) and vice-versa: d(m1v1)/dt = q1(E(2) + v1 × B(2))

;

d(m2v2)/dt = q2(E(1) + v2 × B(1))

(23)

No wonder that this two-body problem would violate the linear momentum conservation law, since the sum of internal forces would be different from zero! The replacement of particle linear momentum p by (p - q.A) - as suggested by the "operator formalism" of quantum mechanics - doesn't save the conservation law.

The inability of Lorentz force to describe the simplest system of two interacting charges is presented in textbooks and monographies as due to the fact that "at least one charge path has to be closed", which is obviously false! In a dense plasma, for example, even in external magnetic fields, where charges are permanently colliding with each other, there may well be no closed paths at all. The fact that the external magnetic field is produced by the closed circuits of the electromagnets is irrelevant for the plasma system!

There exists a rich experimental evidence for the failure of Maxwell-Lorentz electrodynamics at low velocities (v/c << 1), which is lethal to MLE, since the laws of Gauss, Ampère, Faraday were all formulated according to the experimental results obtained for low velocities.

Moreover, the interactions between electric currents and magnets were all investigated by using metallic conductors. The microscopic nature of currents in metallic conductors remained undecided, till Weber introduced atomism, i.e. quantized electric charges in physics.

He assumed that electric currents consists of a stream of electrons and made first the identification: Ids = qv

(24)

With this, Weber succeeded to derive Ampère's law between metallic current elements: d²FA = (I.I'R/R3)[-2ds.ds' + 3(R.ds)(R.ds')/R²]

(25)

(I, I' denote currents and R = r - r') from his interaction law between discrete, moving electrons in a metallic conductor: FW = (qq'R/R3)[1 + V²/c² - 3(V.R)²/2c²R² + R.dV/dt.c²]

(26)

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vhere V = v - v' and dV/dt denote the relative velocity and the relative acceleration between the moving charges. This truly relativistic (Machian) and instantaneous force law explains all known experiments at low velocities with metallic currents, including Ampère's moving bridge one and the 'electromagnetic rail gun' used in frame of the SDI program [12] which both imply longitudinal forces between parallel metallic current elements. It is notorious that the Lorentz force - acting perpendicular on current elements - is unable to account for these experiments. In spite of this, the belief in uniqueness of the GrassmannBiot-Savart-Lorentz (GBSL) force law is so strong, that Ampère's law (25) - called by Maxwell "the cardinal formula of electrodynamics" - is not even mentioned in the vast literature on electrodynamics. Once again, this belief is motivated by the seeming compliance of the Lorentz force (8) with the LT, i.e. with STR. Wesley put his finger on the sorepoint of the interminable controversy about Lorentz vs. Ampère force. The supporters of the LF cramp to the equivalence of the two forces when two closed current loops are involved. This is totally irrelevant as it is only a question of the analysis of the mechanical forces between the two objects, the metallic bridge and the remainder of the circuit as a mechanical object.

However, Grassmann's derivation of his law (equivalent with that of Lorentz) is only valid for mechanically rigid electrical circuits. This means that the GBSL law cannot be applied to the electrical circuit involved in the non-rigid Ampère bridge!

Weber's law correctly describes the motion of electric charges in vacuum - for example in the electron microscope - since in this case E and B are external and B is produced by closed current loops. The useful phenomenon of "self-focussing", or "pinch effect" wellknown to electron microscopist, is also explainable within the traditional frame of Maxwellian electrodynamics, as attraction between parallel currents.

Remarkably, Ampère's and Weber's laws comply with Newton's third law (actio = reaction), since the forces act instantaneously along the line joining the current elements, or the moving charges. This condition for law velocities is one of the requirements for a system being non-radiating even for charges moving with high (v >> c) velocities. As a matter of fact, both the hydrogen atom and the 'rotating ring electron model' are conservative, i.e. non-radiating, provided the forces are of Weber type!

VII. Some comments on rapidly varying fields and radiation 1/ The characteristic feature of Maxwell's equations is the presence of the terms ∂D/∂t and ∂B/∂t which couple the electric and magnetic fields and lead to the existence of electromagnetic waves, or radiation. The field equations completed with the Lorentz force law (the MEL equations) are therefore incoherent, since the fields in the LF expression are static, or quasistatic, which means that radiation is neglected. No wonder that the attempts of Dirac and others to add "radiation terms" to the equation of motion of the electron leads to strange "runaway solutions" and other unsolved difficulties.

2/ The 104 years old Liénard-Wichert formula [9] for the retarded potentials corresponding to a point-charge moving with acceleration a along the positive direction of the x-axis has been seriously questioned by Chubykalo and Smirnov-Rueda [13] and independently by Wesley [9]. This indicates that the "special" relativistic Maxwell-Lorentz electromagnetism is an unsatisfactory theory by itself, although the reason is hidden in the mathematics of d'Alembert's wave equation, rather than in the ME themselves.

It is textbook knowledge [13] that the solutions of the wave equation (d'Alembertian) are: Φ =

∫∫∫

[ρ]/R.dV + Φ0

;

A =

∫∫∫

[j]/R.dV + A0

(27)

114

which are the retarded potentials. Φ0 and A0 denote the solutions of the homogeneous wave equation. This is OK. From here one usually derives: Φ = q/(R - v.R/c)

;

A = qv/(cR - v.R)

(28)

and the fields: E = - q(1 v²/c²)(R - vR/c)/(R - R.v)3 + qR × {(R - vR/c) × a}/(R - R.v/c)3c²

(29)

B = (R × E)/R Chubykalo and Smirnov-Rueda show that formula (29) does not satisfy the d'Alembert equation along the x-axis at any time. This follows from the fact that the wave equation for Exdescribes only transverse modes and - on the other hand - the x-component according to (29) is different from zero. Thus, the Liénard-Wichert potentials, as solutions of the complete set of Maxwell equations, are inadequate for describing the properties of electromagnetic field along the direction of an arbitrarily moving charge. Whitney [14] found another inadequacy of the Liénard-Wichert potentials for describing the properties of relativistic fields. Further, it is easy to verify that the Poynting vector calculated with Eq. (29) equals zero, i.e. no energy transport takes place along the x-axis, while the energy conservation law requires both energy density and divergence of the Poynting vector to be different from zero!

The criticism of Wesley [9] is even more fundamental and relies upon the fact that in the wave equation of a field theory, the four variables x, y, z, t have to be independent (Eulerian) as explained also in [4]. Despite this clear mathematical requirement that r' and t' be independent variables, in the integral representation (28) of the retarded potentials Liénard and Wiechert argued incorrectly that the independent space variable r' is a dependent function of the time variable t'.The change in the 'delta function' - which accounts for the point-like nature of the charge - leads to the correct expressions for the retarded Coulomb potential: Φr = q'/Rr

(30)

where Rr = R(t)/(1 - v/c) for an observer moving directly away with v < c from the point charge.

3/ The ubiquitous presence of radiation, i.e. of electromagnetic fields detached from their fields requires the existence of a unique, fundamental frame of reference, relative to which the energy transmission velocity is "c". This is a consequence of the fact that the velocity of light doesn't obey either the hypotheses of Ritz ("ballistic propagation", or dependence on the state of motion of the source), or the untenable second postulate of "special" relativity which is discused in [15]. The existence of a fundamental frame of reference which could be experimentally approached by successive approximations, is in line with Maxwell theory, but disagrees with "special relativistic electrodynamics" which states the validity of ME in any inertial frame of reference.

VIII. Conclusions - Maxwell's equations (ME) retain their validity for closed current loops.

- ME have to be completed with a force-law and a corresponding equation of motion.

- In all applications the force of Lorentz is a phenomenological external force, with different

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sources for E and B, the latter being produced by closed circuits.

- MLE fails to explain low-velocity experiments with non-rigid loops.

- Ampère and Weber's force law accounts for all electrodynamic phenomena in which radiation can be neglected.

- MLE in its accepted form is unable to account for all induction phenomena.

- The correct law of induction is given by the total derivative of the vector potential. This is compatible with ME, but destroys the Lorentz covariance of the theory.

- The vector potential is of primary importance and is uniquely defined for specific systems.

- There is no "gauge invariance".

- Low-velocity Weber electrodynamics is truly relativistic in the sense of Mach.

- The presence of radiation requires an absolute, fundamental frame of reference.

References [1] Dyson F. J. "Feynman's proof of Maxwell equations", Am. J. Phys. 58 (1990) 209-211 [2] Jordan E. C. and Balmain K. G., "Electromagnetic Waves and Radiating Systems" (Prentice-Hall, Inc., New Jersey, 1968) p. 103 [3] Post E. J. "Formal Structure of Electrodynamics" (North Holland Publ. Co.,Amsterdam, 1962); "Kottler-Cartan-van Dantzig (KCD) and Noninertial Systems", Found. of Physics, 9 (1976) 619-640 [4] Galeczki G., "Minkowski Scalar Invariant Incompatible with any Equation of Motion" (Proc. 2-nd Intrnational Workshop: "Physics as a Science", Koeln, 1997) [5] O'Rahilly A., "Electromagnetic Theory: A Critical Examination of Fundamentals",Dover Publ. Inc., New York, 1965) Vol. 2, p. 561 [6] Galeczki G., "What does the Lorentz force have to do with Maxwell's equations?", Galilean Electrodynamics, 9 (1998) 95-98; Galeczki G., "What does the Lorentz force have to do with special relativity?", Galilean Electrodynamics 8 (1997) 1-4 [7] Bartocci U. and Mamone Capria M., "Symmetries and Asymmetries in Classical and Relativistic Electrodynamics", Found. of Physics 7, (1991) 787-801 [8] Jefimenko O. D., "Comment on "On the equivalence of the laws of Biot-Savart and Ampère", by T. A. Weber and D. J. Macomb [Am. J. Phys. 57, (1989) 57-59]", Am. J. Phys. 58, May 1990, 505 [9] Wesley J. P.,"Induction Produces Aharonov-Bohm Effect", Apeiron, 5 (1998) 89-95; [10] Selected Topics in SCIENTIFIC PHYSICS" (Benjamin Wesley, Blumberg, 2002) [11] "Force between two identical coaxial toroidal solenoids" (in print) [12] Graneau P. and Graneau N, "Newton versus Einstein: How Matter Interacts with Matter"

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(Carlton Press, Inc., New York, 1993); "Wesley J. P., Selected Topics in Advanced Fundamental Physics" (Benjamin Wesley, Blumberg, 1991 [13] Chubykalo A. E., "Action at a distance as a full-value solution of Maxwell equations: The basis and application of the separated-potentials method", Phys. Rev. E, 53, (1996) 5373-5381 [14] Landau L. and Lifchitz E. M., "ThĂŠorie du Champ" (Ă&#x2030;ditions de la Paix, Moscou, 1965) [15] Whitney C. K. "A quantum of light shed on classical potentials and fields", Apeiron (?)

[16] Galeczki G. and Marquardt P., "Requiem fuer die Spezielle Relativitaet" (Haag und Herchen, Frankfurt a. M., 1997)

Acknowledgement I am indebted to Paul Wesley, Thomas Phipps Jr., Jan Post and Patrick Cornille for stimulating exchange of ideas during the years.

----George Galeczki received a Licence in Physics from Bucharest University in 1968, M.Sc. (1975) and D.Sc. (1979) degrees from The Technion - Israel Institute of Technology - in Haifa (Israel), for works in the field of ordered magnetism. In 1979 he received the Michael Landau for his research beyond his work toward a degree. After lecturing three semesters at the Technion, he moved to the governmental research center RAFAEL, where he did (mostly classified) work on HgCdTe-infrared detectors. After cumulating two sabbatical years, he left Israel, responding to an invitation from the University of Cologne (Germany). There he did research on heterodyne HgCdTe-infrared detectors for astrophysical applications and continued, in parallel, his critical work on fundamental physics started in 1978 under the influence of Nathan Rosen ("the EPR one") and Marinov's successful experiment to measure the absolute velocity of the Earth. He published about 50 papers on magnetism, narrowbandgap semiconductor physics, nanoscopy, and about an equal number of papers criticizing "special" and general relativities, Copenhagen quantum mechanics, and Big Bang theory. He is the co-author (with Peter Marquardt) of REQUIEM TO SPECIAL RELATIVITY (in German, published by Haag + Herchen, Frankfurt/Main, 1997) and organizer (with P. Marquardt and J. P. Wesley) of three (1997, 2000, 2002)International Workshops: PHYSICS AS A SCIENCE. He is presently an independent science consultant, science writer, president of the Society for the Advancement of Physics, R.S. and member of the Natural Philosophy Alliance.

Society for the Advancement of Physics, R.S. nc-galeczge@netcologne.de

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The State of Experimental Evidence for Length Contraction, 2002 (Delbert J. Larson) Dedication.

I wish to dedicate this work to the memory of John E. Chappell, Jr. In all my travels I have never met anyone so singly and heroically devoted to debunking the special theory of relativity. John led a difficult life, made difficult largely because of his questioning of the correctness of the scientific status quo coupled with his stubborn refusal to simply go away quietly and do something else. It is unfortunate that John lived his life when he did. In most of the recent past centuries, John's view that logic should prevail over absurdity was accepted as an axiom. It is my hope that most future centuries will return to that common sense notion as well, sparing future logic-based scholars the torment and ridicule that John had to endure during his time in this world. The earthly community of space time research has suffered a severe loss with his passing. We shall miss him. ***** Abstract. The idea that physical objects become shorter as they move is now well established in physical theory. Both the classical theories of Lorentz, Larmor, Fitzgerald and Poincare and the more radical special theory of relativity of Einstein incorporate a physical length contraction into their worldview. However, no direct measurement of length contraction has ever been done. One experiment that tried to observe the effect of a length contraction was done by Sherwin, who found no evidence of a length contraction. This paper will analyze the assumptions underlying Sherwin's experiment to show that Sherwin's experiment is in fact equivocal concerning the existence of a length contraction. This paper will also make mention of another important recent observation that has relevance to the issue of the existence of physical length contraction. ***** Introduction.

In an earlier work (see reference 1) I tried to completely analyze the state of evidence for and against the existence of a length contraction in nature. My conclusion at that time was that one could not with scientific certainty state that a length contraction really exists. While there was and is strong evidence for a time dilation (see reference 2), there has never been any direct measurement of length contraction. In fact, one very important experiment, by Sherwin (see reference 3), seemed to provide compelling evidence that there was indeed no length contraction. The intervening years between my earlier work and the present have not changed the fact that no direct measurement of length contraction has been made. However, I now understand that Sherwin's experiment may not be as strong a refutation of length contraction as Sherwin and I had at first believed. In addition, a second set of experiments has come into existence in the last several years concerning earth tide measurements that has a bearing on the experimental evidence for length contraction. This paper will look in some depth into the possible physics behind Sherwin's experiment, and briefly discuss the issues involving measurements of earth tides at CERN.

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Sherwin's Experiment.

My earlier work (reference 1) showed that despite the vast majority of experiments done to that time no firm conclusion could be made as to whether or not a length contraction really exists. Indeed, the earlier paper showed that if 1) moving observers incorrectly assume that the speed of light is isotropic and equal to c in their reference frame; and 2) a Larmorian (or Lorentzian) time dilation exists in nature; then 3) the observers will arrive at the conclusion that the Lorentz transformations are valid for electrodynamic phenomena, even if a length contraction does not actually exist in nature. But beyond the issue of electrodynamics (such as that used in the design of particle accelerators) reference 1 also shows that no other experiment done can definitely prove that there is a length contraction. Especially important is the Michelson Morley experiment. Reference 1 goes into detail about the possibility that the null result of the Michelson Morley experiment might be caused by node entrapment. The node entrapment theory is that the electromagnetic oscillation is forced to be null at a pair of boundaries (the mirrors), and it is this enforced boundary condition that also forces zero fringe shifts to result from the Michelson Morley experiment. Once you remove that famous experiment (and others directly related to it) from the evidence in support of length contraction, you quickly find that there are no experiments that show the reality of the length contraction.

However, while there are no experiments that unequivocally prove the existence of a length contraction, I emphasized one experiment that strongly suggested the absence of a length contraction. That crucial experiment was the one done by Sherwin (reference 3).

In Sherwin's experiment, a spring was made to revolve at a high rate. Sherwin realized that if the Lorentz worldview was correct, that the spring would undergo a length contraction when it was aligned with its motion through the ether, while it would not experience the length contraction when it was aligned perpendicular to its motion through the ether. By arranging for the rotational motion of the spring to be in resonance with the spring's natural harmonic motion, Sherwin expected to see oscillations excited in the spring. He saw no such oscillations. Sherwin interpreted the lack of oscillations as experimental support for Einstein's special relativity (reference 4), and experimental evidence in contradiction to the Lorentz theory (reference 5). In my earlier work (reference 1) I interpreted Sherwin's null result as indicating the lack of a length contraction. Further thought indicates to me that the actual situation is less than clear, and that both Sherwin and I were basing our conclusions on an unstated assumption.

The relevant issue is what happens to the spring as it makes its rotation, and the essence of this question gets down to a matter of what fundamentally determines an object's length. As far as present science is advanced, I would summarize my belief that length is determined by the spacings between the nuclei of the atoms making up the object. Those spacings can be analytically determined by quantum mechanics. Within a single atom, the distribution of the electron cloud is determined by two competing effects. More energy is required for increased curvature of the wave function - the favored lower energy states would have larger physical size from this effect. However, the Coulomb potential energy favors smaller physical size.

The equilibrium physical size of an individual electron cloud is determined by minimizing the total energy found by combining these two effects as approximated by the Shroedinger equation, and more accurately by QED. For lattices, such as those found in metals and springs, the calculation is more complicated, but the same basic interplay between wave function curvature and Coulomb forces is what determines an object's length.

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The issue of length contraction in Sherwin's experiment can be simplified by looking at several atoms (or ions) within the spring. Four such atoms are depicted in Figure 1. In the figure, a circle (or ellipse) indicates that region within which an ion's electron densities are to be associated with the nucleus at the center of the circle (or ellipse). (In scanning tunneling microscope pictures of the atoms on a solid surface, one sees bumps and valleys corresponding to high and low densities of the electron clouds. The circles and ellipses of Figure 1 would correspond to the valleys of such scans.) Figure 1 depicts the four representative atoms aligned in the x direction. The figure shows two cases. The first case is a depiction of the atoms at rest with respect to a Lorentzian ether, while the second case shows the atoms when they are moving in the y direction through a Lorentzian ether and hence length contracted.

Figure 1. A cartoon of four atoms within a spring. Top half of the figure corresponds to a spring at rest with respect to a Lorentzian ether. Bottom half of the figure corresponds to a spring moving at velocity v with respect to a Lorentzian ether. The velocity v is assumed to be in the y direction. The spring extends in the x direction.

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In Sherwin's experiment the spring is constantly rotated. Figure 2 shows the four representative atoms when they are aligned in the y direction. Figure 2 again shows two cases.

The first case is a depiction of the atoms at rest with respect to a Lorentzian ether, while the second case shows the atoms when they are moving in the y direction through a Lorentzian ether. The second case shows the atoms after they are length contracted.

Figure 2. A cartoon of four atoms within a spring. Left half of the figure corresponds to a spring at rest with respect to a Lorentzian ether. Right half of the figure corresponds to a spring moving at velocity v with respect to such an ether. The velocity v is assumed to be in the y direction. The spring extends in the y direction.

Sherwin realized that the length contraction proposed by Lorentz was different than that proposed by Einstein. The Lorentz contraction was real, whereas the Einstein contraction was relative. Hence, since any frame is equivalent to any other in relativity, and the spring's motion in the earth-based inertial frame is symmetric about the center of motion, there is no orientation dependent length contraction predicted by special relativity as determined by an earth based observer. Since any inertial frame is as good as any other in special relativity, the prediction made by special relativity is that no resonant oscillations of the spring should be observed. However, for the real length contractions of the Lorentz theory, the spring should truly contract along its long dimension when it is aligned with it's velocity through the ether.

The Lorentzian situation is shown in Figure 3.

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Figure 3. A cartoon of four atoms within a spring moving through a Lorentzian ether in the y direction at velocity v. Top half of the figure corresponds to a spring oriented along its direction of motion. Bottom half of the figure corresponds to an orientation perpendicular to the direction of motion.

By synchronizing the rotational motion of the spring with the spring's natural harmonic motion, Sherwin hoped to excite resonantly driven harmonic oscillations of the spring. His argument was that length disturbances should propagate no faster than the speed of sound throughout the spring, since that is what they do in any other type of length disturbance.

Therefore, when the longer spring (extended along x) rotates 90 degrees (so that it extends along y) there isn't enough time for it to come to its new equilibrium, and the natural F=kâ&#x2C6;&#x2020;x forces (from Hooke's Law) will excite oscillations.

Sherwin found no such oscillations. He took this to indicate a lack of a Lorentz contraction. In my original work (reference 1) I found nothing wrong with Sherwin's original arguments, so I pointed to his experiment as providing evidence that a length contraction did not exist in nature. However I now realize that both Sherwin and I were relying on an unmentioned assumption. We both assumed that the spring was a rigid body - rigid all the way down to its atomic connections. Looking again at Figure 3, I am assuming that the connection between atoms is always such that point A connects to point C. That is, I assume that there is a rigid connection point between each atom, and that as the spring revolves, the centers of the atoms

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revolve around the spring's rotation point, and the atoms themselves rotate once as they revolve, ever keeping points A and C connected between each atom in the spring.

But there is another possibility. Rather than being rigidly connected at points A and C, it is possible that the individual atoms slide along their common boundary as the spring is rotated.

This situation is shown in Figure 4.

Figure 4. A cartoon of four atoms within a spring moving through a Lorentzian ether in the y direction at velocity v. Top half of the figure corresponds to a spring oriented along its direction of motion. Bottom half of the figure corresponds to an orientation perpendicular to the direction of motion.

The situation is further clarified in Figure 5. Figure 5 shows five atoms within the spring in three possible orientations. If the spring is rotating counterclockwise in the figure, the atoms start out with their points A and C in contact. After less than a 90 degree rotation, the atoms are still in contact, but now they are not in contact at points A and C. After a 90 degree rotation, the atoms have their points B and D in contact.

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Figure 5. A cartoon of five atoms within a spring moving through a Lorentzian ether in the y direction at velocity v in three rotated positions.

If the atoms slide along their common boundary, Figure 5 shows how a null result of Sherwin's experiment can be obtained within a Lorentzian ether. Rather than the speed of the length contraction be required to propagate along the spring at the speed of sound, the length contraction is already there! It is just that the contact point moves along the atomic boundaries as the spring is rotated.

The simple diagrams above show the relevance of slippage versus rigid contact in one dimension. But of course the springs are three dimensional. Still, the same principle can be shown to apply for three dimensional objects. Figure 6 shows the case of two rows of atoms within a spring. Again, if the atoms slide along their common point of contact they are able to smoothly transition from the case of a longitudinal length contraction of the spring to that of a transversely contracted spring. For the case of three dimensions one would only need to add atoms centered above and below the gaps between the two dimensional image shown in Figure 6.

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Figure 6. A cartoon of ten atoms within a spring moving through a Lorentzian ether in the y direction at velocity v in three rotated positions.

From the above analysis it can be seen that if solids behave such that the individual atoms within them slide along their common boundary as they rotate, then the null result of Sherwin's experiment can be understood even in the presence of a Lorentzian ether. If however, individual atoms within a solid maintain rigid contact at the atomic level, Sherwin's original arguments remain valid. Once again, an underlying assumption about nature must be made in order to interpret the results of an experiment. Therefore no conclusive statement can

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be made concerning whether or not Sherwin's experiment can be used to rule out (or in) any particular space time theory.

Earth Tides.

An additional experiment has also been conducted since the time that I wrote reference 1 that has bearing on the question of length contraction. CERN researchers have detected changes in the time it takes particles to orbit their particle storage rings and have correlated those orbital period changes to lunar position. From these experiments they have inferred a change in path length that the particles must have traversed, assuming that the speed of the particles was constant. (At LEP, under standard relativity or the Lorentzian theory, the electron velocity is constant and extremely close to the speed of light.)

These experiments could, in principle, be used as evidence for or against a length contraction.

If there were no Lorentzian length contraction, and if Lorentzian time dilation alone is responsible for our inference of a length contraction (as shown in detail in reference 1), and if the speed of the particles is indeed constant, then the daily rotation of the earth could lead to different orbit times for the orbiting particles as a function of time of day.

A full analysis of the LEP observations is very worthy of future study.

Conclusion.

At the time I wrote my earlier work (reference 1) I concluded that the experimental situation was not entirely clear as to whether or not nature contained a length contraction. By looking at all of the experimental evidence, it is clear that Einstein's relativity is the most in doubt, because of the experimental tests (reference 6) of Bell's Theorem (reference 7). At that earlier time I stated that the experiment of Sherwin appeared to support the case that there was no length contraction, but that Lorentz's theory should not be ruled out solely due to Sherwin's result. However, given my understanding of the experimental situation at the time, I made the point that there was some suggestion in the experimental data that a length contraction does not, in fact, exist.

With the further analysis done herein it is now clear that Sherwin's test does not clearly indicate whether or not a Lorentzian length contraction exists. In addition, further analysis of the situation with regard to earth tide measurements at CERN may provide some suggestion that a length contraction does exist.

But even with the additional insight and experimental data, I remain firm in my conviction that it will remain questionable whether or not there is a length contraction until a definitive experiment can be done. A definitive experiment could involve accelerating spheres of sufficient size so that ultrashort laser pulses could be fired across the spheres as they move.

Then, the shadows thereby produced could be measured. The spheres would then have to be slowed down and brought to rest again. By measuring their size, as determined by the shadows of the light, both before, during, and after their motion, a unique measurement could be done concerning length contraction. (The before and after measurements are required in order to ensure that the spheres are not somehow mechanically altered during the acceleration and deceleration processes.) While even that experiment might be questioned (as can any experiment) it would be a far more direct measurement of length contraction than anything done to date.

As of July, 2002, it is still not proven that a length contraction exists.

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References.

1.

D. J. Larson, Physics Essays 7, 476, 1994.

2.

J. Bailey, K. Borer, F. Combley, H. Drumm, F. Krienen, F. Lange, E. Picasso, W. von Ruden, F.J.M. Farley, J.H. Field, W. Flegel and P.M. Hattersley, Nature 268, 301 (1977).

3.

C.W. Sherwin, Phys. Rev. A. 35, 3650 (1987).

4.

A. Einstein, Ann. Phys. 17, 891 (1905).

5.

H.A. Lorentz, Proc. R. Acad. Amsterdam 6, 809 (1904).

6.

A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).

7.

J.S. Bell, Physics (NY) 1, 195 (1965).

July 15, 2002 ----Delbert Larson, Ph. D. in Physics in 1986, in the field of particle accelerators, has published over 50 papers on a variety of physics topics. He has designed and built several complete particle accelerator systems over the years, including a 2.5 MeV, ampere intensity electron beam system and a 10 MeV He3 ion beam system for PET isotope production. He served as a leading designer of the cancelled Superconducting Super Collider, doing longitudinal dynamics designs for that lab. Dr. Larson has written computer applications for space charge inclusive transverse ion optics and a separate code for longitudinal particle optics. Dr. Larson's computer codes have been used at laboratories around the world. Dr. Larson is presently leading the design of particle accelerators for use in medical therapy.

Delbert7@aol.com

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The Most General Fundamental Failures of Modern Physics (Delbert J. Larson) I have some thoughts on the most general and fundamental failures of modern Physics I would like to share. As I see it, there are three general and fundamental failures of modern physics: Failure 1 - Abandonment of Objective Reality.

I believe that the first fundamental failure of modern physics is the forfeiture of the concept of an objective reality. This failure has it's roots in relativity and quantum mechanics. In their famous paper, Einstein, Podolski and Rosen (EPR) showed how, assuming an objective realty, quantum mechanics must be incomplete. Their argument was refined by Bohm, but it fell to Bell (name forever to be praised) to develop inequalities capable of testing whether or not quantum mechanics does indeed violate relativitistic causality. The tests have been done, (Aspect, et al, were the first, but there have been many more experiments since) and quantum mechanics does indeed predict the correct results of the Bell's inequality experiments. But underlying the EPR argument was an assumption. The assumption was that relativity was correct, and it is a readily obtained result of relativity that no cause can create an effect if the cause is separated from the effect by a relativistic spacelike interval. Faced with the conundrum of Bell's inequalities being an experimental reality, modern physics therefore faced a choice. One could either set relativity aside, or set objective reality aside. Modern Physics chose the latter. I believe that the wrong choice was taken. Einstein was very clear in his reverence for an objective reality, and so am I. It is clear to me that relativity should have been set aside as a result of the tests of Bell's inequalities, and that the concept of an objective reality should have remained paramount. (Note that the Lorentzian theory has no problem with cause and effect being separated by a relativistic spacelike interval - what is important there, since simultaneity is absolute, is simply that the cause precede the effect. With absolute time, the concept of "precede" is well established in the Lorentz theory in all frames, and one does not need to specify event separations as "space like", "time like" or "light-like".) Also note that the Lorentzian theory leads to almost all of the same experimental predictions as relativity. I have discussed this, and other issues, more fully in [1].

Failure 2 - The Trend toward Complexity.

I believe the second fundamental failure of modern physics is it's continued growth into complexity. Renormalization theory, quark generations, mixing angles, and on and on, have been considered to be "revolutionary advances" in understanding. And, as each one individually has come about, each one, individually, does indeed advance understanding. But, physics has now reached the point where one really needs to study for decades to "understand" the present state of the art, as many, many single steps keep being added to the "standard model". I view this situation as being very similar to that which existed just prior to Copernicus. The "music of the spheres" was a celebrated theory to explain the motion of the stars and planets in the skies. Now, this theory is much maligned by present day physics, as it is clear now that the Copernican way (with Kepler, and later, Newton) was far, far simpler.

But rather than ridicule the "music of the spheres" it would be far better if modern physics stopped to think about what the science was at that time. It took a great deal of careful observations to map the stellar and planetary motions. It further took a great deal of detailed

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mathematics to understand the "music of the spheres" theory, as there were many such spheres that, as a system, came together to accurately - and correctly - predict the motion of all heavenly bodies. The theory was very complex, and took many years, and a high intellect, and mathematical study, to understand. But once understood, it passed all experimental tests!

That is why it was so fevently held on to. It wasn't that the scientists of the time were stupid (as is often smugly inferred). Rather, the opposite was true. They were very intelligent to understand such a complicated theory. And after devoting decades to understanding things, building upon the theory year after year, the practitioners were quite understandably reluctant to consider any simple alternative. Afterall, a simple alternative was - simplistic! And far less intellect was needed to understand it. Clearly Kepler was just naive!

I have had an amusing incident that is relevant here. I have come up with a "preon" model.[2] It dovetails into the quark-lepton model, but it only postulates 6 fundamental particles, and it identifies the weak force as a radioactive decay, reducing the forces of nature from four to three. Hence, it is FAR SIMPLER that the standard model. (The standard model now employs 6 quarks, plus 6 antiquarks, and they each come in three colors. That's 36 quarks! Then there are 12 leptons. And gluons, photons, weak intermediate vector bosons and gravitons. Mixing angles are employed to further explain events. How many spheres do they need?) But in reviewing my paper for Physical Review Letters, the reviewer quoted Occoms Razor, saying that the Standard Model employed far fewer "spheres" than did my new proposal. Recalling Galileo (name forever to be praised) "Shall we Laugh, or Shall we Cry?" Failure 3 - An Insistance on the Illusion of the Simplicity of Point-like Entities.

I believe that the third fundamental failure of modern physics is it's insistance on point-like particles. In some sense this harkens back to the ancient particle versus wave argument. But it is more than that, because a particle would not necessarily have to be of zero size. While the concept of a point is mathematically simple, it also leads directly to physical infinities, and the need for "renormalization". It is my view (again see [1]) that while the math might be more inconvenient with finite distributed bodies, nature might not be mathematically convenient. But I believe that nature will prefer finite solutions to her problems.

References.

[1] "An Absolute Theory for the Electrodynamics of Moving Bodies", Physics Essays, volume 7, number 4 1994 page 476.

[2] "The A-B-C Preon Model", Physics Essays, volume 10, number 1, 1997, page 27.

Also, if anyone is interested in a rigorous ether model, please see: [3] "A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical Aether", Physics Essays, volume 11, number 4, 1998.

----[A presentation of the author can be found at the end of his previously published paper]

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Le basi sperimentali della propulsione non newtoniana (Emidio Laureti) Il concetto di propulsione denominato dall'ASPS (Associazione Sviluppo Propulsione Spaziale) PNN (Propulsione Non Newtoniana) nel dettaglio propulsione senza espulsione di massa di reazione (o di fotoni) nasce con la fondazione dell'ASPS nel 1979. Nel 1992 viene concepito un sistema di propulsione elettromagnetico (SC23) che sfruttando opportunamente le fasi delle correnti e dei campi magnetici nei circuiti in alta frequenza rendeva possibile in linea teorica l'apparente violazione del principio di conservazione della quantità di moto nella accezione newtoniana. Tale apparenza è in realtà dettata dal semplice fatto che in elettrodinamica proprio per l'inesistenza di una interazione istantanea del campo e.m. (tutte le interazioni si propagano al massimo con la velocità della luce c) il principio di azione e reazione nella accezione newtoniana non vale in quanto informulabile [1]. Mentre continua a valere la conservazione dell'impulso totale, se si include nel sistema dei corpi che esercitano fra di loro forze di azione e reazione anche il campo e.m..

Attraverso la procedura illustrata nel prototipo denominato SC23 [2] (a cui è stato concesso il brevetto nell'Aprile del 2000 ) si realizza una sequenza di interazioni e.m. in cui il principio di azione e reazione non vale mai essendo le forze elettrodinamiche di azione e reazione dirette nella stessa direzione e verso. Identicamente si ha una sequenza di istanti in cui è appunto L'INCLUSIONE del campo e.m. nel principio di conservazione della qdm a conservare il principio stesso [3] in quanto l'impulso totale acquistato dal sistema in una direzione è uguale e opposto a quello del campo e.m. (va sottolineato [3] che tale impulso non deve essere confuso con quello del sistema di propulsione funzionante a rinculi fotonici). Tutta questa procedura passa necessariamente attraverso una condizione sperimentale che non è stata debitmente controllata per oltre 200 anni.

Sui testi classici di elettrodinamica infatti si nega che possano esistere forze elettrodinamiche tra circuiti aperti in cui scorre corrente oscillante, ovvero che tali forze abbiano significato per circuiti aperti solo matematico e non fisico [4], [5]. Tale impostazione era necessaria poichè l'esistenza stessa di forze elettrodinamiche tra tratti di circuito aperto, in cui scorre corrente variabile, implicitamente avrebbe dato la possibilità di violare il Principio di Azione e Reazione come classicamente si definisce, permettendo la propulsione senza espulsione di massa di reazione. Che tale violazione sia possibile e necessariamente conseguente lo dicono gli autori stessi che parlano delle formule di Laplace riferite a circuiti aperti [4], [5]. Solo se la generazione di forze tra circuiti aperti è impossibile, il Principio di Azione e Reazione può evitare la "particolarizzazione" e il superamento.

Ad esempio il testo di E. Amaldi (uno dei "ragazzi" di via Panisperna) dice che le formule di Laplace sono "espressioni matematiche vuote di significato fisico" [4]; mentre il testo del Perrucca dice " ... in casi meno simmetrici, a voler dedurre le azioni elettrodinamiche dalla successiva applicazione delle due leggi di Laplace non risulta di regola soddisfatto il principio di azione e reazione … " [5]. L'unica forza elettrodinamica tra circuiti aperti che può esistere in alta frequenza sarebbe il solo striminzito impulso fotonico p = E/c , dove p è l'impulso requisivo scambiato, E è l'energia, e c è la velocità della luce.

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Per dimostrare che queste erano solo assunzioni dovute all'assenza di sperimentazione sull'elettrodinamica in alta frequenza occorreva verificare soprattutto che la forza ettrodinamica in alta frequenza poteva essere anche ATTRATTIVA e non solo repulsiva.

In primis va ricordato che ricercatori esterni all'Asps, pur con obbiettivi diversi dalla PNN, realizzarono alcune configurazioni sperimentali sui circuiti aperti [6]. Questi autori [7] nel perseguire l'obbiettivo di dimostrare l'inapplicabilità della forza relativistica di Lorentz nel caso di circuiti aperti, incidentalmente dimostrarono che l'Equazione Cardinale di Ampere (non relativistica) era valida per i circuiti aperti. Essi scrivono esplicitamente "No where in the literature before appears such investigation of the forces between physically non closed circuits … " che è quello che dice pure da tempo l'Asps, con l'aggiunta di una spiegazione elementare alla mancanza di tale investigation: ovvero che l'accettazione acritica e/o limitativa delle Maxwell equazioni (nello specifico l'uso che l'autore fa della cosiddetta "corrente di spostamento") ha in pratica bloccato ogni iniziativa di sperimentazione fisica sulla dinamica dell'elettromagnetismo ad alte frequenze [8], [9],[10], [11], [12].

Negli anni immediatamente seguenti il 1992 l'Asps iniziò faticosamente a acquisire apparati sperimentali idonei alla PNN o più correttamente e ad adattare alla PNN l'esistente.

Soprattutto si definirono e si migliorarono progressivamente le tecniche di rilevamento dei dati sperimentali. Dal 1999 iniziarono sistematicamente i primi esperimenti circa la possibilità di esistenza di forze elettrodinamiche tra circuiti aperti.

Uno step delle nostre attività sperimentali è stato appunto quello di dimostrare in primo luogo che tali forze esistono se si approntano gli apparati sperimentali in grado di dimostrarne l'esistenza.

In un esperimento condotto dall'Asps un conduttore aperto appeso a un pendolo balistico viene attratto da un dipolo emittente onde e.m. se il conduttore è opportunamente condizionato e progettato per essere un circuito in cui la corrente di autoinduzione è in fase con quella della sorgente emettente il campo e.m..

Negli ultimi mesi del 2001 dopo innumerevoli tentativi e modifiche venne realizzata prima una configurazione sperimentale in cui alcuni dei bracci dei dipoli del sistema di propulsione non newtoniano SC23 si spostavano in un unico verso della stessa direzione [13] con un impulso maggiore di E/c ,sotto alimentazione del generatore di potenza SXP2000.

Alcuni bracci di SC23 "nuotano" in pratica nel campo elettromagnetico da loro emesso, perché ogni campo e.m.,una volta emesso,è indipendente dalla sorgente.

Nello stesso periodo (Dicembre 2001) una sintesi e una reinterpretazione di tutte le esperienze condotte permetteva di concepire un prototipo finalmente operativo: SC2.12.

Successivamente nel Febbraio 2002 si ottimizzarono alcuni parametri di tale prototipo portandolo addirittura a competere con le spinte dei motori a ioni.

Si ricapitolano brevemente gli eventi di tale esperienza: Secondo la procedura già illustrata in Nova 91 Gennaio-Febbraio-Marzo 2002 [14], il prototipo SC2.12 (vedi foto qui di seguito) è attaccato a un pendolo balistico lungo circa 1 metro, mentre i sistemi che ne rilevano lo spostamento sono un laser che illumina di taglio la superficie del prototipo e un fascio di luce prodotta da quello che è chiamato "il nostro occhiale", ovvero un sistema laser + lente che proietta un'iride sulla parete.

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La scatola contenente la variante di SC2.12 è nascosta da una copertina di Nova Astronautica, issn: 0393-1005, Organo Ufficiale dell'ASPS. L'occhiale illumina una "appendice-indice" attaccata in basso sulla copertina che copre il prototipo SC2.12 e proietta una iride circolare su una parete.

SINTESI: Un laser illumina la coopertina quasi orizzontalmente, mentre l'occhiale illumina piĂš in basso l'indice attaccato alla copertina (indice non presente nella foto di SC2.12 con copertina).

Il prototipo sotto alimentazione elettrica irraggia un campo e.m. rilevato dal "Field Strength Meter" (non presente nella foto di SC2.12 con copertina).

Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico rilevato dal "Field Strength Meter" SC2.12 avanza nella direzione dell'osservatore di circa 3,136 millimetri e conseguentemente l'illuminazione del laser si allunga da destra verso sinistra, per poi tornare indietro quando l'alimentazione elettrica al prototipo viene disattivata.

L'illuminazione dell'indice da parte dell'occhiale è proiettata su una parete del Lab del Dip. Ra-1 dell'ASPS in forma di iride. L'occhiale è a circa 13 cm dall'indice e a circa 373 cm dalla parete. L'iride proiettata sulla parete ha un diametro di circa 11 cm.

Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico rilevato dal "Field Strength Meter" SC2.12 avanza da sinistra a destra nella direzione orizzontale con uno spostamento amplificato di circa 9 cm. La proiezione dell'indice torna indietro quando l'alimentazione elettrica e quindi il campo e.m. viene disattivato.

Il rapporto Fpnn/p tra la spinta pnn Fpnn e il rinculo fotonico p (pag.8 di Nova Astronautica n.

91) [14] era pari a 1363 , se alcuni parametri PNN non erano ottimizzati.

Lo spostamento S in millimetri sul pendolo balistico era pari a: S=1,045 millimetri A 50 watt il rinculo fotonico dava una spinta di 0,017 milligrammi (pag.7 di Nova 91).

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Moltiplicando 1363*0,017milligrammi si ottiene una spinta Fpnn = 23,171 milligrammi per quanto descritto in Nova 91 [14].

Viene illustrata una spinta ottimizzata con modifica di alcuni parametri di SC2.12 L'Iride in media ha un diametro di circa 11 cm.

Come da riferimento sulla scala graduata sul muro lo spostamento dell'indice è di circa 9 cm in modo che si evince uno spostamento Sm in millimetri del prototipo sul pendolo pari a: Sm = 90 millimetri * (13/373) = 3,136 millimetri cioè è triplo rispetto al precedente (e sempre a 50 watt).

Ricordando i parametri precedenti la spinta Fpnn diventa pari a: Fpnn=(3,136/1,045)* 23,171 milligrammi = 69,535 milligrammi Il guadagno rispetto al rinculo fotonico è di circa 4090 volte.

Conclusioni e ulteriori analisi Le esperienze condotte dall'Asps su pendolo balistico hanno dimostrato che nella definizione dell'intensità della forza in alta frequenza intervengono anche dei parametri inaspettati ma sempre legati strettamente alla corrente e al campo magnetico con cui si determina l'interazione.

L'intensità di spinta Fpnn che la PNN può determinare attualmente è compresa tra circa: 23 milligrammi < Fpnn < 70 milligrammi Essa è confrontabile con la propulsione ionica ma con il vantaggio di un elevatissimo impulso specifico dato che il sistema PNN non espelle massa di reazione ma utilizza solo energia e.m. per generare la spinta.

Come da esperienza riportata in Nova Astronautica n.91 2002 (pag.3-8) [14], anche la spinta amplificata di SC2.12 nel Febbraio 2002 presentava ROS, ovvero SWR elevati.

Un calcolo successivo portava a quantificare l'utilizzazione di almeno il solo 40% dei 50 watt erogati dall'alimentatore.

La spinta pnn Fpnn a 70 milligrammi utilizzava pertanto circa 20 watt.

Ora la spinta di un FEEP thruster è di circa 1 millinewton per 60 watt, ovvero 102 milligrammi.

La spinta di SC2.12 a 60 watt utilizzati per la spinta va pertanto triplicata e risulta essere dell'ordine dei 210 milligrammi ovvero doppia a parità di consumo energetico rispetto a quella del FEEP Thruster, ovvero dell'ordine dei 2 millinewton.

Da notare che l'Impulso Specifico dei motori dello Space-Shuttle è di 460 secondi.

L'Impulso Specifico dei motori ionici tipo FEEP thrusters è compreso tra 6000 e 10000 secondi.

L'Impulso Specifico Ipnn di SC2.12 è invece: Ipnn =(23*10-6 Kg x (9 x 1016 metri2/sec2)/50 watt) = 4.14 x 1010 secondi .

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Ovvero più di un milione di volte più elevato di quello del motore a ioni.

Bibliografia [1] E. Laureti, "Non validità del Principio di Azione e Reazione in elettrodinamica", Nova Astronautica, Vol. 20 n.86, 2000.

[2] E. Laureti, "Il Prototipo SC23", Nova Astronautica, Vol.18 n. 77, 1998.

[3] E. Laureti, "La PNN e il Principio di Azione e Reazione", Nova Astronautica, Vol. 19 n. 82, 1999.

[4] E. Amaldi, Fisica Generale II, Università di Roma, 1965, pag. 290-291.

[5] E. Perrucca, Fisica Generale e Sperimentale II, Un. Tip. Ed. Torinese 1949, pag. 627-628.

[6] P.T. Pappas & T. Vaughan, "Stigma Antenna Force Experiments", in The Thorny Way of Truth, IV, East-West, Graz, 1989, pag. 158-168.

[7] P.T. Pappas,"Forces on a Stigma Antenna", Physics Essays, 3, 3, 211, 1990.

[8] E. Laureti, "Brevetto di SC23 e Attività Sperimentali", Nova Astronautica Vol.20 n. 96, 2000.

[9] A.P.French, J.R.Tessman, Am. J. Phys., 31, 201, 1963.

[10] F.W. Warburton, "Displacement Current, a Useless Concept", Am. J. Phys., 22, 229,1954.

[11l J.C. Maxwell, "A Treatise on Electricity and Magnetism", V2, Dover, New York, 1954.

[12] E. Laureti, "Riflessioni sulla Conservazione della quantità di Moto e Basi sperimentali della PNN", Nova Astronautica, Vol.21 n. 87, 2001.

[13] E. Laureti, "Per Santa Rita e San Gabriele santi Protettori dell'ASPS Hurra!", Nova Astronautica Vol. 21 n. 90, 2001.

[14] E. Laureti, "Setup sperimentale di SC2.12", Nova Astronautica Vol. 22 n. 91, 2002.

----Emidio Laureti è nato a Roma nel 1947. Si è laureato in Fisica nel 1974 presso l'Università di Roma, con una Tesi dal titolo "Correzioni Relativistiche al Fattore di Forma Elettrico del Deuterio". Attualmente è docente di Matematica e Fisica nelle scuole medie superiori. Fondatore e Presidente dell'Associazione Sviluppo Propulsione Spaziale (ASPS) nel 1979, si occupa insieme ad altri collaboratori di attività sperimentali su concetti di propulsione di tipo "propellantless", all'ASPS definiti Propulsione Non Newtoniana (PNN). Dal 1982 è Direttore Responsabile di Nova Astronautica (issn: 0393-1005), Organo Ufficiale dell'ASPS. Associazione Sviluppo Propulsione Spaziale Via Nino Martoglio 22 , 00137 Roma - Italia Tel: 06-87131068

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http://www.asps.it - as.ps@flashnet.it

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Neopitagorismo e Relatività (Rocco Vittorio Macrì) «Da quando i matematici hanno invaso la teoria della relatività, io stesso non la capisco più» (Albert Einstein)

Ci troviamo in un'epoca che - per la prima volta nell'intero arco del pensiero scientificofilosofico - vede la fisica padroneggiare, porre confini e dettare legge all'interno della sfera filosofica. Siamo a quasi un secolo di distanza dalla seconda rivoluzione scientifica, la quale ha scosso i pilastri della stessa gnoseologia: i concetti di spazio, tempo, simultaneità, cosmo, esistenza… vengono fatalmente rielaborati e trasformati, tallonando la cosiddetta crisi dei fondamenti della matematica. Gli stessi principi primi aristotelici subiscono "scacco matto": «Mediante la meccanica quantistica viene stabilita definitivamente la non validità del principio di causalità» sentenzia Heisenberg1. Nasce la logica quantistica. È la fisica che, per la prima volta, "ridisegna" la filosofia…

Sulle macerie del pensiero classico aleggia la figura, diventata oramai leggenda, che incarna e personifica la rottura col passato, l'autorità che ha cambiato per sempre la nostra immagine del mondo, la scintilla divina con la quale il Fato innescò "la rivoluzione", come egli stesso ebbe a dire: «Per punirmi del mio disprezzo nei confronti dell'autorità, il Fato fece un'autorità di me stesso»2. Albert Einstein fu l'artefice della metamorfosi moderna, che avendo posto «la matematica al centro dell'esperienza», come documenta Gaston Bachelard, e introducendo una visione elastica dello spazio e del tempo, sarebbe diventato pietra angolare del più grande cataclisma intellettuale della storia del pensiero scientifico. Nel suo continuo "detonare e detronizzare", la rivoluzione einsteiniana avrebbe attivato una serie di «choc epistemologici» nel cuore stesso della comunità scientifica, che - scrive Bachelard nel 1934 - obbligano lo scienziato a rimettere tutto in discussione: «Il fisico è stato costretto tre o quattro volte da vent'anni a questa parte a ricostruire la propria ragione, e, intellettualmente parlando, a rifarsi una vita»3, fino al punto di mettere all'indice le stesse categorie di pensiero che avevano resistito e brillato per più di due millenni. L'unica possibilità di accesso alle nuove conquiste relativistico-quantistiche - ammette Abraham Pais - è «quella data da Einstein, è che la stessa logica classica deve essere modificata»4.

Si tratta ora di analizzare l'influenza, il rapporto e perfino il legame parentale che la "gaussiana" concezione del pensiero matematico che spazia da Gauss a Cantor fino a Hilbert ha avuto nei riguardi della sconvolgente ideazione, progettazione ed elaborazione della fisica e metafisica contemporanee, e se Einstein può essere visto (suo malgrado) come l'anello di collegamento tra la cosiddetta Scuola di Göttingen e la Scuola di Copenhagen, tanto più che è ormai ben assodato che la seconda ha completato il lavoro di "svuotamento categoriale" iniziato dalla prima5. Allora il fisico moderno potrebbe essere considerato un «pitagorico» non solo perché - come abbozza quel «genio rivoluzionario tra i fisici» 6 - «considera il criterio della semplicità logica come strumento indispensabile ed efficace per la sua ricerca» 7, ma soprattutto perché «sostiene che il principio veramente creativo, nella fisica teorica, è quello della costruzione matematica»8. Anzi, si dovrà ammettere altresì, che si è andati oltre Pitagora - parliamo appunto di "neopitagorismo" - dal momento che «Einstein accetta il punto di partenza dell'assiomatica, secondo cui il contenuto logico-formale della matematica è nettamente separato dal suo contenuto effettivo o intuitivo»9.

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1. Il "ritorno" a Pitagora Fa parte ormai della mentalità scientifica comune che, «le grandi teorie raramente sono semplici»10 e per comprenderle «c'è bisogno di un livello davvero elevato nella conoscenza della matematica»11. «La scienza moderna si fonda quasi per intero sulla matematica» 12.

Raffinati modelli matematici hanno oggi assunto la guida non solo durante la creazione dei modelli fisici, ma addirittura durante il relativo processo ermeneutico, ridando splendore a Pitagora e all'affermazione del suo discepolo Filolao: «Senza il numero non sarebbe possibile pensare né conoscere alcunché». Sotto questa luce le parole di Dirac (1931) appaiono paradigmatiche: «Il più potente metodo di avanzamento che può essere suggerito oggi è quello di impiegare tutte le risorse della matematica pura, nel tentativo di perfezionare e generalizzare il formalismo matematico che costituisce la base esistente della fisica teorica, e, dopo ogni successo in questa direzione, di tentare di interpretare le nuove forme matematiche in termini di entità fisiche»13.

«La cultura occidentale è caratterizzata da una sorta di mito della matematica, dalla fede, forse dovuta a Pitagora, in una sua virtù esplicativa e quasi trascendente. A molte persone, descrivere in termini matematici una struttura sintattica o delle relazioni di parentela sembra già una "spiegazione" sufficiente»14. Nel passare dal «Nihil certi habemus in nostra scientia nisi nostram mathematicam» del Cusano al programma di Dirac («Scoprire prima le equazioni e poi, dopo averle esaminate, gradualmente imparare ad applicarle […] È più importante avere bellezza nelle equazioni che trovare accordo tra equazioni ed esperimenti» 15) transitano 5 secoli, ma visti da una prospettiva epistemologica hanno l'aspetto di un viaggio a ritroso di due millenni: è, in un certo senso, un ritorno a Pitagora. Contrariamente alle aspettative di Bertrand Russell che avrebbe desiderato per il Novecento «una ritirata da Pitagora»16 il sentiero intrapreso dalla fisica contemporanea porta ad una rivalutazione della Scuola di Kroton, il ritorno cioè «a una tradizione molto antica» 17. «Sembra che i pitagorici siano stati i primi ad intendere la forza creativa inerente alle formulazioni matematiche», bisbiglia Heisenberg18. «Frammisti ai loro discorsi sui numeri amici e nemici, i pentagrammi mistici, i numeri perfetti, l'armonia delle sfere e così via, troviamo quelle proprietà dei numeri e delle figure spaziali, chiare da un punto di vista logico, che successivamente troveranno posto nel limpido giardino degli Elementi di Euclide»19. È vero che Aristotele denuncia nella sua Metafisica che i Pitagorici abbiano attribuito al numero quella funzione di causa materiale che gli Ionici attribuivano all'elemento sostanziale della realtà corporea: «Costoro sembrano ritenere che il numero sia principio non solo come costitutivo materiale degli esseri, ma anche come costitutivo delle proprietà e degli stati dei medesimi»20, e che la fisica contemporanea incarna tale credo quasi come "mistero orfico" seguito dai nuovi adepti con nomi altisonanti quali quelli di Hilbert, Minkowski, Einstein, Heisenberg, Pauli, Dirac, ecc. Pur tuttavia, la "metrica pitagorica" originaria era ben lontana dal moderno nichilismo hilbertiano che svuota il pensiero matematico in una asettica e fredda intelaiatura logica priva di semantica e contenuti intuitivi. Al contrario, era fondata sull'evidenza e l'intuizione che l'"umano" si ritrovava già nella sua intima costituzione psichica: l'elevazione mistica e la poetica visione del kosmos come armonia ne danno diretta testimonianza. In fondo Copernico, Keplero, Galileo, Newton… depositano a favore di questa prospettiva21. Ma come direbbe ai nostri giorni un Russell: «La logica e la matematica… sono l'alfabeto del libro della natura, ma non il libro stesso»22.

Esisteva inoltre la visione iperuranica di un sapere matematico che intelaia la struttura del mondo in modo monolitico, irremovibile, unitario, anelastico, intrasferibile, non assoggettabile o soggiogabile: professione di fede che da Pitagora, rimbalzando su Platone, attraversa i secoli come un raggio luminoso riflesso ora da Cartesio, ora da Leibniz fino ad arrivare a Husserl: «Nessun Dio può minimamente modificare ciò, come non può modificare il fatto che 1 + 2 = 3 o che sussistano altre verità essenziali» 23. Perfino Hume, dopo aver

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"dissacrato" e "soggettivizzato" ogni supremo principio sotto la guida dell'empirismo, si inginocchia reverente dinanzi all'«apoditticità» della matematica, a «quelle realtà che sono sicurissime e certissime»24, come testimonia lo stesso Kant nella sua Critica della ragion pratica: «Eppure lo stesso Hume non estese l'empirismo al punto da comprendervi anche la matematica. Egli pensava che le proposizioni matematiche siano analitiche, e, se questo fosse esatto, esse sarebbero effettivamente apodittiche»25.

Vedremo come questa certezza inizierà a incrinarsi all'inizio dell'Ottocento e come Gauss segnerà un'era nuova di stampo strumentalista e trans-intuizionista, che porterà prima alla nascita ed accettazione delle geometrie non-euclidee e successivamente alla matematica formalista e pragmatista del nostro secolo, attraversando i transfiniti di Cantor. «Dopo quel radicale mutamento del pensiero matematico - rileva Renato Nobili - anche nella fisica fu aperta la via alla determinazione di nuove costituzioni di significato e alla costruzione di modelli matematici astratti, totalmente irriducibili al genere delle rappresentazioni fenomenologiche del mondo visibile. Parallelamente a ciò, anche le istanze epistemiche generali del pensiero fisico subirono trasformazioni profonde; cosicché, ad esempio, quelle nozioni oggettivistiche e metafisiche forti che furono le Verità, le Leggi e i Principi della Natura nel volgere di pochi decenni furono abbandonate e rimpiazzate da nozioni deboli, soggettivistiche e pragmatistiche, quali sono le rappresentazioni, le leggi e i modelli matematici copiosamente fioriti sul diramato albero della fisica teorica contemporanea»26.

2. "Gaussbuster" ovvero all'origine della metafisica moderna Esiste un curioso parallelismo tra Gauss e Einstein: entrambi hanno messo in moto un processo epistemologico rivoluzionario - che sbocciò sulle masse come inedite e sbalorditive immagini del mondo incrinanti l'"autorità", il "senso comune", le "evidenze", le "certezze" del pensiero classico - più grande di quanto potessero sospettare, un passo più grande di loro stessi il cui controllo fatalmente sfuggirà di mano e a nulla varranno i tentativi di recupero.

Similmente alla "canonizzazione" avuta da Einstein nel novembre del 1919 per la conferma delle previsione della sua Relatività generale in seguito alle misure sulla deflessione della luce durante l'eclissi del 29 maggio 1919 fatte dalla spedizione guidata da Eddington 27, Johann Carl Friedrich Gauss (1777-1855) ebbe la sua nel dicembre 1802, quando l'astronomo Wilhelm Olbers, ad un anno di distanza dalla scoperta di Cerere e dalla successiva scomparsa28, posizionò il telescopio seguendo i dati forniti da Gauss, "riscoprendo" così l'asteroide dileguato. Il risultato fece di Gauss «una celebrità europea» 29. La riscoperta di Cerere fu per «il principe dei matematici» un successo clamoroso, a commento del quale Laplace veniva a definire Gauss «uno spirito ultraterreno in un corpo umano»30.

Con l'avvento dell'era gaussiana la definitiva accettazione e sistemazione dei numeri complessi31 e la scoperta delle geometrie non euclidee fecero vacillare l'intera struttura epistemologica, che dovette rinunciare a ogni pretesa di assolutezza: potevano esistere altri numeri, altre algebre e altre geometrie di pari dignità epistemica. Come ebbe a osservare il matematico tedesco Felix Klein, «Gauss si erge alla testa del XIX secolo non solo cronologicamente»32. La nuova visione gaussiana che veniva a imporre i caratteri empiriostrumentaliste sul terreno della teoresi greca doveva però pagare un prezzo altissimo: la rinuncia all'autoevidenza33. Un tradimento al pitagorismo antico indicato dai Frammenti rimasti del discepolo più illustre, Filolao: «La natura del numero e dell'armonia non ammettono alcun inganno perché l'inganno non è loro proprio. La natura dell'indeterminato e dell'impensabile e dell'irrazionale porta l'inganno e l'invidia». Ciò veniva a manifestarsi sulle due colonne del fondamento del pensiero classico: l'aritmetica e la geometria, pietre angolari del pensiero umano dal tempo degli antichi Greci, «fortezze inespugnabili» fondate su verità autoevidenti che avrebbero trovato un inesauribile campo di applicazione nello studio della natura. «Coloro i quali credevano - spiega Russell - (come in generale si credeva sul continente) che fosse possibile una conoscenza del mondo reale certa e indipendente

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dall'esperienza non avevano che da additar[le]… : soltanto un pazzo avrebbe messo in dubbio la [loro] validità, e soltanto uno sciocco ne avrebbe negato il riferimento oggettivo»34.

Il carattere certo e unitario che rivestiva la nostra conoscenza del mondo veniva intaccato alla radice: l'incontrovertibilità delle verità autoevidenti era stata messa in questione da convenienze empirio-pragmatiste, e «insieme con essa vacillavano secoli di fiducia nell'esistenza e nella conoscibilità di verità inattaccabili relative all'universo» 35. «Anche se non abbiamo elementi per stabilire se Gauss sia stato influenzato direttamente dagli scritti di Hume», appare evidente come Gauss all'inizio dell'Ottocento «pensasse che l'intera matematica è priva di verità»36. In una lettera a Bessel del 21 dicembre 1811 scrive: «Non dobbiamo mai dimenticare che le funzioni [di variabili complesse], come tutte le costruzioni matematiche, sono solamente nostre creazioni; quando la definizione da cui siamo partiti cessa di avere senso, non dovremo domandarci "che cos'è", ma piuttosto "che cosa conviene assumere per mantenerla significativa"»37.

Uno sguardo indietro di qualche secolo ci consente di avere un quadro complessivo più esauriente riguardo le novità concettuali apportate dalla "gaussite" durante la crescita del pensiero scientifico. Furono la Germania e l'Italia a fornire il maggior numero di matematici all'inizio del rinascimento, ma l'opera più importante venne composta in Francia nel 1484 da Nicolas Chuquet: Triparty en la science des nombres. Qui veniva espresso per la prima volta un numero negativo isolato in un'equazione algebrica. Ciò nonostante, per le radici di equazioni che comportavano soluzioni immaginarie l'autore così si esprimeva: «Tel nombre est ineperible»38. Nella prima metà del XVI secolo i numeri negativi cominciavano ad essere più facilmente "manipolati" grazie all'introduzione della notazione tedesca con i nuovi simboli "+ e -" al posto della "più sana" notazione italiana "p e m". Pur tuttavia, nonostante si avesse completa familiarità con le proprietà dei numeri negativi, questi venivano ancora chiamati "numeri absurdi"39, a testimonianza del forte grado di diffidenza e perplessità diffuso nei matematici dell'epoca40 (ancora ben lontani da quel morbus mathematicorum recens col quale Frege accuserà la struttura assiomatica moderna). Soltanto l'uso e l'abuso nella pratica delle tecniche e procedimenti operativi porterà all'"accettazione perché funziona" tramite la oramai paradigmatica - logica del successo. Si arriva così alla oggettualizzazione delle procedure, ossia alla cristallizzazione di veri e propri oggetti matematici che acquisteranno una realtà indipendente dalle circostanze nelle quali sono stati introdotti. Per questa stessa ragione verranno accettati e accolti i numeri immaginari41.

Scrive Kline: «Senza aver completamente superato le difficoltà connesse con i numeri irrazionali e con i numeri negativi, i matematici europei accrebbero i loro problemi andando a inciampare in quelli che noi oggi chiamiamo numeri complessi» 42. Dalla scoperta di Scipione del Ferro dell'esistenza di una soluzione algebrica dell'equazione di terzo grado, allo stimolo che questa dette a Nicolò Tartaglia nel sistematizzarla fino all'Ars magna di Gerolamo Cardano del 1545 che rese di dominio pubblico le procedure risolutrici delle equazioni di terzo e di quarto grado (grazie all'aiuto di Ferrari), si incominciava a intravedere un residuo protagoreo sull'opportunità di un utilizzo infido delle radici quadrate di numeri negativi, radici che tuttavia Cardano chiamava «sofistiche»43. Il passo successivo fu fatto dall'algebrista Raffaele Bombelli nella sua Algebra del 1560 (ma stampata nel 1572) che tramite «considerazioni sofistiche»44 - come egli stesso ebbe a dire - arrivò all'«idea assurda» del seme germinale del concetto di "numero complesso". Fin qui i concetti di numero immaginario, numero complesso (o, come venivano chiamati allora, numeri "falsi" o "silvestri"), e quello stesso di numero negativo vengono "supposti" ma non "proposti", ossia procedono sul filo metafisico della "plausibilità empirica" di stampo protagoreo: «Siccome funziona, usiamolo». Nel 1629 il matematico francese Albert Girard riconobbe definitivamente la natura delle soluzioni negative e complesse, e fu così in grado di perfezionare il lavoro sulla relazione che intercorre tra le radici e i coefficienti di un'equazione algebrica, già iniziato da François Viète45. Per una copertura epistemico-razionale dovremo però aspettare fino a Gauss che, grazie ancora una volta all'abuso del "miracolo cartesiano" di

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collegamento tra il mondo algebrico e quello geometrico riuscirà a proclamare il "diritto di cittadinanza" a ciò che Eulero nel 1770 definiva entità «immaginarie o impossibili» 46. Come è stato giustamente inneggiato allo stesso Gauss in occasione del suo cinquantesimo di dottorato: «Lei ha reso possibile l'impossibile»47.

Grazie al parallelismo geometrico Gauss veniva a dare inizio a una nuova era dove delle entità metafisicamente contraddittorie48 venivano "addomesticate" perché sovrapponibili empiricamente a costruzioni geometriche recuperanti l'evidenza perduta dall'altro versante.

Così, d'altra parte, era già stato fatto secoli prima per l'uso dei numeri negativi che, a quell'epoca, «sollevavano maggiori difficoltà, poiché non potevano facilmente venire approssimati da numeri positivi, ma la nozione di senso (o di direzione su una linea) li rendeva plausibili»49. Il sodalizio algebra-geometria ha salvato "in corner" e reso ammissibili spesso operazioni definiti impossibili dalla prima (come il caso della «lussuria» dei numeri immaginari, con le parole di Thomas Jefferson del 179950), come questa d'altra parte ha reso omaggio alla seconda rendendo possibile operazionisticamente quel "salto" che l'intuizione molte volte non dava licenza di fare, come nel caso della geometria non-euclidea. Gauss estenderà tale sodalizio anche alla fisica, quando metterà in dubbio - scrutando tra le tre vette51 - il carattere euclideo dello spazio fisico… e Einstein completerà l'opera.

3. L'eredità di Gauss: dalla "perdita dell'intuizione" alla "libertà cantoriana" Il sigillo di Gauss recava il motto «pauca sed matura», ma in realtà quello che avvenne fu lo sviluppo di una serie continua di nuovi oggetti matematici privi di una adeguata fondazione filosoficamente ineccepibile e accettati in base alla suprema legge del più spregiudicato e "antieuclideo" pragmatismo: l'applicabilità. Nuove algebre e nuove geometrie venivano ad accumularsi nell'atanor sempre più "spazioso" dell'esistente matematico. Scrive mirabilmente Kline: «Dopo tutto, i consueti numeri reali e complessi venivano impiegati con scopi totalmente differenti e la loro applicabilità sembrava fuori discussione. Nonostante ciò, l'apparire di nuove algebre bastò per insinuare nella mente dei matematici il dubbio sulla verità dell'aritmetica e dell'algebra ordinaria proprio come accade a chi, entrato in contatto con le abitudini di una civiltà sconosciuta, comincia a mettere in discussione il proprio modo di vivere»52. La "creazione" continua di nuovi continenti matematici sui tracciati metodologici empiristi, fuori dalla sfera intuitiva, portò una specie di cataclisma concettuale preeinsteiniano nei teorici dell'epoca: «E così la triste conclusione che i matematici furono costretti a trarre è che nella matematica non esiste verità […] Il tentativo greco di garantire la verità della matematica partendo da verità autoevidenti e impiegando solo la dimostrazione deduttiva è stato inutile. Per molti attenti matematici era troppo duro accettare il fatto che la matematica non fosse un corpo di verità; sembrava quasi che Dio avesse creato una molteplicità di algebre e di geometrie con il proposito di confonderli, proprio come aveva confuso le genti di Babele facendo loro parlare lingue differenti»53.

I grandi matematici che avevano affinità o intuito filosofico diedero voce alle obiezioni dei nuovi universi razionali. Basterebbe pensare a William R. Hamilton («Nessuna persona sincera e intelligente può dubitare delle proprietà principali delle rette parallele, così come le espose duemila anni fa Euclide negli Elementi»54), a Francis Masères («Le radici negative… non dovrebbero mai dovuto essere ammesse in algebra, e bisogna sperare che ne vengano escluse»55), a Eulero («È chiaro che non si può neppure includere la radice quadrata di un numero negativo fra i numeri possibili, e bisogna dunque dire che è una quantità impossibile»56), a William Frend («Gli algebristi […] possono trovare dei numeri impossibili i quali, una volta moltiplicati fra loro, generano l'unità. Questo è un linguaggio incomprensibile e ripugna al senso comune; tuttavia, una volta adottato, come tante altre finzioni esso trova i più strenui difensori fra coloro che amano accettare le cose senza un attento esame e disprezzano la voce del retto pensare»57), ad Augustus De Morgan («L'espressione immaginaria… e l'espressione negativa… hanno una caratteristica comune: quando si trova

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una di esse come soluzione di un problema, ciò indica la presenza di qualche incoerenza o assurdità»58), per non parlare di Cartesio, Newton, Leibniz, Carnot, ecc. Sembrava quasi materializzarsi l'anatema scagliato da George Berkeley nel 1734 quando provocava i matematici con: «È vero che [i matematici] non si sottomettono ad alcuna autorità, non accettano nulla per vero senza prove, e non credono ad argomentazioni inconcepibili? È vero che essi non hanno i propri misteri, e quel che è più importante, le loro avversioni e le loro contraddizioni?»59. Come scrisse Poincaré nel 1899: «La logica talvolta genera mostri»60.

Einstein aveva visto giusto quando osservò che «il sogno della conoscenza assoluta aveva agonizzato a lungo, ma era stato David Hume… a dare il colpo finale ai sogni di Platone» 61.

Fu Gauss che recuperò gli "algoritmi metafisici" di Hume all'interno del pensiero matematico tramite l'empirismo dell'applicabilità e la logica del successo: «Qui [nella rappresentazione geometrica] si mostra come il significato intuitivo di − 1 sia del tutto fondato, e per ammettere queste quantità nel dominio degli oggetti dell'aritmetica non è necessario nient'altro»62. La "spinta gaussiana" avrebbe portato successivamente al nuovo paradigma euristico accettato in matematica. Il motto di De Morgan - «Ricordatevi di − 1 »63 - ne rappresenta l'archetipo. «Ma fu ancora Gauss - scrive Kline - ad accorgersi della conseguenza più rivoluzionaria [della geometria non euclidea]. […] Gauss… essendosi reso conto che la geometria euclidea non è necessariamente la geometria dello spazio fisico, cioè non è necessariamente vera, mise la geometria nella stessa classe della meccanica e affermò che il carattere di verità deve essere attribuito soltanto all'aritmetica (e all'analisi che ne costituisce uno sviluppo). Questa fiducia nell'aritmetica è di per sé curiosa. L'aritmetica, infatti, non possedeva in quel periodo nessuna fondazione logica e la sicurezza che l'aritmetica, l'algebra e l'analisi fornissero delle verità sul mondo fisico derivava unicamente dall'esperienza. La storia della geometria non euclidea dimostra in maniera lampante quanto i matematici siano influenzati non dai ragionamenti che effettuano, ma dallo spirito dei tempi. Saccheri aveva respinto gli strani teoremi della geometria non euclidea e ne aveva concluso che Euclide era stato emendato da ogni neo. Un centinaio di anni dopo, invece, Gauss, Lobačevskij e Bolyai accettarono fiduciosamente la nuova geometria. Essi pensavano che la loro geometria fosse logicamente coerente e che perciò fosse altrettanto valida di quella di Euclide. Non avevano però nessuna dimostrazione di questa coerenza. Anche se dimostrarono molti teoremi senza imbattersi in evidenti contraddizioni, rimaneva aperta la possibilità che si potesse dedurre una qualche contraddizione»64.

La scoperta che la geometria euclidea non era una verità unica, necessaria e assoluta riguardo al mondo fu perciò sbalorditiva, ed ebbe effetti di vasta portata e irreversibili. Essa minò alla base le concezioni assolutistiche della conoscenza umana in ampie regioni del pensiero: «I matematici vi si opposero a lungo - scrive Barrow - ma coloro che cercavano di sovvertire le tradizionali certezze euclidee videro in essa un segnale dell'avvento del relativismo. Il termine "non euclideo" venne a indicare qualche cosa di più generale di quanto valeva per le linee nello spazio»65. Una volta spalancata la porta della "trans-intuizione" e della "trans-evidenza" allora si aprì alla «regina delle scienze» un intero mondo di potenzialità latenti, pronte alla cristallizzazione per coerenza. La matematica poteva finalmente essere libera e volare poeticamente attraverso la creatività dello scienziato. «La geometria greca classica - chiarisce Kline - non aveva soltanto imposto delle restrizioni sul dominio della matematica, ma le aveva anche impresso un livello di rigore che ostacolava la creatività. Gli studiosi del XVII secolo avevano spezzato entrambi questi vincoli. Il progresso in matematica richiede un disprezzo quasi completo per gli scrupoli logici»66.

"Disprezzo" che Cantor coltivò più di ogni altro. «La matematica - scriveva nel 1883 - nel suo sviluppo è completamente libera e vincolata soltanto all'evidente condizione che i suoi concetti siano in sé non contraddittori»67. Cantor era sopraffatto dal timore che i vincoli posti alla ricerca avrebbero potuto tagliare le ali alla creatività matematica, «giacché - egli affermava - l'essenza della matematica risiede proprio nella sua libertà»68. Senza di questa, sosteneva Cantor, non ci sarebbero stati i grandi sviluppi registrati nel corso del secolo; non

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avremmo avuto la moderna teoria delle funzioni se Gauss o Cauchy o Jacobi o Weierstrass e Riemann avessero dovuto «sottoporre le loro idee nuove a un controllo metafisico» 69. D'altra parte è proprio la completa assenza del «controllo metafisico» che favorirà l'empirismo logico prima e la «novità relativistica» poi, nel campo della fisica, fomentando - in seno a quest'ultima - un recupero avventato della "libertà cantoriana" e realizzando così quella che poi Gaston Bachelard rileverà come «impronta di una induzione così audacemente estensiva da poter sviare una mente poco abituata alle libertà matematiche» 70. La linea filosoficoprogettuale di Cantor, largamente diffusa tra i matematici, la quale - con le parole e il disappunto di Gottlob Frege - considera sufficientemente giustificata una definizione che «si presta spontaneamente a costituire la base dei nostri ragionamenti, senza condurre mai ad alcuna contraddizione»71, si trasmetterà in seguito nel campo della fisica, tramite Einstein prima e Heisenberg poi, dove il contagio porterà a una vera e propria epidemia di FLOP 72, sintomatica peste delle strutture portanti della scienza contemporanea. Già per il campo della matematica era necessario ricordare che il criterio di non contraddittorietà consente solo di raggiungere «una certezza empirica» - come aveva fin da allora avvisato Frege - giacché bisogna «in ogni caso essere pronti a incontrare da un momento all'altro qualche contraddizione che mandi in rovina l'intero edificio»73. Come esponeva H. Weyl nel 1917: «Una parte essenziale di quest'edificio è costruita sulla sabbia», ed una delle cause essenziali di questa circostanza «va ricercata unicamente nell'arbitrio (commesso sin dall'inizio in matematica) di considerare un campo di possibilità costruttive come un aggregato chiuso di oggetti esistente in sé»74. Ma oramai si era infiltrato anche nella fisica il nuovo credo dei matematici, quello che con enfasi scriveva Dedekind all'amico Weber in una lettera del 1888: «Noi siamo di razza divina e possediamo […] il potere di creare»75.

4. Dagli assiomi ai postulati: il programma di Hilbert tradotto in fisica «La teoria generale della relatività contrastava con la mirabile struttura euclidea del "sacro volumetto di geometria" che aveva incantato Einstein in gioventù; ed essenziale, ai fini della teoria stessa, era la negazione dell'assoluta validità del teorema di Pitagora, per il quale, da ragazzo, aveva trovato una dimostrazione per proprio conto. […] A quasi tutti gli studiosi della geometria elementare, un'alternativa valida del sistema euclideo sembrerebbe impossibile. Invero, il filosofo Kant aveva dichiarato che il sistema euclideo era inevitabile, una necessità del pensiero umano. Ma, a cominciare dagli inizi del diciannovesimo secolo, dopo un periodo di incubazione che risaliva fino a Euclide, matematici audaci proposero effettivamente alternative non euclidee e, come si rese conto Gauss, una volta che Euclide avesse avuto dei concorrenti, la geometria sarebbe divenuta, per necessità di cose, una scienza sperimentale»76. Viene così tracciata da Hoffmann e Dukas la linea di collegamento tra Gauss e Einstein. Le "certezze euclidee" impostate dall'antichità e indicate come rocce inabissabili «in mezzo ai mari agitati della speculazione umana» 77 venivano poste prima in uno stato ipotetico e incerto dall'empirismo gaussiano, poi rese costruzioni immaginarie della creatività umana dal libertinismo cantoriano, e infine ricapitolate nel popperiano mondo 3 delle congetture perché inadeguate per la neopitagorica struttura del mondo: eccessivamente semplicistiche e obsolete per l'universo einsteiniano. «E in virtù di queste… rivoluzioni scrive William Clifford - l'idea dell'universo, il Macrocosmo, il Tutto, come soggetto della conoscenza umana, e perciò di interesse umano, è andato in frantumi» 78. Scrive Russell: «La rivoluzione di Einstein ha spazzato via tutto...» 79. «Dal punto di vista della dialettica hegeliana la teoria della relatività era una comoda fonte di antinomie: non era necessario… trovare una soluzione all'interno della fisica, ma bisognava riconoscere che la materia fosse un'astrazione irreale e che nessuna scienza della materia poteva essere logicamente soddisfacente» 80. Così l'universo di Einstein - grazie alla gaussiana mentalità che si era venuta a creare - avrebbe travalicato i confini pitagorici dell'evidenza e dell'intuizione: «Il mondo di Einstein è un mondo di numeri; questi non suppongono prima di essi né una verità a priori come la

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condizione della loro espressione formale, né una immagine intuitiva come una condizione del loro significato fisico»81. La successiva meccanica quantistica ipostatizzerà questa sorta di metafisica e tramite l'«irrazionale» - per usare i termini di Meyerson -, quell'essenza aberrante di «aritmetizzazione del possibile», concederà quel "passo" contemplato da Bachelard: «Un passo ancora e il reale non è più che la causa occasionale del pensiero» 82. Tanto che ai nostri giorni un Feynman può asserire: «Mi auguro quindi che riuscirete ad accettare la Natura per quello che è: assurda»83.

Innegabile è dunque il tallonamento della nuova fisica nei confronti dello "svuotamento semantico-categoriale" della nuova matematica. Lo strano mondo della fisica del Novecento è intimamente collegato a quello astratto e immaginifico della matematica post-gaussiana84.

Dopo Einstein le geometrie non euclidee non esistevano più soltanto come sistemi logici su fogli di carta: l'architettura dell'universo era non-euclidea e ciò si poteva toccare con mano.

Così come, dopo Heisenberg, le nuove e strane algebre "non commutative" sviluppate a partire dai quaternioni di Hamilton85 - riflesso diretto della rivoluzione gaussiana - potevano finalmente innalzarsi dai "mondi di carta" ed esigere altrettanta dignità "interfenomenologica" del mondo fisico così come lo era stato per le geometrie non euclidee 86. Era la vittoria del freddo costrutto matematico - esterno e alieno alla sfera dell'evidenza, dell'intuizione, del senso comune - che trionfava sui detriti delle categorie kantiane, «completamente annichilite - postillerà Heisenberg - dalle scoperte del nostro secolo» 87.

Hermann von Helmholtz poteva finalmente cantare vittoria - «Essa [l'intuizione] è una conoscenza empirica ottenuta con l'accumulazione e il rafforzamento di impressioni simili ricorrenti nella nostra memoria, e non una forma di intuizione trascendentale data prima di ogni esperienza»88 - così come David Hilbert poteva finalmente vedere realizzato il suo sogno «di dare una formulazione puramente matematica agli assiomi della fisica» 89, liberando «gli assiomi che stanno a fondamento delle discipline matematiche dall'obbligo di corrispondere ai loro significati intuitivi originari e naturali» 90. Siccome per Hilbert «la matematica… possiede coerenza ma nessun significato»91, era arrivato il momento di trasformare gli assiomi in postulati92 (portando così a compimento l'ideale del tracciato epistemologico che da Gauss arriva a Cantor). D'altra parte, sottolinea il matematico Meschkowski, «se sul pensiero di Hilbert non riluce più, come su quello di Platone, "lo splendore dell'essere"», ciò è direttamente collegato alla rivoluzione gaussiana: «l'"esistenza" della geometria non euclidea rende impossibile all'uomo moderno di restare fermo alla concezione spaziale di Platone e di Kant»93.

Il programma hilbertiano, pur lacerato dal celeberrimo teorema di Gödel, continuò a sopravvivere sotto le "vesti metafisiche" della fisica del Novecento, da Einstein in poi 94. Lo sviluppo di un'algebra astratta manipolante enti matematici con procedimenti puramente formali, evitando ogni interpretazione sulla natura di essi, preparerà il terreno epistemico delle teorie scientifiche contemporanee, tanto da rendere possibile affermare che «per esempio, l'integrale di Feynman non corrisponde, per il momento, ad alcun oggetto matematico preciso. È tuttavia è il pane quotidiano dei fisici teorici»95. L'approccio astratto-assiomatico-formalista hilbertiano della fisica moderna è nettamente strumentalista, si nutre dell'efficacia empirica all'interno di un humus positivistico ancorato all'idea machiana di "scienza-formulario"96. È la filosofia dello 0! = 1 , del (-1) 0 = 10 = 11 = 1! = 0! . Eppure il matematico contemporaneo giudizioso avverte: «Malgrado lo stato insoddisfacente della matematica, la molteplicità delle scuole, il disaccordo sugli assiomi da accertare, e il pericolo che nuove contraddizioni, qualora scoperte, possano invalidare gran parte della matematica, alcuni matematici applicano tutt'ora questa scienza ai fenomeni fisici»97. Ma lo scienziato della nuova era, accecato dal potere predittivo della nuova scienza, ha barattato la verità con il successo: «Tutto quello che si può richiedere da una teoria fisica è che le sue predizioni siano in accordo con le osservazioni»98. Come osserva Russell: «Il male è intellettuale… Per conto mio, non ho soluzioni da prospettare; la nostra è un'epoca che sostituisce sempre più il potere agli ideali primitivi, e ciò accade nelle scienze come in altre cose. Mentre la scienza come

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conseguimento di potere diviene sempre più trionfante, la scienza quale conseguimento di verità è uccisa da uno scetticismo generato dall'abilità degli scienziati».

5. Conclusioni: le basi metafisiche della teoria della relatività L'avvento della Relatività, facendo saltare i quadri abituali di riferimento spazio-temporali insieme all'edificio concettuale della fisica newtoniana - che a Kant appariva come «quella conoscenza del sistema del mondo chiara e immutabile per tutto l'avvenire» - e rendendo inintuitivo lo spazio così come il tempo «una creazione del nostro pensiero» 99, veniva a materializzare sullo sfondo della realtà fisica l'ideale "gaussiano-cantoriano-hilbertiano" concepito e architettato precedentemente nell'universo del costrutto matematico. La «rivoluzione copernicana della Relatività» avrebbe apportato un vero e proprio «terremoto dei concetti» - per usare dei termini che Bachelard dichiaratamente mutua da Nietzsche - sulle stesse fondamenta gnoseologiche, dove «tutto l'edificio della ragione è "scosso"»: «Con la scienza einsteiniana incomincia una rivoluzione sistematica dei concetti fondamentali» 100.

Dunque il frutto epistemologicamente più profondo dell'impatto einsteiniano sulla fisica è il suo stesso sconfinamento dal mondo dei numeri e della materia a quello del pensiero, della logica e dei pilastri della conoscenza, come sottolinea Hans Reinchenbach: «La teoria della relatività di Einstein ha dato una forte scossa ai fondamenti filosofici della conoscenza» 101. La stessa Meccanica Quantistica può essere vista come una conseguenza estrema, una ipostasi del tracciato epistemico della teoria di Einstein: non abbiamo fatto altro - avrebbe rilevato lo stesso Born, uno degli artefici della meccanica matriciale - che «avere fedelmente proseguito sulla via che egli [Einstein] ci aveva indicato nei suoi giorni migliori» 102. Confesserà Heisenberg: «Avevo soltanto… applicato il tipo di filosofia che egli stesso aveva posto alla base della sua teoria della relatività ristretta» 103. È stato «Einstein - confermerà Gamow - ad abbandonare le vecchie idee di "senso comune" sul computo del tempo, la misura della distanza e la meccanica, … [arrivando] alla riformulazione della "insensata" Teoria della Relatività. […] Heisenberg ne dedusse che la stessa situazione esistesse nel campo della Teoria dei Quanti»104. Ecco in sintesi la storia di come si sia arrivato a relativizzare la stessa logica. Oramai si parla di una «pluralità» di logiche… Scrive B.L. Whorf in Le lingue e la logica: «Nuovi tipi di logica possono forse aiutarci a capire com'è che gli elettroni […] sembrano comportarsi illogicamente»105.

Rileva Bachelard che intere schiere di scienziati e filosofi che durante i secoli avevano cercato un continuo accumulo e perfezionamento nella decodifica del reale sotto l'ombra di un'unica e primordiale razionalità vengono adesso travolti e devastati dalla «novità relativistica»: una «scienza senza antenati», la Relatività, in quanto non sarebbe «potuta sbocciare che nell'atmosfera di una matematica perfezionata; ecco perché la dottrina manca veramente di antecedenti»106. La matematica assurge così a «vero e proprio metodo di invenzione» 107; da "descrittore" a "creatore", la sua "carica deduttiva" diventa "induttiva": «L'espressione matematica da sola consente di pensare il fenomeno» 108. Il calcolo tensoriale è per Bachelard esempio perfetto di «strumento matematico che crea la scienza fisica contemporanea come il microscopio crea la microbiologia», «Langevin diceva che: "Il calcolo tensoriale conosce la fisica meglio dello stesso fisico"»109.

Il «pensiero relativistico» è, dunque, animato da un'«audacia induttiva», una proprietà "rivelata" dello strumento matematico che nella Teoria gioca un ruolo privilegiato. Ciò, però, non esime ma, anzi, estremizza «lo scandalo della ragione», per usare ancora una volta dei termini bachelardiani. Come mette bene in evidenza Bouasse nella sua critica risoluta al potere esplicativo della teoria di Einstein, decisamente minore rispetto a quella classica: «Si sopprime l'etere e ci si esime dall'insegnarci con che cosa dobbiamo sostituirlo!» 110. Non possiamo dunque accettare l'invito di Hume («Allora buttatelo nel fuoco») di bruciare, tramite Einstein, l'unità del pensiero logico-intuitivo plurimillenario che soggiace nell'"incoscio collettivo" dell'umanità tutta intera. Noi non facciamo - osserva Bouasse - «i sillogismi

144

diversamente da Aristotele: anzi, Aristotele ne conosceva la teoria molto meglio della maggior parte dei nostri filosofi moderni. Bacon, Descartes… si sbagliavano spesso nelle applicazioni; ciò non toglie che i loro attrezzi, dei quali talvolta essi si servivano male, erano esattamente i nostri. Se Bacon, Descartes… risuscitassero, si farebbe loro facilmente comprendere in che cosa essi si sbagliavano, perché i loro cervelli e i nostri sono costruiti allo stesso modo», né sono «suscettibili di perfezionamento». E dunque - si chiede Bouasse come è possibile «simultaneamente rigettare i dati intuitivi del nostro cervello sullo spazio e sul tempo, e serbargli […] fiducia quando si tratta di ragionare? […] Voi dite che il nostro cervello è un falso testimone, poi conservate la metà della sua testimonianza! […] È assurdo. […] Io dico che i dati intuitivi del nostro cervello formano un blocco che non avete il diritto di dividere. Se ne rigettate una parte, siete fatalmente condotti a rigettare il tutto: cosa che sopprime ogni possibilità di conoscenza»111.

Bachelard ammette il "cartesicidio" caratteristico della fisica post-relativistica, simbolo di agonia e sprezzo per la "dea intuizione" e parenti stretti "evidenza", "chiaro" e "distinto": «Siamo di fronte - egli dice - a una vera dialettica. Si procede sistematicamente negando il postulato di analisi cartesiana, esattamente nello stesso modo in cui si sviluppa la geometria non-euclidea negando il postulato di Euclide»112. E se un Cassirer parla di «crisi dell'intuizione» avvenuta «dopo le geometrie non-euclidee e dopo la relatività speciale e generale»113, non può essere nascosto al proprio intelletto - "scolasticamente" inteso - che «come ipotesi metafisica, la teoria di Einstein risulta contraddittoria» 114. Inefficace la certificazione data da Heisenberg che «"non contraddittorio" si riferisce… alla consistenza e completezza matematica del formalismo che viene costruito a partire dagli assiomi» 115, quando è ormai ben noto invece che la formalizzazione matematica di una teoria è ben lungi dallo schermare la stessa dall'incoerenza latente che sfocia a livello di quello che Bridgman definisce come «sfondo descrittivo enorme». Dietro alle equazioni c'è una enorme struttura qualitativa fatta di risultati empirici, ipotesi, generalizzazioni, scelte filosofiche, gusti personali, convenienze: «Quando si prenda atto, finalmente, di questa ricca realtà confrontandola con il ritratto della teoria scientifica tramandato dall'empirismo logico, che vale meno di una caricatura, si comprenderà facilmente che la teoria, accanto ai suoi innegabili successi, non solo può presentare punti deboli, ma può anche sopravvivere ai suoi stessi fallimenti»116. Come conferma lo stesso Bridgman: «Ogni sistema di equazioni può comprendere solo una piccolissima parte della situazione fisica effettiva: dietro le equazioni vi è uno sfondo descrittivo enorme, tramite il quale esse stabiliscono legami con la natura»117. È solo grazie all'«oscurità matematica» 118 che regna sovrana sulle nuove teorie che il novello "apprendista stregone" può ritenersi degno di possedere l'arcana chiave meta-ermeneutica e il potere ad essa congiunto. Sentendosi appartenente alla pitagorica classe dei neo-mathematicoi non si abbassa ad una «umana, troppo umana» rappresentazione, figlia dell'intuizione.

L'"ammassato" gruppo degli acousmaticoi - cioè coloro che, come denunciava Cartesio già ai suoi tempi, «si astengono dall'esaminar molte cose... poiché stimano che possano esser comprese da altri forniti di maggior intelligenza, abbraccian[d]o il parere di coloro sulla cui autorità maggiormente confidano»119 - si accascia ai bordi delle corsie preferenziali del pensiero scientifico, affidandosi ciecamente ai cosiddetti "esperti" («cieca schiavitù al dogma», direbbe Herbert Dingle120), nella convinzione che quanto non si sia riuscito a intendere sia dovuto ad un inadeguato e insufficiente numero di neuroni a loro disposizione; una sorta di "filosofia del rimando" «di cui sono preda non solo tanti studenti, ma anche tanti docenti»121. Ed ecco così il «mastery, instead of the servitude, of mathematics in relation to physics» denunciato da Dingle122. Non deve sorprende allora che il matematismo entri a far parte della nuova ermeneutica contemporanea e a sostituire interi blocchi kantiani della psiche in altrettanti moduli "gaussiani". Confessa senza malizia un docente universitario di ingegneria elettrica del calibro di Paul Nahin: «Later, in college, I would learn that the operation of radio is impossible to understand, at deep theoretical level, without an understanding of − 1 »123. È la matematica che prende il posto del sillogismo aristotelico.

145

Come manifesta apertamente Dirac: «Le nuove teorie, considerate al di là della struttura matematica, sono costruite con concetti fisici che non possono essere spiegati in termini di cose precedentemente note allo studente, che neppure possono essere spiegati adeguatamente con le parole»124. Riesce facile concepire, a questo punto, come si stia approdando con sempre più facilità a riconoscere con Bridgman che «tutta la nostra conoscenza è relativa» e che in questo senso «la relatività in senso generale diventa un puro truismo» 125. Si arriva così alla signoria della sintassi sulla semantica, all'indebolimento, detronizzazione e perdita del fondamento126, come anche di una umana comprensione127.

Il pericolo di un matematismo sofisticato e "trans-categoriale" alla guida delle teorie scientifiche è estremamente elevato, e, se lasciato a se stesso, rischia di diventare un alieno alla ragione stessa: dovremo allora abituarci a vedere sorpresi e sconcertati gli stessi creatori delle teorie scientifiche quando i razzi di questo "Math-Alieno" travalicano e sconfinano gli universi dell'intuizione, come accadde allo stesso Einstein quando si scontrò con la precessione di Thomas128. Bisogna recuperare lo status baconiano di una matematica al servizio della ragione e non viceversa: quella che l'Einstein non ancora condizionato dalla spinta minkowskiana129 era solito sottostare, come dimostra una frase dello stesso riportata da un suo amico nel 1920: «I'm afraid I'm wrong again. I can't put my theory into words. I can only formulate it mathematically, and that's suspicious» 130. E nel 1927, in occasione del secondo centenario della morte di Newton, in una lettera al segretario della Royal Society e poi riportata su Nature (119) e su Science (65) scrive: «È solo nella teoria dei quanti che il metodo differenziale di Newton diviene inadeguato, e infatti viene meno la causalità in senso stretto. Ma non è detta l'ultima parola. Possa lo spirito del metodo di Newton consentirci di riportare l'armonia tra la realtà fisica e ciò che è alla base di tutto il suo insegnamento: la causalità in senso stretto». Auspichiamoci la stessa cosa, anzi recuperiamo con Newton l'essenza stessa della matematica, quando nel 1728 scrisse: «Ma è giusto che le radici delle equazioni debbano essere spesso impossibili [complesse], per timore che esse debbano esibire i casi di problemi che sono impossibili come se fossero possibili»131.

Note 1

W. Heisenberg, Il contenuto intuitivo della cinematica e della meccanica nella teoria quantistica, in S. Boffi (ed.), De Broglie - Schrödinger - Heisenberg, Onde e particelle in armonia. Alle sorgenti della meccanica quantistica, Milano 1991, p 181.

2

Cit. in B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, Milano 2002, p. 30.

3

G. Bachelard, Il nuovo spirito scientifico, Roma-Bari 1978, p. 156.

4

A. Pais, Il danese tranquillo. Niels Bohr, un fisico e il suo tempo, 1885-1962, Torino 1993, p.75.

5

Per un approfondimento si veda U. Bartocci - R.V. Macrì, Il linguaggio della matematica, «Episteme», 5, 2002.

6

W. Heisenberg, Fisica e filosofia, Milano 1994, p. 44.

7

A. Einstein, Replica alle osservazioni dei vari autori, in P.A. Schilpp (ed.), Albert Einstein, scienziato e filosofo. Autobiografia di Einstein e saggi di vari autori, Torino 1958, p. 629.

8

9

V.F. Lenzen, La teoria della conoscenza di Einstein, in P.A. Schilpp (ed.), op. cit., p. 307.

Ibidem, p. 326. Dal rischio reale di una accecante reverenza da parte della fisica nei confronti della matematica contemporanea, tale da ammaliare e sottomettere l'eredità di Galileo nelle mani della Scuola di "prestigio matematico" del momento ci mette in guardia Morris Kline nel suo capolavoro

146

Matematica: la perdita della certezza, Milano 1985, p. 15: «Le teorie fisiche più sviluppate, nella maggior parte dei casi, sono interamente matematiche (pur ammettendo che i risultati di tali teorie sono interpretati in termini di dati sensibili e di oggetti fisici: si possono sentire i suoni emessi da una radio pur senza avere la più pallida idea di cosa sia un'onda radio da un punto di vista fisico). Perciò anche gli scienziati che non si occupano in prima persona del problema dei fondamenti devono nondimeno porsi il problema di quale matematica possono utilizzare con sicurezza se non vogliono sprecare anni di lavoro servendosi di una matematica priva di salde basi».

10

M. Polanyi, La conoscenza personale. Verso una filosofia post-critica, Milano 1990, p. 92.

11

P.A.M. Dirac, in D. Monti, Equazione di Dirac, Torino 1996, p. 120. Racconta Sommerfeld che a seguito del successo che ebbe la teoria di Einstein dopo la spedizione dell'«apostolo ispirato della dottrina di Einstein, […] Il grande astronomo inglese Sir Arthur Eddington, […] nel 1920, un inviato della "Kölnische Zeitung" mi chiese qualche particolare su di essa, gli dissi che non era argomento per il grosso pubblico, sfornito com'è delle conoscenze matematiche necessarie per la comprensione di questa teoria» (A. Sommerfeld, "Per il compleanno di Albert Einstein", in P.A. Schilpp (ed.), op. cit., Torino 1958, p. 53).

12

J.D. Barrow, Teorie del tutto. La ricerca della spiegazione ultima, Milano 1992, p. 316.

13

P.A.M. Dirac, op. cit., p. 116.

14

J.P. Changeux - A. Connes, Pensiero e materia, Torino 1991, p. 12.

15

P.A.M. Dirac, op. cit., p. 122. Esattamente di parere opposto la tradizione dei fisici italiani di inizio secolo che, intendendo le rappresentazioni fisico-matematiche come parametrizzazioni descrittive di ciò che non può avere altro fondamento che nel territorio dell'evidenza fenomenica, con le parole di Antonio Garbasso nel 1910 così si pronunciava: «A voler considerare le cose con pieno rigore, si direbbe anzi che di necessità il modello analitico [matematico] sia più lontano dalla natura che il modello, in apparenza più rozzo, della fisica sperimentale. Perché se la percezione fornisce una immagine della realtà, e l'analogia fisica è già una rappresentazione mediata, il calcolo che traduce quest'analogia nel linguaggio dell'algebra, costituisce in qualche modo un'icona dell'icona dell'icona» (A. Garbasso, Fisica d'oggi, filosofia di domani, Milano 1910, p. 118).

16

B. Russell, La mia filosofia, Roma 1995, p. 177.

17

W. Heisenberg, La tradizione nella scienza, Milano 1982, p. 32.

18

W. Heisenberg, Fisica e filosofia, op. cit., p. 84.

19

P.P. Wiener - A. Noland (edd.), Le radici del pensiero scientifico, Milano 1971, p. 1.

20

Aristotele, Metaph., I, 5, 985 b 23 - 986 a 16.

21

Cfr. T.M. Tonietti, Verso la matematica nelle scienze: armonia e matematica nei modelli del cosmo tra Seicento e Settecento, in M. Mamone Capria (ed.), La costruzione dell'immagine scientifica del mondo, Napoli 1999. Il mondo antico è completamente intessuto da tale concezione. Cfr., solo per fare qualche esempio, Proclo, In Platonis theologiam, IV, 34; Boezio, De institutione arithmetica, I, 1 e 2; Agostino, Ad Orosius contra Priscianum et Origenem, PL 42, 674, e De quantitate animae, 8-12, PL 32, 1042-1047; Alberto Magno, Metaphys., I, tr. 4, c. 2; Bonaventura, Itinerarium mentis in deum, 2, n. 10; Alano di Lilla, Sermo de trinitate, 255.

22

B. Russell, op. cit., p. 238.

23

E. Husserl, Idee per una fenomenologia, Torino 1981, I, p. 95.

24

Nicola Cusano, La dotta ignoranza, Roma 1991, p. 76.

147 25

E. Kant, Critica della ragion pratica, a cura di V. Mathieu, Milano 1996, p. 53.

26

R. Nobili, La cognizione dello spazio e il principio di dualità, Pavia, preprint 1990, p. 5.

27

Cfr. il paragrafo 16c di A. Pais, «Sottile è il Signore…»: la scienza e la vita di Albert Einstein, Torino 1991, per una rassegna dei titoli del "Times" e di altre riviste scientifiche e non durante il momento della "beatificazione" di quel memorabile novembre: «Rivoluzione nella scienza. Nuova teoria dell'universo. La concezione newtoniana demolita», «Euclide al tappeto», «Notizia sconvolgente, che farà sorgere i dubbi perfino sull'affidabilità della tavola pitagorica», «Tempi duri per persone colte», «All'assalto dell'assoluto», ecc.

28

Il 1° gennaio del 1801 l'Osservatorio di Palermo poté vantare una sensazionale scoperta fatta dall'astronomo Giuseppe Piazzi: il primo asteroide mai osservato, Cerere. Piazzi, tuttavia, aveva potuto osservare solo 9° dell'intera orbita del pianeta; una porzione fino allora considerata insufficiente per consentire il calcolo dell'orbita completa. Gauss accettò la sfida e arrivò a calcolare un'orbita ellittica innovativa rispetto ai tentativi utilizzati fino allora, che in seguito si rivelò esatta.

29

R. Tazzioli, Gauss, principe dei matematici e scienziato poliedrico, Milano 2002, p. 36.

30

Ibidem, p. 39.

31

Gauss completerà l'interpretazione geometrica dei numeri complessi solo a partire dal 1831, perfezionando il cammino intrapreso nella sua dissertazione discussa a Helmstedt nel 1799, dove è contenuta la dimostrazione del famoso teorema fondamentale dell'algebra, che afferma che ogni polinomio a coefficienti complessi ammette almeno una radice complessa. Lo studio delle funzioni complesse venne poi proseguito da Cauchy che nel 1825 propose una generalizzazione dell'integrale definito che includesse anche le variabili complesse.

32

Ibidem, p. 6.

33

È vero quanto asserisce Russell: «L'autoevidenza è uno degli argomenti più problematici di tutta l'epistemologia» (B. Russell, Teoria della conoscenza, Roma 1996, p. 248). D'altra parte la soluzione tentata da questi sembrerebbe ben lontana da una compiutezza filosofica soddisfacente. Si veda, per completezza, oltre che Autoevidenza, in B. Russell, op. cit., pp. 248 e sgg., anche La matematica e i metafisici, in B. Russel, Misticismo e logica, pp. 71 e sgg., dove viene sottolineato che «l'evidenza è spesso un fuoco fatuo» (p. 74).

34

Cit. in J.D. Barrow, La luna nel pozzo cosmico, Milano 1994, p. 31.

35

J.D. Barrow, op. cit., p. 40.

36

M. Kline, Matematica: la perdita della certezza, op. cit., p. 98.

37

Ibidem. La similitudine con Einstein arriva addirittura nella conversione in età matura e nel rigetto del proprio credo epistemologico avuto prima della pienezza. Come il "secondo" Einstein nella maturità rinnegherà il "primo" per aver accettato la metafisica operazionista, anche Gauss, nella fase matura della sua vita, rimediterà e rimetterà in discussione la matrice empirista e strumentalista che l'aveva guidato per tutto l'arco degli anni fruttuosi e memorabili. Così come anche tutte e due le "riconversioni" avverranno troppo tardi in rapporto all'avvio degli sviluppi successivi, che cristallizzeranno invece il cammino empirio-operazionista della scienza posteriore.

38

C.B. Boyer, Storia della matematica, Milano 1990, p. 322.

39

Ibidem, p. 326.

148 40

«Quanto ai numeri negativi, sebbene essi fossero diventati noti in Europa attraverso i testi arabi, la maggior parte dei matematici del XVI e del XVII secolo non li accettava come numeri o, se lo faceva, non li accettava tuttavia come radici delle equazioni» (M. Kline, Storia del pensiero matematico, vol.

I, Torino 1996, p. 294). Racconta Kline che «Pascal considerava la sottrazione di 4 da 0 come una totale assurdità» e che Cartesio «chiamava false le radici negative delle equazioni sulla base del fatto che esse pretendono di rappresentare numeri minori di nulla» e soltanto per il fatto da lui dimostrato che «le radici false possono essere mutate in radici reali, Descartes era disposto ad accettare i numeri negativi» (Ibidem, pp. 294-295).

41

Termine coniato da Cartesio allorché approfondì l'impossibilità di "trasmutare" le radici complesse in radici reali, come invece era riuscito a fare per quelle negative: «Esse non sono perciò reali ma immaginarie, cioè non sono numeri. Descartes tracciò una distinzione più chiara dei suoi predecessori fra le radici reali e immaginarie delle equazioni» (Ibidem, p. 296).

42

Ibidem, p. 295.

43

C.B. Boyer, op. cit., p. 330.

44

Ibidem, pp.332-333.

45

Sottolinea però Kline che «le opinioni avanzate di Girard non ebbero tuttavia alcuna influenza» (M. Kline, Storia del pensiero matematico, op. cit., p. 296).

46

Paul J. Nahin, An Imaginary Tale. The Story of

47

Ibidem, p. 82.

− 1 , Princeton 1998, p. 31.

Scriveva De Morgan nel 1831: «Abbiamo dimostrato che il simbolo − 1 è privo di significato, anzi addirittura auto-contraddittorio e assurdo.» (P.J. Nahin, op. cit., p. 82). Aggiunge ai nostri giorni M. vos Savant: «Yet it is accepted, and imaginary numbers are used routinely. But how can we justify using them to prove a contradiction?» (Ibidem, p. 224).

48

49

C.B. Boyer, op. cit., p. 332. Il "sospetto di contraddizione" che nasce dalla manipolazione con i numeri negativi viene così candidamente spiegata da Paul J. Nahin: «This suspicion of negative numbers seems so odd to scientists and engineers today, however, simply because they are used to them and have forgotten the turmoil they went through in their grade-school years. In fact, intelligent, nontechnical adults continue to experience this turmoil, as illustrated in the following wonderful couplet, often attributed to the poet W. H. Auden: "Minus times minus is plus. The reason for this we need not discuss."» (P.J. Nahin, op. cit., pp. 13-14).

50

P.J. Nahin, op. cit., pp. 224-6.

51

«Per verificare l'applicabilità della geometria euclidea e della sua geometria non euclidea Gauss misurò effettivamente la somma degli angoli del triangolo formato dalle cime delle tre montagne Brocken, Hohehagen e Inselberg» (M. Kline, Storia del pensiero matematico, vol. II, Torino 1996, p.

1017).

52

M. Kline, Matematica: la perdita della certezza, op. cit., p. 103.

53

Ibidem, pp. 106-7.

54

Ibidem, p. 107.

55

Ibidem, p. 132.

56

Ibidem, p. 134.

149 57

Ibidem, pp. 168-9.

58

Ibidem, p. 170.

59

Cit. in B. Russell, La mia filosofia, op. cit., p. 217.

60

M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1136.

61

D. Overbye, Einstein innamorato. La vita di un genio tra scoperte scientifiche e passione romantica, Milano 2002, pp. 126-7.

62

M. Kline, Matematica: la perdita della certezza, op. cit., pp. 172-3.

63

M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1139.

64

Ibidem, p. 1026.

65

J.D. Barrow, La luna nel pozzo cosmico, op. cit., p. 35. «All'origine della svolta c'era stata l'opera di Gauss sulla geometria delle superfici, che iniziava lo studio delle proprietà intrinseche delle superfici, indipendenti cioè dallo spazio in cui erano immerse» (E. Giusti, Ipotesi sulla natura degli oggetti matematici, Torino 1999, p. 84). Nell'opera di Gauss del 1828, Disquisitiones generales circa superficies curvas, l'idea chiave è quella di considerare «la superficie non come la frontiera di un solido» ma di per sé stessa, con le parole di Eugenio Beltrami «come un velo infinitamente sottile».

L'approccio di Gauss sarà ripreso anni dopo da Riemann, il quale - nella sua lezione di abilitazione tenuta proprio di fronte a Gauss nel giugno del 1854 - esporrà la sua celebre teoria delle varietà pluriestese. I perfezionamenti successivi di Beltrami e Ricci Cubastro riveleranno la grande fecondità dell'idea gaussiana nella formulazione matematica della Relatività generale, come ebbe a sottolineare lo stesso Einstein: «L'importanza di Gauss per lo sviluppo della fisica moderna e specialmente per i fondamenti matematici della teoria della relatività è enorme» (Cit. in R. Tazzioli, op. cit., p. 64).

66

M. Kline, Storia del pensiero matematico, vol. I, op. cit., p. 465.

67

Cit. in U. Bottazzini, Insiemi di punti e numeri transfiniti, in Paolo Rossi (ed.), Storia della scienza moderna e contemporanea, vol. III, tomo I, Milano 2000, p. 62.

68

Ibidem, p. 63.

69

Ibidem. Per questo motivo Kant era odiato da Cantor: «Kant era la sua bestia nera» (B. Russell, Una filosofia per il nostro tempo, Milano 1995, p. 24). Per un motivo opposto a quello di Cantor, Kant stava sullo stomaco anche a Russell. Sulla copertina di un libro di Cantor spedito dall'autore medesimo a Russell c'era scritto: «Vedo che il vostro motto è Kant o Cantor» (Ibidem). Ricorda Alan Wood in una conversazione avuta con Bertrand Russell la teatrale manifestazione di contrarietà che questi aveva «circa l'affermazione di Kant riguardo all'esistenza di un elemento soggettivo nella matematica: il tono della voce può essere descritto solo come di disgusto, simile a quello di un fondamentalista posto di fronte all'ipotesi che Mosè abbia inventato di sana pianta i Dieci Comandamenti: "Kant mi ha stufato."» (A. Wood, La filosofia di Russell. Uno studio sulla sua evoluzione, in B. Russell, La mia filosofia, op. cit., p. 223)". Einstein invece parteggiava per la tesi cantoriana, la quale - oltre a «fare rivoltare Kant nella tomba» (D. Overbye, op. cit., p. 131) - propendeva per una vittoria della libera creatività sulla rigidità delle kantiane forme a priori: «Gli assiomi della matematica sono altrettanti esempi dell'opinione di Einstein per cui i concetti sono libere creazioni della mente umana. […] In Kant… l'attività creativa della mente era limitata dalle forme a priori dell'intuizione. Ma il pensiero matematico se ne liberò con la scoperta di geometrie non euclidee, e si capisce quindi come Einstein abbia dotato il pensiero di una maggiore libertà di creazione che con Kant» (V.F. Lenzen, La teoria della conoscenza di Einstein, op. cit., p. 327).

70

G. Bachelard, La valeur inductive de la Relativité, Paris 1929, p. 61.

150 71

Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p.

257.

72

FLOP = Falsificatore Logico Potenziale, neologismo del presente autore. Si veda, per un approfondimento, I FLOP nella trattazione relativistica del tempo, in F. Selleri (ed.), La natura del tempo, Bari 2002.

73

Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p.

257.

74

Cit. in U. Bartocci, Riflessioni sui fondamenti della matematica ed oltre, «Synthesis», n. 3, anno III, 1994, p. 26.

75

Inevitabile la ricaduta di tale mentalità sulla fisica contemporanea. Scrive Weizsäcker, ad esempio, che gli elettroni rimangono stabili sulle loro orbite perché le «leggi della meccanica quantistica… glielo impongono» (Cit. in P. Plichta, La formula segreta dell'universo, Casale Monferrato 1998, p.

177).

76

B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, op. cit., p. 144. Einstein sigillerà irreversibilmente, in seguito, tale visione gaussiana. Con le parole di Max Jammer: «Fu Einstein che chiarì come la geometria, allorché viene applicata in questo modo all'indagine dello spazio fisico, cessa di essere una scienza assiomatico-deduttiva e diviene una fra le scienze naturali» (M. Jammer, Storia del concetto di spazio, Milano 1981, p. 148).

77

J.D. Barrow, op. cit., p. 34.

78

W.K. Clifford, Philosophy of the Pure Sciences, in Lectures and Essays, London 1879, vol. I, p.

300, cit. in D. Overbye, op. cit., p. 131.

79

B. Russell, La mia filosofia, op. cit., p. 39.

80

Ibidem, p. 41.

81

L. Brunschvicg, L'expérience humaine et la causalité physique, Paris 1949, p. 410.

82

G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 197.

83

R.P. Feynman, QED. La strana teoria della materia e della luce, Milano 1996, p. 25.

84

Scrive Heisenberg in Fisica e filosofia: «È vero che ci apparirà anche subito chiaro che questi concetti non sono ben definiti nel senso scientifico e che la loro applicazione può condurre a varie contraddizioni; ma noi sappiamo tuttavia che essi toccano la realtà. Può essere utile a questo proposito ricordare che perfino nella parte più precisa della scienza, nella matematica, noi non possiamo fare a meno di servirci di concetti che implicano delle contraddizioni. È ben noto, ad esempio, che il concetto d'infinito conduce a contraddizioni che sono state analizzate; eppure sarebbe praticamente impossibile costruire senza questo concetto le più importanti parti della matematica» (op. cit., p. 233).

85

«L'abbandono dell'antica ipotesi di Euclide ebbe un parallelo nella elaborazione di nuove algebre che rinunciavano a un altro assunto profondamente radicato, secondo il quale, quando l'operazione A era seguita dall'operazione B, il risultato doveva essere identico a quello prodotto compiendo prima B e poi A. […] La costruzione di Hamilton segnò l'inizio di un periodo in cui i matematici presero a creare liberamente sistemi di simboli servendosi di regole prestabilite e compatibili che ne governassero le combinazioni reciproche senza curarsi che tali sistemi descrivessero alcunché nel mondo reale» (J.D. Barrow, op. cit., pp. 38-9).

151 86

Così come «la teoria della relatività - scrive Heisenberg - sembra da principio una cosa astratta ed estranea», bisogna abituarsi («il nostro pensiero si può adattare solo lentamente all'ampliato dominio sperimentale e al nuovo mondo concettuale») con la teoria dei quanti «a una rinuncia ancor più profonda ai concetti finora abituali» (W. Heisenberg, I princìpi fisici della teoria dei quanti, Torino 1987, p. 74). Bisogna solo aspettare, cioè, pazientemente che i nuovi concetti rivoluzionari e astrusi sedimentino sufficientemente nella nostra mente, come il «Maestro della Scuola Copenhagen» suggerisce ad Alice, sconcertata dal mondo dei quanti: «Ci farai l'abitudine presto, non temere» (R. Gilmore, Alice nel paese dei quanti, Milano 1996, p. 78). Rileva a questo riguardo Jenner Barretto Bastos Filho: «Il paradigma di Copenhagen-Göttingen ha dominato lo scenario della fisica […] Il positivismo, la sopravvalutazione della misura, la fuga verso il formalismo matematico, e addirittura le "onde di coscienza", hanno abitato stabilmente nei corsi di meccanica quantistica, operando un vero lavaggio del cervello» (J.B. Bastos Filho, La dissoluzione della realtà: irrealismo e indeterminismo nella fisica del microcosmo, in M. Mamone Capria (ed.), op. cit., pp. 448-9).

87

W. Heisenberg, Fisica e filosofia, op. cit., p. 107.

88

Hermann von Helmholtz, Sull'origine e il significato degli assiomi geometrici, in A. Einstein, Relatività: esposizione divulgativa, Torino 1967, p. 249.

89

J.D. Barrow, op. cit., p. 197.

90

R. Nobili, op. cit., p. 3. «Il programma di Hilbert era più innovativo di quanto a prima vista potesse apparire. Fino ad allora, per accertare la coerenza di una struttura matematica era stato necessario fornire un'interpretazione particolare (ossia un "modello", come veniva chiamato) degli assiomi in questione. Se questo modello nel mondo reale esisteva, il sistema matematico veniva considerato coerente, nella convinzione che la realtà fisica fosse esente da contraddizioni. […] Hilbert abbandonò questo infruttuoso procedimento per cercare prove di coerenza che non facessero uso di modelli (né fisici né matematici) del significato degli assiomi» (J.D. Barrow, op. cit., p. 198).

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J.D. Barrow, op. cit., pp. 194-5. Scrive Bertrand Russell: «La matematica pura è interamente costituita da asserzioni per effetto delle quali, se un tale enunciato è vero per qualcosa, allora il tale altro enunciato è vero per quella cosa. È essenziale non discutere se il primo enunciato è realmente vero, e non indicare quale sia la cosa per la quale si suppone che sia vero. […] Così la matematica può essere definita come la materia nella quale non sappiamo mai di che cosa stiamo parlando, né se ciò che stiamo dicendo è vero» (B. Russell, Misticismo e logica, op. cit., pp. 71-2).

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La differenza sta nell'autoevidenza: i primi sono di per sé «chiari e distinti» direbbe Cartesio, mentre i secondi dovranno sottostare alla "spada di Damocle" di una possibile ventura contraddizione, cantorianamente potenziale. Mentre gli assiomi sono, nelle parole di Benjamin Fedorovich Kagan (1869-1953), «verità ammesse da ogni uomo, alle quali l'uomo inevitabilmente ricorre tanto in ciascuna scienza, quanto in qualsiasi ragionamento quotidiano», i postulati costituiscono precise richieste che «il lettore deve accettare accingendosi allo studio di una disciplina, affinché i ragionamenti successivi non suscitino obiezioni da parte sua» (Cit. in R. Tazzioli, op. cit., p. 66).

93

H. Meschkowski, Mutamenti nel pensiero matematico, Torino 1973, p. 87. Come rileva giustamente Umberto Bartocci: «Logicismo, formalismo, crisi dei fondamenti, etc., sono tutti riconducibili nell'illustrato contesto ad esiti naturali del tentativo di espungere la geometria euclidea dai fondamenti della matematica» (U. Bartocci, op. cit., p. 24).

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È paradigmatico «il detto di Einstein che "la base assiomatica della fisica teorica… deve essere liberamente inventata"» (F.S.C. Northrop, La concezione della scienza di Einstein, in P.A. Schilpp (ed.), op. cit., p. 341).

95

96

J.P. Changeux - A. Connes, op. cit., p. 16.

Scrive, ad esempio, Roger Penrose: «La teoria ha due argomenti molto efficaci a suo favore e solo uno, di scarso rilievo, a sfavore. Innanzitutto, la teoria è sorprendentemente esatta rispetto a tutti i

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risultati sperimentali fino ad oggi ottenuti. In secondo luogo [...] si tratta di una teoria di straordinaria e profonda bellezza dal punto di vista matematico. L'unica cosa, che può essere detta contro di essa, è che, presa in assoluto, non ha alcun senso!» (Cit. in A. Zeilinger, Problemi di interpretazione e ricerca di paradigmi in meccanica quantistica, in F. Selleri (ed.), Che cos'è la realtà. Dibattito nella fisica contemporanea, Milano 1990, p. 123).

97

M. Kline, Matematica: la perdita della certezza, op. cit., p. 15.

98

S.W. Hawking - R. Penrose, The Nature of Space and Time, Princeton 1996, p. 116.

99

E. Schrödinger, L'immagine del mondo, Torino 2001, p. 115.

100

G. Bachelard, La dialettica filosofica dei concetti della relatività, in P.A. Schilpp (ed.), op. cit., p.

511.

101

H. Reichenbach, Relatività e conoscenza a priori, Bari 1984, p. 59.

102

Cit. in F. Selleri, La fisica del novecento. Per un bilancio critico, Bari 1999, p. 94.

103

W. Heisenberg, La tradizione nella scienza, op. cit., p. 127.

104

G. Gamow, Trent'anni che sconvolsero la fisica, Bologna 1966, p. 107.

105

Scrive il logico americano Alonzo Church: «Noi non attribuiamo alcun carattere di unicità o di verità assoluta ad alcun sistema logico particolare… possiamo considerare l'analogia di una geometria tridimensionale utilizzata nella descrizione dello spazio fisico… può esservi, e in realtà vi è, più di una geometria il cui uso è lecito nella descrizione dello spazio fisico. Analogamente, esiste senza dubbio più di un sistema formale che può essere utilizzato come logica, e di questi sistemi uno può essere più proficuo o più comodo di un altro; non si può, però, dire che uno sia giusto e l'altro sbagliato» (Cit. in J.D. Barrow, op. cit., p. 43).

106

G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 99.

107

G. Bachelard, Il nuovo spirito scientifico, op. cit., p. 39.

108

Ibidem, p. 50.

109

Ibidem.

110

H. Bouasse, La question préalable contre la théorie d'Einstein, Paris 1923, p. 18.

111

Ibidem, pp. 18-20. La trad. it. è a cura di M.R. Abramo in Gaston Bachelard e le fisiche del novecento, Napoli 2002, pp. 21-2.

112

G. Bachelard, L'expérience de l'espace dans la physique contemporaine, Paris 1937, p. 42.

113

E. Cassirer, Determinismo e indeterminismo nella fisica moderna, Firenze 1970, p. 243.

114

H. Bouasse, op. cit., p. 17.

115

W. Heisenberg, La tradizione nella scienza, op. cit., p. 137.

116

F. Selleri, Introduzione, in F. Selleri (ed.), La natura del tempo, op. cit., p. 22. Dinanzi al voltafaccia dell'Einstein maturo che cambia rotta e fa una "inversione a U" sul tracciato epistemologico intrapreso negli anni memorabili, Max Born - sbigottito e dispiaciuto per la «tragedia» di aver perso «il nostro capo e portabandiera» - ammette: «Dobbiamo accettare il fatto che anche nella

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fisica, come in tutte le altre attività umane, le convinzioni fondamentali vengono prima del ragionamento» (M. Born, Le teorie statistiche di Einstein, in P.A. Schilpp (ed.), op. cit., p. 68).

117

P.W. Bridgman, La logica della fisica moderna, Torino 1965, pp. 83-84.

118

M. Mamone Capria, La crisi delle concezioni ordinarie di spazio e di tempo, in M. Mamone Capria (ed.), op. cit., p. 347.

119

R. Descartes, Regulae ad directionem ingenii, in Opere filosofiche, vol. I, a cura di E. Garin, RomaBari 1991, p. 64.

120

H. Dingle, Science at the Crossroads, London 1972, p. 13.

121

U. Bartocci - R.V. Macrì, Il linguaggio della matematica, op. cit..

122

H. Dingle, op. cit., p. 130.

123

P.J. Nahin, op. cit., p. XV.

124

F. Selleri, La causalità impossibile. L'interpretazione realistica della fisica dei quanti, Milano 1988, p. 45.

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P.W. Bridgman, op. cit., p. 52. Ciò viene tradotto all'interno dell'immagine scientifica del mondo come un continuo susseguirsi di teorie rivoluzionarie senza arrivare mai alla verità: una «corsa che non avrà mai fine» (F.A. Levi, Esplorazione del tempo e dello spazio, Milano 1981, p. 126), quando invece lo stesso artefice della nuova visione del mondo si affannava per trovare la chiave "definitiva".

Ciò fu osservato distintamente da Wolfgang Pauli, il quale a proposito della tenacia e dell'inventiva di Einstein a garantire ogni anno una nuova teoria unitaria scrisse: «È interessante dal punto di vista psicologico che per qualche tempo la teoria corrente sia ritenuta dal suo autore "la soluzione definitiva"» (Cit. in R. Highfield - P. Carter, Le vite segrete di Albert Einstein, Padova 1994, p. 190).

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Un approfondimento si ha in R.V. Macrì, Relativismo e pensiero debole: la perdita del fondamento, «Episteme», n.1, 2000.

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L'esasperato formalismo matematico che accompagna l'immagine scientifica del mondo nella nostra epoca sembra voler spezzare il nesso storico ed epistemologico tra scienza e filosofia, dimenticando che la prima è figlia della seconda: «La filosofia e la scienza sono assai più intimamente legate che non credano gli scienziati che disprezzano la prima e i filosofi che ignorano la seconda» (A. Garbasso, "Scienza realistica", in Scienza e poesia a cura di J. de Blasi, Firenze 1934, p. 220). Bisogna dunque domandarsi perché per una parte considerevole della comunità scientifica l'opera di divulgazione è temeraria e temuta: per la paura legittima di inquinare ciò che è puro (matematico) o non piuttosto per la paura di scoprire in uno stato chimerico quello che si credeva matematicamente compreso? Può la (falsa) matematica ostruire il cammino ad una "umana" (o fisica, o filosofica) comprensione? A sentire lo stesso Einstein il pericolo non è illusorio: «Da quando i matematici hanno invaso la teoria della relatività, io stesso non la capisco più» (A. Sommerfeld, Per il compleanno di Albert Einstein, in P.A. Schilpp (ed.), op. cit., p. 54).

128

129

Cfr. A. Pais, "Sottile è il Signore…", op. cit., cap.7 (7a.3), pp.158-159.

Scrive Lewis Pyenson nel suo meritevole The young Einstein: the advent of relativity (Bristol Boston 1985, p. 80): «Minkowski thought that by mathematising special relativity he clarified the essential physical features of Einstein's theory. Although Einstein accepted Minkowski's mathematisation as only a technical improvement on his own work, many other physicists and mathematicians attempted to extend Minkowski's formulation of matter and electromagnetism. Few realised that there were major differences between Minkowski's and Einstein's approaches to the principle of relativity». Per quanto riguarda l'influenza dei matematici su Einstein, in particolare della Scuola di Göttingen, oltre al suddetto testo di Pyenson si cfr. anche S. Walter, Minkowski,

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Mathematicians and the Mathematical Theory of Relativity, in H. Goenner et al. (edd.), The Expanding Worlds of General Relativity, Birkhäuser 1999.

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Cit. in L. Pyenson, op. cit., p. 28.

131

I. Newton, Arithmetica universalis, 2ÂŞ ed., 1728, p. 193.

----[Una presentazione dell'autore si trova nel numero 1 di Episteme] "RVM" <rvm2000@inwind.it>

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Did Einstein Claim That Nature Has Mathematical Structure?

(JarosĹ&#x201A;aw Mrozek) Abstract This paper is an attempt to analyse some of Einstein's utterances concerning the relationship between mathematics and the world and its ontological structure. The author tries to interpret, in a non-standard way, Einstein's standpoint expressed in the words: as far as the proposition of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. Einstein's words prove that he rejected a possibility of direct correspondence of mathematics and the world. Therefore the author of the paper questions the view according to which Einstein claimed that nature is mathematical. It seems that Einstein's words can be interpreted as claiming the possibility of applying mathematics to the study of nature, about which we don't need to assume that it is mathematical. Such an approach better explains the successes as well as failures of applications of mathematics. Mathematically 'indifferent' nature can be examined to some degree using mathematical methods and it can also resist these methods. Thus the hypothesis of amathematicality of nature is closer to the 'scientific practice' of naturalists. ***** Albert Einstein was probably the most outstanding physicist of the XXth century. His scientific authority is so great that - although he wasn't a professional philosopher, his philosophical views deserve full attention. It is known that Einstein was an advocate of a realistic standpoint in ontology - he maintained that the world exists and that in its essence it is deterministic. As regards his epistemological views, I would like to expose his conviction that it is possible to get to know the world and that it can be understood thanks to the harmony present in the world. Einstein expressed his conviction in an aphorism: Raffiniert ist der Herrgott, aber boshaft ist er nicht (God is sophisticated, but he is not malicious). It is just this possibility of getting to know the world which, despite its complexity, seems to Einstein to be the greatest mystery of epistemology - bordering on a 'miracle'.

The reported Einstein's utterance sometimes has a 'stronger' interpretation. This aphorism is treated as Einstein's expression of mathematical structure of the world. Physics - as a science examining nature - uses mathematics as its tool. For this to be possible - in accordance with this interpretation - nature must be mathematical, that is, it must possess the structure corresponding to the structure of mathematics. God, while 'creating' the world, was sophisticated, creating it as a highly complicated and complex system, but he wasn't 'malicious' because the structure of the world can be deciphered using theoretical (mathematical) means available to man.

Indeed, in the philosophical works of Einstein we find fragments and phrases, which can be considered as utterances about the mathematical character of nature, for instance: 'nature is the realisation of what is the simplest to think of as regards mathematics' 1. However other utterances of Einstein show that he didn't find mathematicality to be an immanent characteristic of nature. Einstein - in my opinion - treated the issue of the ontological structure of the world rather in the categories of intelligibility or rationality of the world. Nevertheless, we cannot exclude other interpretations of Einstein's ideas. Besides, he encourages philosophers to treat distrustfully the declarations found in the works of scientists, claiming

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(in a slightly different context): if you want to learn from physicists theoreticians something about the methods they use, I propose to stick to this rule: Don't listen to their words, but watch their deeds2. I think that by tracing Einstein's practice of applying mathematics to physics, an attentive researcher can feel encouraged to adopt a slightly different approach to mathematics. The argument supporting such a possibility is that, when confronted with the question "[h]ow can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"3, Einstein answers it without referring to the mathematical structure of the world.

Einstein characterizes mathematics as a science whose theses are absolutely certain and unquestionable, favouring here a widespread conviction that the status of mathematics differs from the status of natural sciences. According to him mathematics is a formal-logical science, not empirical. In this context, for Einstein as a physicist and a philosopher, the usefulness of mathematics in the examination of the world is just amazing. If Einstein shared the view about mathematicality of nature, there wouldn't be anything surprising there. Everything would be clear. Why can we refer mathematics to reality? - because nature has mathematical structure; why do we apply mathematics in natural sciences? - because it is mathematics that is the 'key' to the knowledge of the world of nature. Einstein, however, gives a different answer: "[i]n my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality"4.

It seems that Einstein's words can be interpreted as a viewpoint claiming that it is possible to apply mathematics to examine nature, about which we need not assume that it is mathematical. It follows from the suggestion that if mathematical propositions refer to reality, they are not certain. If nature were mathematical, then - as I understand Einstein - referring mathematical propositions to it wouldn't lead to the loss of their certainty because then the whole operation would occur between isomorphic domains - nature having mathematical structure and mathematical theories. With such an approach, the only problem could be to discover, identify or construct a suitable - for a given area of reality - mathematical theory which would provide notions for the adequate modelling of physical processes.

Let's consider this issue 'from the point of view' of mathematics - as long as propositions are certain, they don't refer to the world. Mathematical propositions refer to the possible formal relations between mathematical entities, which we approach mentally and then they are apodictic. The certainty of its theses is a result of the previously accepted premises and the agreement as to the acceptable methods of reasoning. It is, thus, aprioric in the methodological sense - it can develop autonomously and it is most often created independently of external or extramathematical influences. Mathematics as such cannot say anything about objects imagined or real. However let's notice that such an approach to this issue excludes only the possibility of direct reference of mathematics to the world. It doesn't follow from it that mathematical propositions should not be referred to reality. It is possible and - as mathematical natural science shows - very fruitful.

However the application of mathematical propositions leads to the loss of certainty (if we refer mathematical propositions to reality, they cease to be certain). But it is not the reason that would make it impossible to refer mathematical propositions to the world. Einstein in 'practice' shows that although mathematical propositions in themselves don't refer to reality, with the help of suitable physical procedures they can be applied in order to grasp the characteristics of natural reality, gaining real meaning. However it should be remembered that in such a case mathematical propositions lose their absolute certainty. Mathematics applied to physical phenomena cannot guarantee by itself the truthfulness of conclusions to which it

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leads by making use of a deductive method appropriate to it. It operates, after all, on unfamiliar ground. In the 'kingdom' of physics there applies methodology which is suitable for an empirical science - that means standards and rigours of justification and acceptance of propositions, different than in formal sciences. Therefore mathematical propositions, showing some possibilities of such and not a different behaviour of a physical system, on the ground of physics are not able to predict the real course of a phenomenon as this course can be ascertained by means of methodological criteria, appropriate to the domain of natural sciences.

Summing up, Einstein's standpoint concerning the relation between mathematics and the external world can be formulated like this. What gives some content to mathematical notions does not belong to mathematics but is a physical interpretation. Therefore Einstein in his work of applying mathematical methods introduces some 'medium' between mathematics and the world. This intermediary field, in which mathematical structures and really existing nature's structures meet, is obviously physics. Reconstructing Einstein's standpoint expressed by the words: as far as the proposition of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality, we can state that instead of abstract considerations of the relation between mathematics and the world, in his scientific work Einstein in fact considers the triple connection: nature - physical theories - mathematics, because mathematics itself does not refer to reality.

In this light, if the issue of the structure of reality itself is concerned, it shouldn't be approached dogmatically. In particular, with reference to Einstein's standpoint, we could hypothetically assume that natural reality is neither mathematical nor non-mathematical, it is simply amathematical (similarly as it is not moral or immoral, but simply amoral). Such a neutral approach to the problem of nature's structure has its advantages. Thanks to this it is possible, in my opinion, to avoid the difficulties of realistic standpoint, as well as overcome the hurdles of instrumental interpretation of mathematics' applications. Mathematically 'neutral' nature can - to some extent - be 'approached' with mathematical methods, as well as to some extent - resist these methods.

In this context, successes and failures of applications of mathematics become well understood. Naturalists know that to apply mathematics effectively, a lot of effort is needed to 'tailor' mathematical methods so that they 'work' in accordance with the accepted premises.

Let's mention here at least the problem of infinite remains, appearing in the quantum theories of the field, which are removed by ad hoc5 mathematical means, or Hawking's attempts to eliminate, on the ground of the quantum theory of gravitation, the boundary conditions for the Universe6, described by Robert Mathew as 'mathematical hocus pocus' 7. Obviously such 'inconvenient' facts are not exposed by the enthusiasts of effectiveness of mathematics in natural sciences, but they can be traced in the whole history of mathematics' applications in physics.

Suspending the judgement as to the issue of mathematical structure of nature, we don't exclude at the same time that some of its aspects can be subjected to mathematical description, are 'approachable' or 'interpretable' mathematically. Amathematicality of nature does not exclude a priori the elimination of mathematical methods from natural sciences.

Mathematical methods, as outstanding physicists have shown in their scientific activity, supported by physical principles, can become a highly effective tool for expressing at least some aspects of the surrounding nature.

It seems that Einstein's standpoint as to the issue of the relation between mathematics and the world contains a significant novum compared to classical approaches (Platonic,

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Aristotelian, Cartesian and Kantian). It is the treatment of the correspondence between mathematics and the world as the relationship which is generated in the course of the development of natural scientific theories applying mathematics. Such an approach does not require the acceptance of strong metaphysical assumptions about the nature and structure of the world and mathematics as it does not assume that correspondence of mathematics and the world is a guaranteed state, something existing in advance, a priori - but it treats this correspondence as something worked out in the process of knowledge development.

In my opinion Einstein showed in his works that the epistemological role of mathematics is not just restricted to grasping - or not - the structure of the world in itself (as realists understand it) or only the external and intermediary participation in the articulation of the contents of natural scientific theories (in accordance with instrumentalist convictions). It seems that the process of examining the external world has a more basic and essentially creative character. It doesn't consist only in fitting mathematical categories to the examined object but rather in co-creating or constituting this object - that is reality. (The 'range' of this process is the simultaneous generation of mathematical categories). In this way the relation between mathematics and the world ceases to be only the juxtaposition of these two different domains and becomes a process, the effect of which is the epistemological grasping of reality by means of mathematical categories. Mathematicized physical theory makes use of the categorial apparatus worked out in formal sciences, in particular of mathematical notions and methods, however at the same time it still remains a physical theory, having 'contact' with physical reality. This contact ensures mathematical notions an operational scope by entangling them in physical meanings ( in the course of applying them) and in this way by assigning them real contents on the ground of natural sciences.

The mechanism of effectiveness of mathematics is, as I think, conventional - adaptive and generally speaking it consists in, on the one hand, forcing physical aspects of reality to fit mathematical formulas and, on the other hand, creating mathematical theories that correspond to physical data or modifying these theories in order to get adapted to this data. There is nothing like prefect congruence between mathematics and the world - this congruence has a rather pragmatic character and is conditioned by these physical theories in a more basic way than it seems to us.

Notes 1

See, A. Einstein, On the Method of Theoretical Physics, Clarendon Press, Oxford 1933

2

Ibidem

3

A. Einstein, Geometry and Experience, in: A. Einstein, Ideas and Opinions, Crown Publishers, Inc. New York 1954, p. 233 4

Ibidem, p. 233

5

See. S. W. Hawking, A Brief History of Time: From the Big Bang to Black Holes, A Bantam Books, New York 1988 6

Ibidem

7

See, R. Matthews, Unravelling the Mind of God. Mysteries at the Frontier of Science, Virgin Publishing Ltd, 1992

-----

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University of Gdańsk Institute of Philosophy and Sociology ul. Bielańska 5, 80-851 Gdańsk, Poland Jarosław Mrozek, (born 1955), assistant professor in Department of Logic, Methodology and Philosophy of Science, University of Gdańsk, Discipline: Philosophy of Mathematics, Philosophy of Science. M.A. - University of Gdańsk (1977), PhD - University of Gdańsk (1985); dissertation: Epistemological Aspect of Relation Between Mathematics and Outer World. Head of Department of Logic, Methodology and Philosophy of Science (1997 - 1999); Vdirector of Institute of Philosophy and Sociology, University of Gdańsk (1999 2002), Member of Polish Society of Philosophy. Among others academical publications: Einstein's Conception of the Relation Between Mathematics and the World, The General Function of Mathematics in Physical Sciences, Cosmology and Anthropic Principle, The Problem of Understanding Mathematics. filjam@univ.gda.pl

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The Problem of Reciprocity and Non-Reciprocity in Special Relativity Theory (Francisco J. M端ller) Abstract: The implications of the two relativistic postulates are analyzed in terms of their reciprocity and symmetry aspects. Whereas the first postulate entails a perfect equivalence of all frames, the second postulate, as reflected by the Einstein-Lorentz equations, implies an asymmetry of values (not of forms) that clashes not only with the first postulate equivalence but with the possibility of experimental verifications, all of which are "asymmetric" in each concrete case. A double index notation is proposed at the end, in order to show more clearly these asymmetries, and to interpret in a realistic way, the referential (physical) meanings of the four space/time variables. Lorentzian versus Einsteinian relativities are contrasted. The former seems to cope better with the asymmetric experimental realities. The latter only does so by subreptitiously changing the meaning of the physical variables.

In the introduction of his 1905 relativity paper (1) Einstein gives a hint that the 2 nd relativistic postulate about the universal constancy of the speed of light might be "apparently irreconcilable with the former" postulate, that is, with the first Postulate about the formal validity of physical laws for all frames of reference. Few physicists have pondered why Einstein posited this dialectical contradiction at the very beginning of his paper. It is the purpose of this article to dig into this question. A superficial interpretation of the possible contradiction views it as the clash between the classical, or Galilean composition of velocities, and the counter-intuitive "scandal" that light seems to travel at the same speed for all relatively moving observers. But there are more hidden aspects to this problem. The prototype of this light "scandal" was provided by the null Michelson-Morley experiment. This experiment, however, have always been performed in a "proper frame", without even the possibility of observing it from the viewpoint point of a moving frame (for example, from the Sun)(2). Yet, the theory elaborated by Einstein, introduces a perfectly "reciprocal" treatment of the experiment, (in its equivalent gedanken version) both in a proper and in a non-proper frame.

After all the theoretical work was done by Einstein, arriving at the Lorentz equations, the reciprocity and symmetry of such equations have been greatly studied and formalized.

Group theory assimilated the equations as part of its program. This theory is perhaps the best mathematical tool to investigate such symmetry properties of physical phenomena as rotations, nuclear particles, relativity, Quantum symmetries, hypersymmetries, antisymmetries, etc. etc.

Relativistic formalization versus physical realities An essential aspect of these formalizations is to consider variables like x,y,z,t with primed and unprimed characters. The operators, matrices, generators, etc. are said to "transform" one set of un-primed variables into the primed ones, and viceversa. Reciprocity and symmetry are, here, practically synonyms. Reciprocity, however, usually refers only to the relationship (also termed "inverse") between one set of variables and another "corresponding" set. In contrast, symmetry can be discovered within one such single set. For example the elements Aij and Aji are equal in a "symmetric" matrix or tensor. In contrast the word "anti-symmetric" has been used to described the case when Aij = -Aji . When the reciprocity simply consists in changing (+) and (-) signs some authors still consider it "symmetric", others "anti-symmetric" and some even "asymmetric".

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Leaving the heavens of pure mathematics, the physical use of such primed and unprimed quantities have been mostly to denote variables pertaining to a "moving" versus a "non-moving"(resting) frame of reference. Yet, on account of the relativity principle and the equivalence of all frames (First Postulate), nobody takes seriously the labels "moving" versus "non-moving" any more. Being perfectly "interchangeable" or "reciprocal", the primes and unprimes become, again, a mere mathematical formality.

This leads to the familiar interpretation of the Lorentz equations, for example, as a "rotation" in 4-dimensional space. To the performance of succesive Lorentz steps as mere multiplications in group theory. And to the "raising" of the time variable to an "equivalent" status as the space variables through the artifact of an X4 = ict terminology.

This enables to write the "fundamental relativistic interval dS" in a very beautiful way.

But the danger of all these mathematical myths is that, by taking them too seriously, (and isolating them from their referential meanings) the physical reality that they "signify" becomes more and more obscured , ignored and even confusing. This confusion applies especially to the concept of "event".

The elusive "event" (physical versus mathematical) A first problem that arises in this respect is the nature, the uniqueness, or even the existence, of the "event" (the space/time point) that is being "observed", "seen", "transformed", by a certain number of observers, (minimally by two) in relative "motion". Mathematically speaking this event can be common to any set of reference frames, regardless of their "motions", because the world of Mathematics is intrinsically static and motionless. If we mark a point XY in the plane of a Cartesian system K and then refer that "same point" to another frame K' that has been "rotated" respect the first, there is absolutely no difficulty in expressing X' = RX and Y' = RY where R is the "rotation matrix". The original point does not "belong" any more to the K system as to the K' one. In fact, nothing has to move and, indeed, nothing has moved.

But when we return to physical reality a given "event" is not only a set of coordinates, but a physical entity, a "happening", a phenomenon. This could be a Coulomb force between two (real) charges; or a photon being emitted or received, or a ticking clock, etc. Then it is dramatically important to distinguish in which frame the said entity or event is AT REST and in which it is seen as a "moving" reality. This physical event is certainly not interchangeable and non-reciprocal. In theory yes, we could set the physical entities in ANY of the two frames, but in each concrete experiment one and only one of the frames is the proper one.

It is in this sense that the Lorentz equations yield "asymmetric values", although being formally symmetric (or anti-symmetric). Panofsky and Phillips, very well established authors of the 1960's, explicitly recognized this when they described the Lorentz contraction, X<X', saying (3): "This relation is asymmetrical in X and X', since it gives the relation between measurement of a proper length X' (at rest) in Ε' and an improper length X (not at rest) in Ε.

In another place, however, they say that Lorentz equations show that "except for the sign of v, [the frames] Ε and Ε' are equivalent, in agreement with the second relativity postulate".(4) (Both emphases are mine).

So for these authors the (±) anti-symmetry of the velocity v, is in one place judged as an "asymmetry", yet in another as an "equivalence". Be this as it may, the important point is not to lose "track" of where the event is proper and where it is not. The labels of

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"moving" and "resting" are absolutely interchangeable and in that sense they are "trivialized" Yet, the primed and unprimed notation of formalized group and transformation theory only pays attention to such irrelevant tags, and is oblivious of the most important point: the residence of the unique physical reality that confers one frame the character of being "proper" and the other "non-proper". Even worse, by ignoring the residence of that unique physical event the primed/unprimed notation opens the way to the removal, altogether of the unique physical event. Then the scenario of the twin paradox is wide opened and all its concomitants debates start to proliferate.

Let me expand on this.

Methodological origin of the clock or twin paradox In the twin paradox the time of each twin plays the role of a proper time. Each twin's clock is resting in each twin's frame. Why should the "moving" twin return younger, when in its own proper clock nothing has absolutely happened according to the first relativity Postulate? From where comes the "asymmetry" of their times or "ages"?

We know the standard relativistic answer: "from the fact that only the 'traveling' twin accelerated". And we know also the standard non-relativistic objection: "accelerations are as relative and as interchangeable as the velocities. If distances are relative and their first derivatives are so, why not their second derivatives?" "Because a force, indeed" answer the relativists, "must have been used by the 'moving' twin to produce the acceleration". But again the non-relativists accuse the relativists of introducing a "non-inertial" element in their theory (a force!), thus violating the logical presuppositions under which the whole Lorentzian deduction was made. This debate can keep going on and on. I do not pretend to end it here. But what I want to point out here is the origin of the debate, which is this: a mis-application of the Lorentz transformation.

The Lorentz equations, at least as conceived by its original author in 1904 (5), were only geared to study how that unique physical reality of which I have spoken before, (an electron, a ray of light, etc), is "seen", or "measured" by TWO observers in relative motion. We can call this a ternary structure: two observers and ONE physical event. (2O1E for short). In contrast, the twin paradox scenario uses a binary structure: two clocks or "twins" in relative motion and no common event independent of their own clocks or "ages" to be studied or observed. Such a binary scenario leaves the theory totally empty and devoid of objective purpose. It is futile, in search of some objectivity, to speak of the twins as "observers" and the clocks as "events". That language is but a picturesque antropomorphism that has creeped only too much into relativistic textbooks. (Einstein himself is partially guilty of this antropomorphism when using expressions like: the observers "judge", or "ascertain", or "declare", etc, etc).

Critical comment What, then, should we conclude here about the debates on the clock paradox?

That they have been a waste of time. Relativists will keep insisting in their "asymmetrizing" acceleration factor, while non-relativists will insist in the intrinsic equivalence of all truly inertial frames. In reality, the struggle here is between the equivalence, reciprocity and formal symmetry that springs from the First Postulate on the one hand, and on the other, the (numerical) asymmetry that results from the Lorentz equations (2nd Postulate) when applied to a concrete situation. Indeed, we have returned here to that "apparent contradiction" between the two Postulates that Einstein envisaged at the beginning of his paper. The fact that the Lorentz equations are in harmony with c = c for both (or all) frames does not remove the clash between the asymmetry of the

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numerical values it predicts for the rest of the physical realities, in comparison with the perfect equality and equivalence predicted for those same realities by the First Postulate.

In reality the reason why physicists do not perceive this methodological (even logical) "mis-match" between the two relativistic postulates is that they have gone too far into mathematics and have abandoned too much the real physical qualities. They imply, following Minkowski, that those qualities are mere "shadows", and only their mathematical connections in a four-dimensional (mythical) language remain formally invariant.

In this respect it is frequently said that relativity theory ended the "mechanistic" philosophy of the etherists. But in reality relativity has "ended" all physical qualities, (electromagnetism included), in the name of pure games of kinematically related frames.

This is not only mechanistic, but "geometristic". The world of relativity is, thus, a timeless, motionless world. And if we still remember Aristotle we will agree with him when he said that "if we do not understand motion we cannot understand Nature". So relativity does not "understand" Nature at all, since "nothing moves" in the relativistic eternal and timeless heavens.

This critical comment, however, does not entail, in the least, that the effects experimentally tested like time dilation, mass increase, etc, are not real. But only that they cannot be predicted from a symmetristic, equivalential, reciprocating, version of relativity theory as Einstein's version. It seems that only the Lorentzian (nonsymmetristic) version of relativity makes sense. To consider this I will summarize the previous verbal analysis in a more concise and symbolic way, using a "double index" notation, a notation that I think has been long time overdue in relativistic textbooks.

Analysis using a "double index" notation Let A and B be two frames of reference in relative motion. We shall not stipulate which is moving and which is not. Let any property T (like time) be labelled with two subindexes: the first indicating: where the event or object is; and the second by whom or in which frame the observation is made. Thus: 1-

T AA means: the "time" of an event in A as measured by A (a proper value)

2T AB means: the "time" of an event in A as measured by B value ) 3-

(a

non-proper

T BB means: the time of an event in B as measured by B (a proper value)

4T BA means: the time of an event in B as measured by A (a "coordinate" value)

non-proper

or

a

Whenever the two subindexes coincide, we have a proper value. Whenever they are mixed, we have a non-proper value (or "coordinate" value) The previous T variables should be understood as dT's in the case of time intervals. For simplicity I will use the single letter T . With this notation, and the additional symbol L(Âąv) for a Lorentz transformation we can express the First Postulate writing that: (I)

TAA = T BB

(valid also for all TCC , T DD , T EE , etc)

And the 2nd Postulate by means of the reciprocal Lorentz equations:

164

(IIa)

TAA =L(v)T AB

(IIb) TBB =L(-v)TBA Notice that in the Lorentz equations the first subindexes have to be equal, because both frames, A and B are refering to a unique common object either in A, (Eq.IIa), or in B (Eq.IIb). Thus, an equation like T AA = L(v)T BA would be totally meaningless.

Are all equations I and II applicable simultaneously in each concrete situation?

Are all four "referential" parameters defined above simultaneously meaningful? Let us see the possible answers both in an Einsteinian (reciprocal) relativity and in Lorentz's (non-reciprocal) kind.

For both versions of relativity, the First Postulate should be always applicable.

Unfortunately, due to the limitations of the primed/unprimed notation, there is not even a way to express Eq-I as done above. To write T = T' with this purpose would be to invite total confusion when the Lorentz equations later yield T â&#x2030; T' . Especially in this aspect we see the greater advantage of the double index notation.

Now in the Lorentzian context equations II can only be applied one at a time in each case. Suppose we are dealing with (IIa), so that the event is proper in A and not proper in B, (regardless of which "moves" or not). Then T BB and TBA are "empty". No part of this experiment refers to them and, hence, no paradox arises. We could later repeat an "identical" experiment in B and apply (IIb), in which case T AA and TAB will represent nothing of "that" experiment. The conclusion of the experiment is simply, in the first case, that A has a proper time or "age" T AA and B sees it non-properly as TAB and in the second, reciprocal case, that B has a proper time or "age" T BB and A sees it non-properly as TBA . The two reciprocal cases do not "mix" or "apply" together in one single experiment.

In Einsteinian relativity, however, both equations II are taken as perfectly reciprocal (which they are) and as applicable simultaneously but in a "mixed" way.

(Typically this is the clock paradox bynary scenario) What happens here is that relativists speak of the "age" of each twin or clock, in their own proper frames. These "ages" should be denoted by T AA and TBB in the double index notation. That being the case, the only conclusion should be what the First Postulate establishes, namely that T AA = TBB . No possible asymmetric aging can arise. But relativists insist that one frame, for example A, is "really moving" and asymmetrically accelerating. Then they apply (IIa) to conclude that TAA = L(v)TAB , a result which they express verbally by saying that the "age" of twin A is smaller (younger) than the "age" of twin B. But the problem here is that TAB is not the proper "age" of twin B, but only the non-proper "view" or measurement that B has of A's age. The proper age of B is still TBB, a fact that relativists overlook simply because they lack the adequate double index notation that I am proposing here.

Relativists "transform" conceptually the non-proper measurement T AB made by B, into the proper age TBB of B. This happens, as explained above, because in the bynary scenario there is no fixed, unique, common object to be observed. Then the subjectivity of each observer takes the place of the object to be measured. This is what produces the "mixing-up" of equations in Einstein's "symmetristic" relativity which I mentioned above.

This unwarranted "transformation" of the physical meaning of the mathematical variables is, perhaps, the most persistent and irritating error both in Einstein's original paper and its descendants. Parameters like x,y,z, and ct that were used to describe the motion of a "light ray", are suddenly, without justification, used for representing the

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"positions and times" of a moving clock or rod. Again this all can happen because the primed/unprimed notation used exclusively by relativists is totally "blind" to the referential physical meaning of the variables. The prime/unprime notation simply indicates "moving" vs "non-moving" systems, a tag that is perfectly equivalent, reciprocal and interchangeable. But the proper vs non-proper elements of the experiments are, in contrast, non-reciprocal and physically asymmetric. This physical asymmetry is the only thing that experiments can show and verify, a fact that means that in practice, only Lorentzian relativity, with its preferred ether frame, is the one in harmony with experiments. The only way that Einsteinian symmetristic relativity can cope with experimental facts is by converting itself to the Lorentzian scenario as each situation demands. A few examples of this suffices.

The experimental asymmetries oppose Einstein's symmetristic relativity 1 - The GPS community, for example, must use a reference frame fixed to the earth and not rotating with it, in order to account for the Sagnac effect that takes place between the GPS satellites and the terrestrial stations. This is an example of a preferred frame of reference, breaking all reciprocities and symmetries. Likewise, the gyrolasers, nowadays used in commercial aircraft, are based on the "asymmetric" times of flight of two opposing beams of light, S/(c+v) and S/(c-v), observed by proper observers corotating with the gyrolaser. Hence they can deduce the speed v from their observations. Again, Lorentz "wins" and Einstein "looses".

2 - In the Hafele-Keating experiment the results did not show the symmetry they were supposed to show. Any school boy knows that the term v 2/c2 has even parity (+v and â&#x20AC;&#x201C;v yield the same result). So clocks flying to the East must have behaved exactly like those flying to the West. But they did not. The clocks that flew westward were accelerated (!) respect the resting Washington clocks, while the eastbound clocks did show the expected time dilation. To explain these asymmetric results the authors had to adopt the "viewpoint" of observers fixed to the North pole, (ie, not rotating with the Earth, just as the GPS community does). Another triumph for non-reciprocal relativity. In adopting this "polar viewpoint" Hafele-Keating were implying that the observers at rest in Washington (themselves) could see what the North pole observer "should" have seen. If that is the case, then why use any relativistic transformation at all? Regardless of the sloppiness of Hafele-Keating's experiment it showed a remarkably "neat" violation of the symmetristic and transformational relativistic scenario.

Final conclusion In reality what happens in all this is that when we have two really inertial, (noncommunicable) frames of reference, only one side of the story can be verified experimentally in each case. As mentioned above, we cannot perform the MM experiment from a non-proper frame, neither can we observe fast mesons, or for that matter relativistic electrons, simultaneously in the non-proper and proper frame. So physical reality, by selecting in each case a proper frame and not another, breaks the theoretical symmetry of Einstein's relativity. From all this two major conclusions can be derived: 1 - Einstein's symmetristic theory can never be proven right because of methodological impossibilities. But then it cannot be disproved either, for the same reason. Relativists will always supply, in their favor, what the "imaginary" observer "must" have seen.

Hence, strictly speaking, applying Popper's falsification methodology, relativity theory is

166

not a scientific theory at all. It springs from ideal, impossibly symmetristic, thought experiments.

2 - When only primed and unprimed variables are used everything works perfectly in the mathematical heavens of group theory. But when the more "messy" but physically more revealing double index notation is used we see how symmetristic relativity becomes asymmetric by subreptitiously changing the physical meaning of the variables.

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References 1) Einstein, A, "The Electrodynamics of Moving Bodies", (1905) Annalen der Physik, vol.17, 891.

2) Attempts at performing MM's experiment with a star light as source are vitiated by the fact that once the light enters the lens of the apparatus it is re-radiated internally, hence, becoming again an inmediate "proper" source, just like a terrestrial one.

3) Panofsky, W and Phillips, M "Classical Electricity and Magnetism", Addison-Wesley, Reading, Mass., 1962, pg. 291.

4) Panofsky and Phillips, Ibid. pg. 292.

5) Lorentz, H A, "Electromagnetic Phenomena in a System Moving with any velocity less than that of Light," Proc. Acad. Sc. Amsterdam, vol. 6, 809 (1904).

----Francisco J. M端ller is the actual President of the Natural Philosophy Alliance (see the section "Alternative Physics On Line" in this same volume of Episteme), and is known for a criticism of relativity grounded even on original experimental results (see point 16 in the second list of the quoted section).

Varela Academy of Science and Philosophy 8025 SW 15 St. Miami, Florida 33144 U.S.A. fjmuller@bellsouth.net

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On the Impossibility to Describe the Fields of the System of Uniformly Moving Charges in the Frame of Special Relativity (Vladimir Onoochin) 1. Introduction.

In this article, we intend to discuss one point of foundation of the relativistic theory, i.e. the transformational properties of the scalar potential of the uniformly moving charges.

The relativistic theory has the pretension to play a role of an absolutely true theory and this fact seems to be undisputable to such extent that some questions laying in the basis of this theory are treated as postulates or as direct consequences of the postulates. However, the special relativity is based on some experimental facts which cannot be derived from the postulates of the theory. The subject of this article is the analysis of the consistency of the relativistic transformations of the potentials with the experimental facts.

Development of the classical electrodynamics at the end of XIX and beginning of XX century went in a way when the main attention was focused on seeking the transformations for the EM field while going from a frame at a rest to the moving frame. However, the expressions for transformed EM fields have not been studied with necessary thoroughness, namely, only the expressions for the fields created by single point charge were analyzed. But even while analysing these simple expressions some points are overlooked; by the way, these points form the basis of the special relativity. We will show that these 'holes' in basement of the special relativity make the latter to be incorrect. We start from well known Lorentz transformations.

It is known from the special relativity that the coordinates in the laboratory frame and uniformly moving frame are connected by the Lorentz transformations: x′ =

x − vt 1− v2 c2

y′ = y z′ = z t′ =

t − vx / c 2

;

1 − v2 c2

(1)

and, correspondingly, the charge density and the scalar potential must transform as:

ρ = ϕ =

ρ′ 1− v2 c2 ϕ′ 1− v2 c2

;

(2a)

.

(2b)

In Eqs. (2), the quantities ρ ' and ϕ ' are defined in co-moving frame where the charge is at rest so the quantities j x′ and Ax′ are equal to zero.

If the above equations are fulfilled, then the electrodynamical quantities provide invariance of the physical laws in both frames. We emphasize that, despite of widespread belief, these equations are not postulates1, but they either must be proven or derived from the experimental data.

169

The first of equations (2) can be easily proven. Since the charge density of the elementary charge is described by the Dirac delta function, for uniformly moving charge the proof goes as follows:

ρ ( x, y , z, t ) = δ ( r , t ) = δ ( x − vt )δ ( y )δ ( z ) = δ =

δ ( x ′ )δ ( y ′ )δ ( z ′ ) 1− v c 2

2

(

)

1 − v 2 c 2 ⋅ x ′ δ ( y ′ )δ ( z ′ ) =

ρ ( r′ )

=

1 − v2 c2

;

(3)

.

(4)

which agrees with the law of conservation of the total charge:

∫ ρ ( x, y, z )dxdydz = ∫

ρ ( x′, y′, z′ ) 1− v c 2

2

1 − v 2 c 2 dx ′ dy ′dz ′ = q

Validity of Eq. (2b) has been proven by Lorentz who solved the wave equation for the ϕ potential with its rhs describing uniformly moving elementary charge:  1 ∂2 ∂2 ∂2 ∂2   2 2 −  ϕ ( x, y , z, t ) = 4π ρ ( x − vt ) − − ∂ x 2 ∂ y 2 ∂ z 2   c ∂t

(5)

in relativistic approach (here, ρ(x – vt) is the density of the uniformly moving charge).

Finally, we must show that solution of Eq. (5) has the following properties: - It transforms according to Eq. (2b); - It describes the Liénard-Wiechert and Coulomb potentials of the uniformly moving charge in co-moving frame and the laboratory frame respectively.

2. Relativistic solution of the wave equation.

Before starting the procedure of resolution, it must be noted that the wave equation with the extended source in its rhs cannot be treated as a well defined partial differential equation, because some physics is hidden there. This physics is that one cannot calculate the total potential created by the source as the integral of the potentials created by every moving infinitesimal element of the source. The reason of such a limitation in calculating the sum is that calculating the sum means collecting some information at the only point. But the speed of propagation of information is limited by the speed of light c. So during the process of collection of the whole information about the source, this source displaces itself and actually we cannot determine from what element of the source information comes at a given instant of time.

This problem does not exist in pre-relativistic theories because according to them, the characteristics of the source do not change while going to another frame. But in special relativity all characteristics of the source, except for the value of the charge, do change.

Formally we could make some suggestions regarding the changes of the parameters, however, when verifying the foundation of the special relativity, we have to use only quantities which can be measured directly. Taking into account the problem caused by the finiteness of the speed of propagation of information, we conclude that we must use the only way to find the solution in relativistic approach, i.e. we must go to co-moving frame where the source is at rest. In this frame, collecting information from all elements of the source becomes

170

independent on the speed of propagation of information, because the problem reduces to the electrostatic task of finding the ϕ potential created by some extended charge. Then one returns to the original frame so expression for the ϕ potential is transformed too. This expression must describe the ϕ potential in the original frame. We should expect that all transformations during this procedure must satisfy to the requirements of relativistic invariance (covariance).

Below we realize this procedure.

According to the arguments given above, we go from the laboratory frame to the comoving frame for the charge where the charge is at rest, so:  1 ∂2 ∂2 ∂2 ∂2  4π ρ ′ ( x ′ , y ′ , z ′ )  2  ϕ ′ ( x′, y′, z′, t ′ ) = − − − . (6) 2 2 2 2  2 2 ∂ x′ ∂ y′ ∂ z′  1 − v c  c ∂ t′ 1 − v2 c2 1

In opposition to most papers on transformation properties of the electrodynamical

)

(

quantities, we keep the factor

−1

1 − v 2 c 2 in both sides of Eq. (6), in order to show that the wave equations in two inertial frames differ one from another only by the constant factor. So the "principle of invariance" is fulfilled for Eqs. (5) and (6).

Because the rhs of Eq. (6) does not depend on the time variable, the lhs should not depend on t' variable too so this equation reduces to Poisson-like equation (we now omit the factor

(

1 − v2 c2

)

−1

):

 ∂2 ∂2 ∂2    ϕ ′ ( x ′ , y ′ , z ′ ) = − 4π ρ ( x ′ , y ′ , z ′ ) + + 2 2 2  ′ ′ ′ ∂ x ∂ y ∂ z  

.

(7)

Solution of Eq. (7) is known. It is the Coulomb potential created by the charge being at rest: ϕ ′ ( x′ , y ′ , z ′ ) =

∫

ρ ′ ( x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ r' − r'1

.

(8)

The final step is to return to the laboratory frame. By means of Eq. (2b), the scalar potential takes the form: ϕ ( x, y , z , t ) =

ϕ' 1− v c 2

2

=

1 1− v c 2

2

∫

ρ ′ ( x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ r' − r'1

;

(9)

where the rhs of Eq. (9) should be expressed via the original variables x, y , z, t after calculating the integral.

But if we analyze the above procedure for the resolution of the wave equation, we find one strange point. For better understanding, we write step by step the above procedure in symbolic form. So these steps from Eq. (5) to Eq. (7) can be written as (we re-write Eqs. (2a) and (2b) as ρ = γ ρ ′ and ϕ = γ ϕ ′ ): Wϕ = ρ  W ′γ ϕ ′ = γ ρ ′  Wϕ ′ = ρ ′

;

(10)

171

where W is the operator of the wave equation, sign  means "the Lorentz transformations of the variables (and functions of these variables)" and sign ⇔ means "which is equivalent to".

The second equation in this chain is equivalent to the third equation, since the "wave 1 ∂2 operator" 2 2 − ∇ 2 is invariant under the Lorentz transformations, i.e. W' = W . c ∂t The inverse procedure, i.e. transformation of the solution, to the original frame, should be written in symbolic form as:

ϕ ′ = (W − 1 ) ' ρ ′  γ − 1ϕ = (W − 1 )γ

−1

ρ ⇔ ϕ = (W − 1 ) ' ρ

;

(11)

where W-1 is the inverse wave operator. The chain (11) is correct if the "inverse wave operator" is transformed, under the inverse Lorentz transformations of the coordinates, as:

(W ) ' = W −1

−1

.

(12)

;

(13)

But Eq. (12) is incorrect because the integral operator: W −1 =

1 dxdydz R− r

∫

is not Lorentz-invariant. So we obtain a strange result, i.e. if one makes inverse Lorentz transformations of Eq. (8), in analogy with the transformations of Eq. (5), one finds that the solution for the ϕ potential via the charge density ρ does not maintain its original form when transforming from one frame to the other. In different words, despite the form of the wave equation, which is covariant, the solution of this wave equation is not covariant.

The problem can be stated in another way. One is able to calculate the value of the scalar potential in the laboratory frame by two methods. First, by treating the rhs of Eq. (8) as some mathematical expression, one can make the inverse Lorentz transformations of both integrand, taking into account transformation (2) , and the element of volume dV' , and then calculate the integral. The second way is to calculate the integral in the rhs of Eq. (8), i.e. to calculate ϕ as a function of x ′ , y ′ , z ′ , and then to make inverse Lorentz transformation to the variables x, y , z , taking into account that the quantity ϕ transforms according to Eq. (2b) too.

The final results obtained by these two methods are different and this difference is caused by difference in sequence of mathematical operations used while calculating the potential. But because the final result cannot depend on the sequence of mathematical operations (namely, transformation of variables and calculation of the integral), some error must be hidden in the proof of the covariance of the scalar potential.

This difference actually exists. For example, it is known that the Coulomb potential ϕ ′ = q ′ R ′ cannot be transformed into the Liénard-Wiechert potential by using the first method, because, when transforming the charge q', which is invariant (q' = q), and denominator, one obtains: ϕ′=

q′ x′ 2 + y′ 2 + z′ 2

ϕ =

q

( x − vt ) 2 1− v c 2

2

+ y2 + z2

;

(14)

172

and the potential given by Eq. (14) is no the Liénard-Wiechert potential of the uniformly moving charge2.

So, as we have seen above, there is some problem when trying to prove the covariance of the scalar potential of the single uniformly moving charge. But Lorentz used another method in proving the covariance of the ϕ potential3. He compared the relativistic solution (Eq. (9)) with the solution of the wave equation (5) obtained by the method of directly solving the wave equation [3] (Ch. 18.3), and he showed identity of both expressions. Below we analyze the method of Lorentz, and prove why these expressions are not identical.

3. Direct solution of the wave equation.

In this Chapter, we consider why Lorentz obtained the relativistic properties for the Liénard-Wiechert and Coulomb potentials. The solution of Eq. (9), for a charge with spherical shape in a frame where the charge is at rest, is given by the formula:

ϕ ' ( x' , y ' z ') =

q r'

.

(15)

This solution is derived by expansion of the denominator in a series of spherical harmonic functions (Eq. (3.70) of [1]) in a region r > r0 , where r0 is effective radius of the charge. Since the charge has spherical shape, then all terms of the expansion, except the zero term, are equal to zero, and so we obtain (15). Inverse transformation of the potential (Eq. (2)) gives:

ϕ ( x, y , z, t ) =

ϕ ' ( x′, y ′, z′ ) 1 − v2 c2

=

1

[

q

1 − v 2 c 2 x′ 2 + y′ 2 + z′ 2

]

1/ 2

;

(16)

and after the Lorentz transformation of the coordinates we have:

ϕ ( x, y , z, t ) =

q 1 1 1/ 2 2 2 4π ε 0 1 − v c  ( x − vt ) 2 2 2 + y + z   2 2  1− v c 

;

(17)

ϕ ( x, y , z, t ) =

q 4π ε 0

.

(18)

or 1

( x − vt ) 2 +

(1 − v

2

c 2 )( y 2 + z 2 )

The above expression is the well known expression for the LW potential of the uniformly moving charge. Thus, at least in one case, the relativistic approach gives the correct result, despite of the breakdown of the Lorentz invariance of the operator (13). Below we analyze why this is possible. In order to do it, we consider derivation of Eq. (5) by a method of "direct solution of the wave equations" ([3], Ch. 18.3). In this method, one does not use Lorentz transformation of the coordinates, but one introduces some physically reasonable assumptions while solving the wave equation with the source corresponding to uniformly moving charge. Obviously, the field created by such a source must follow this charge.

173

Therefore, the partial spatial and time derivative are not independent one of another, but they are linked by the relation: ∂ = − v⋅ ∇ ∂t

.

(19)

This relation means that any parameter of the field changes, during the time interval dt, at the same value as while displacing to the distance –vdt along the direction of motion of the charge. Taking into account Eq. (19), we are able to transform the wave equation (5) to:  v2  ∂ 2 ∂2 ∂2    1 − 2  2 +  ϕ ( x, y , z, t ) = − ρ ( x, y , z ) + 2 2   c ∂ x ∂ y ∂ z   

.

(20)

One can see that dependence of the potential on the time disappears in the rhs of Eq. (20) so actually Eq. (19) corresponds to the Galilean transformation of the coordinates: x → x − vt ;

y→ y ; z→ z ;

t→ t

.

(21)

;

(22)

By change of variables: x′ =

 1 − v c  y′ = y   z′ = z   x

2

2

Eq. (20) can be reduced to the ordinary electrostatic Poisson equation: ∇ ′ 2ϕ = − ρ

(

1 − v 2 c 2 x′, y′, z′

)

;

(23)

.

(24)

whose solution is: ϕ ( x′, y′, z′ ) =

1 4π

∫

ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ r' − r'1

We have in the lhs of Eq. (24) the scalar potential in the laboratory frame which, however, is still expressed via quantities defined in the co-moving frame. Inverse transition is made by changing the variables: 1 − v 2 c 2 ( x − vt ) = x ′   y = y′   z = z′ 

.

(25)

So finally, we have for the scalar potential in the laboratory frame two solutions obtained in relativistic approach and by direct solving the wave equation. For better understanding, we re-write Eqs. (9) and (24):

174

ϕ =

ϕ =

ρ ′ ( x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ r' − r'1

;

(26a)

ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ r' − r'1

.

(26b)

1 4π 1 − v 2 c 2 1 4π

∫

∫

Because both the above equations are written for the same potential, we must have: 1

∫

1 − v2 c2

ρ ′ ( x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ = r' − r'1

∫

ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ ) dx1′ dy1′ dz1′ . r' − r'1

(27)

This will be the basic equation of our further analysis.

4. Analysis of the function describing the charge density.

This equation can be treated as some integral equation for the functions ρ and ρ ′ .

Unfortunately, because these functions belong to different frames we are not able to compare them4. However, we can get some information about these functions. Since ρ ′ describes a single charge being at rest, it must be represented by some function with spherical symmetry.

By the way, the function ρ has not such a symmetry5. But in order to satisfy Eq. (27) for any r ′ , i.e. in such a way that the method of direct solution gives the same results as the relativistic approach, then it is necessary that the function ρ can be transformed to the form which has spherical symmetry. This can be easily proven by simple consideration. Actually, in order to satisfy Eq. (27), one can evaluate only the values of the function ρ defined in a limited region of the space, i.e. where the charge is located. Formally, the function ρ is defined in the whole space, however, for calculation of the integrals, only values of this function defined in limited region are essential. In opposition to this region of internal variables, the region where r ′ is defined, and it is essential for the calculation of the integral, is much greater, since it must be the whole space. So the only possibility to choose the true form of the function ρ is to assume that this function can be transformed (in the integrand of Eq. (27)) into a symmetric one on the variables x ′ , y ′ , z ′ . Since when v = 0 the function ρ must degenerate into the function having spherical symmetry for the variables x, y , z , finally we have the functional equation for this function (we omit the signs "prime"):

[

]

ρ (1 − v 2 c 2 ) x 2 + y 2 + z 2 =

[

Cρ x 2 + y 2 + z 2 1− v c 2

2

]

.

(28)

It can be shown that this functional equation has two only solutions, i.e.:

[

 ρ = C1 exp − ( x 2 + y 2 + z 2 ) σ 2  2 2 2 2  ρ = C 2 (V ) θ ( x + y + z ) − r0

[

] ]

.

(29)

In the previous formulae C and C1 are some constants, the constant C2(V) does depend on the volume V of the charge, r0 is the radius of the charge, and θ is the Heaviside step function. A parameter σ in the first solution of (29) corresponds to some "effective radius" of the charge. The second solution in Eq. (29) does describe the model of the electron used by Lorentz, where the charge is represented as a particle with the radius r0 and a uniform charge

175

distribution inside. When this charge moves, its size does contract in the direction of the motion, and, since the volume of the charge contracts too, the value of the charge density arises proportionally. After integration over internal variables, this solution yields Eq. (15).

But it is a well established point in classical electrodynamics [3] (Ch. 18.1) that the only known parameter of the electron is its total charge equal to e, and any calculation of the EM fields and potentials based on some specific charge distribution inside the electron cannot be physically meaningful. So one of the fundamental points of the special relativity, i.e. the proof of the covariance of the scalar potential, is derived by using questionable assumptions.

Actually, both charge distributions (29), necessary for the covariance of the scalar potential, are forbidden by quantum mechanics. As a matter of fact, quantum mechanics does not allow the existence of singular distributions (second distribution in Eq. (29) is singular on the boundary of the electron). But the first distribution in Eq. (29) must be caused by some potential of oscillatory type. However, it is not physically sound to suggest that the internal force (PoincarĂŠ tension) arises proportionally with the distance (in this case, the internal force would yield the potential of oscillatory type).

We should remark at last that in classical electrodynamics, the elementary charge is described by some singular distribution, i.e. by the Dirac δ-function. It is known that this distribution has some representation, and despite the multitude of these representations, the final result cannot depend on the specific representation chosen to describe the elementary charge. However, we have that only the two specific representations (29) do satisfy the condition which is required on the shape of the charge in order that the scalar potential created by the charge of a given shape is relativistically covariant. So the existence of only two specific representations for the δ-function, instead of the existence of the whole multiplicity of them, in order to provide for the covariance of the expression for the scalar potential, must be mathematically incorrect.

In conclusion, we obtain that the only relativistically correct method of establishing the connection between the LW and Coulomb potentials is relativistically non-invariant itself.

Therefore, the relativistic connection (2b) between these potentials derived by Lorentz looks like an artefact, which is conditioned by applying the point like approximation (29b) of the elementary charge. But if we consider the connection between the LW and Coulomb potentials in a strictly mathematical way, and at very small distance, we obtain that Eq. (2b) is wrong. Therefore, the scalar potential cannot be treated as the zero-component of a relativistic four-vector.

Notes 1

Despite of this, in most textbooks on classical electrodynamics, relativistic covariance of the scalar potential is treated as a fact which does not need any proof. For example, in [1] (Ch. 11.9) it is noted that covariance of the vector and scalar potential follows from the covariance (invariance) requirements to all electrodynamical quantities. In [2] (Sec. 16), it is written without any explanations that the vector and scalar potentials form relativistic four-vector.

2

The derivation of the LW potential from the Coulomb potential given in [2] (Sec. 63) is incorrect.

Actually, while applying the Lorentz transformation to the lhs of chain (14), it is illegal to change the spatial quantity R' by c(t' - t1'). As a matter of fact, R' = c(t' - t1') is some equation, but not an identity.

3

Actually, Lorentz operated with the fields but not with the potentials, however, the method is the same.

176 4

It is the main trouble of the special relativity that it is impossible to compare quantities which belong to different frames.

5

This function must describe the charge contracted in the direction of the motion.

References [1] - J. D. Jackson, Classical Electrodynamics, 2nd edn (New York: Wiley, 1975).

[2] - L.D. Landau and E.M. Lifshitz, The Classical Theory of Field, (Pergamon, Oxford, 1975).

[3] - W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, (NY, 1955).

----Vladimir Onoochin was born in Gorgii region, Russia, in 1953. In 1990 he took a PhD degree in Physics at Ioffe insititue, St. Petersburg. He is actually the manager of radiophysics (spectrometers) project at Sirius Ltd, Moscow. His main areas of interest are: Electrodynamics of short ultrawideband (UWB) current and EM pulses; Development of the measurement equipment and measurement of the powerful EM pulses in 1 to 150 GHz frequency range; Pulsed power devices. Special points of interest are even some problems in classical electrodynamics usually omitted by mainstream physics, such as penetration of the EM fields through metallic shields, longitudinal EM waves and properties of the EM potentials in different gauges, etc.. To these topics the author has dedicated many research papers.

"Vladimir Onoochin" <a33am@dol.ru>

177

Simmetrizzazione delle equazioni di Maxwell con l'introduzione del campo gravitazionale, un'idea bizzarra?

(Sabato Scala) Introduzione Sono passati circa 15 anni da quando, con un carissimo amico oltre che compagno di studi, affrontammo la preparazione dell'esame di Campi Elettromagnetici con il simpaticissimo oltre che preparatissimo prof. Giorgio Franceschetti.

Fu proprio da una accattivante introduzione al suo libro dedicato a questa affascinante e complessa materia, che, un po' per gioco, nacque l'idea bizzarra che voglio proporre al paziente lettore.

Il tempo passato e la ruggine accumulatasi per effetto della mia attuale professione interamente centrata sullo sviluppo software ben distante dai miei passati interessi, potrà farmi compiere più di un errore per i quali chiedo venia tenendo soprattutto conto che quanto propongo vuole essere semplicemente ciò che fu allora: un complesso gioco di fantasia.

Onestà vuole, anche per inquadrare nella corretta luce il presente articolo, che narri anche del piccolo retroscena che ispirò l'idea di fondo del nostro "gioco" fisico-matematico.

Era appena uscito un volumetto di fanta-storia estremamente affascinante dedicato al famoso "Esperimento Philadelphia". La storia mai confermata dai vertici militari americani, narra di un esperimento svoltosi alla fine del 1945 che, nelle intenzioni degli studiosi che vi presero parte, avrebbe dovuto consentire la "deviazione" della luce con la conseguente mimetizzazione di un qualsiasi oggetto consentendo, in pratica, di vedere ciò che si trovava dietro di esso e quindi rendendo invisibile l'oggetto frapposto.

Il libretto, estremamente ben congegnato con tanto di "soffiate", di "scienziati dissociati", interviste, esperimenti preparatori, ecc., non sembrava affatto scritto da un semplice giornalista ma da qualcuno che aveva una conoscenza notevole di fenomeni elettromagnetici.

Eppure qualcosa non quadrava: nel libro c'era praticamente tutto ciò che serviva per una succosa ricetta di fanta-fisica, ma senza la necessaria conclusione.

L'idea di fondo, del testo, era basata sulla adozione di un campo elettromagnetico prodotto in una apparato contenuto in una misteriosa sfera, collegato ad un alternatore ed impiantato sulla nave che nel libro aveva il nome di Eldridge.

Il nome, che nel libro si dice sia stato attribuito all'esperimento dagli allora vertici militari americani, è "Rainbow Experiment".

La cosa che ci affascinò non fu tanto lo straordinario esito dell'esperimento - che provocò, a detta dell'autore, la reale sparizione della nave - ma i sub-effetti di quell'esperimento, narrati dall'autore con chiaro sensazionalismo e gusto dell'orrido.

La nave sparisce, ma compare in un porto a vari chilometri di distanza e in pochi istanti, ritorna al suo posto. Alla sua riapparizione i marinai sono, in parte impazziti, in parte fusi con la materia del vascello, in parte scomparsi del tutto.

Altra cosa interessante è la narrazione puntigliosa degli esperimenti che precedono quello definitivo, fatta utilizzando condensatori con dimensioni dell'ordine del metro, bobine giganti, e alternatori appositamente realizzati, il tutto condito con segnalazione delle frequenze di alimentazione, della capacità dei condensatori, della entità delle correnti impiegate, ecc.

Tra gli effetti segnalati c'è il sollevamento degli apparati, la loro vibrazione e oscillazione con frequenza pari a quella dell'alternatore ecc.

178

Insomma il tutto, anche se mai in alcuna parte del testo viene riportato, sembra chiaramente dovuto alla generazione di un campo gravitazionale collegato ai campi elettrici e magnetici ad alta frequenza utilizzati per alimentare gli apparati.

La variazioni nello spazio-tempo, anche se mai viene detto nel libro, sembrano dovute proprio agli effetti di un gigantesco campo gravitazionale tale da provocare la deviazione delle onde elettromagnetiche luminose intorno alla nave.

Per dirla in sintesi, sebbene il testo non ne faccia mai riferimento, esso descrive gli effetti del sogno dei fisici di quegli anni (1945): l'unificazione dei campi.

La simmetrizzazione Da qui veniamo a questa bislacca idea e alla ispirazione venutaci dal libro del prof.

Franceschetti, che nulla mai seppe di questo nostro "gioco", visto il motivato timore di "saltare" la seduta d'esami per eccesso di "stupidità".

Prima di tutto andiamo all'oggetto del contendere: le equazioni di Maxwell, vediamole nella forma differenziale: 1) ∇ . D = ρ 2) ∇ . B = 0 3) ∇ × E = -

∂B ∂t

4) ∇ × H = J +

∂D . ∂t

Franceschetti faceva notare nel suo libro l'anomalia costituita dalla mancanza di simmetria del sistema di equazioni, evidente nell'assenza nella equazione 2) di un equivalente della densità di carica elettrica ρ che si trova nella equazione 1) , e nella equazione 3) di un equivalente della densità di corrente J che si trova nella 4) , per non dire dei segni con cui appaiono le due derivate temporali, una volta meno e una volta più.

L'asimmetria ha un effetto fisico evidente che si rileva integrando la 1) e la 2):

∫∫∫

(∇ . D)dV = Q

∫∫∫

(∇ . B)dV = 0 .

In pratica, mentre esiste in natura una entità chiamata "carica elettrica" (Q) , in grado di generare un campo le cui linee partono a raggiera da essa, lo stesso non si può dire per il campo magnetico, poiché non sembra esistere in natura la "carica magnetica".

Nel libro si ipotizza esistente la carica magnetica ρm e si perviene alle seguenti equazioni: 1') ∇ . D = ρ 2') ∇ . B = ρm 3') ∇ × E = Jm -

∂B ∂t

179

4') ∇ × H = J +

∂D . ∂t

In esse è stata introdotta, come dicevamo, una ipotetica densità di carica magnetica ρm e la corrispondente densità di corrente magnetica Jm . Non esistendo il primo dei due termini (o quantomeno non essendo mai stata trovata la carica magnetica) risulta inesistente e quindi inessenziale anche il secondo.

Unica anomalia nella simmetria, resta il segno meno nella derivata parziale rispetto al tempo per il vettore B. Da questa e da altre scarne osservazioni, tra cui l'einsteiniana "Dio non gioca a dadi!", ci ponemmo il problema di un possibile intervento di simmetrizzazione sulle equazioni che, però, includesse anche il campo gravitazionale.

Cominciamo a far osservare le analogie tra il campo elettrico e gravitazionale partendo dalla legge di Coulomb che descrive l'intensità dell'interazione tra due cariche elettriche: Fq =

1 4π ε

0

Q1 Q2 r2

ove ε0 = 8,854188 x 10–12 Kg–1m–3s2C2 .

Questa espressione, formalmente, è simile all'intensità della forza di gravità che agisce tra due masse: Fg = G

M1 M 2 . r2

Dalla equazione della forza di Coulomb si ricava quella del campo elettrico (scalare): Eq =

1 4π ε

0

Q , r2

mentre da quella della forza di gravità si ricava l'analoga espressione per il campo gravitazionale (scalare): X = G

M . r2

A questo punto, supponendo di voler creare un campo elettrico equivalente a quello gravitazionale, introducendo una carica "equivalente" alla massa, uguagliando le forze dovremmo far uso di un'equazione del tipo seguente: Qmequiv = κ0 M , ove κ0 sarà una costante tale che κ02 = 4πε0 G .

Ricordando che G = 6,670 x 10-11 Nm2Kg-2 , si ottiene: κ0 = 4,306 x 10-10 CKg-1 .

Introduciamo quindi una densità di carica equivalente ρmequiv definita come:

180

ρmequiv = κ0 ρk , ove ρk = densità di massa per unità di volume.

Per esprimere un'equazione formalmente analoga a quella del campo prodotto da una carica elettrica anche per il campo gravitazionale è necessario introdurre anche un termine omologo all'ε0 , che chiameremo ζ0 , definito ovviamente dalla: ζ0 = κ0 / 4πG .

La precedente equazione del campo gravitazionale (scalare) assume, quindi, la seguente forma (dove abbiamo abbreviato mequiv in meq): X =

1 4π ζ

Qmeq 0

r2

.

Ricordando la relazione tra il vettore D e il vettore E , campo elettrico nel vuoto (all'interno di altri materiali è necessario moltiplicare per una costante ε tipica dello specifico materiale): D = ε0 E , per analogia definiamo un omologo vettore gravitazionale:

R

associato al vettore

X

del campo

R = ζ0 X .

A questo punto possiamo scrivere le equazioni del campo gravitazionale in forma differenziale, indicando, come detto dianzi, con ρk la densità di massa: 5) ∇ . R = κ0 ρk = ρmeq 6) ∇ × X = 0 .

La seconda equazione si ricava ricordando che il campo gravitazionale è irrotazionale (conservativo), in pratica il lavoro che si compie muovendosi lungo un percorso chiuso è nullo (il lavoro lo si ottiene integrando la 6) ).

Fin qui nulla di nuovo, salvo una forma diversa per le equazioni del campo gravitazionale.

Ora supponiamo per un attimo che le equazioni di Maxwell possano essere messe insieme a queste aggiungendo qualche termine di collegamento. Supponiamo anche che la forma delle equazioni di Maxwell contenga già la "forma" in cui appariranno tutti i termini di collegamento. Intendiamo con ciò dire che ci dovranno essere dei termini omologhi dei ∂D termini J , che appaiono nelle predette equazioni. Questo vuol dire che dovremo ∂t introdurre, ove manca, un termine Jk omologo della densità di corrente elettrica J , ed un altro termine gravitazionale omologo del termine (differenziale) corrispondente al contributo del vettore D . Il tutto andrà fatto supponendo che il termine differenziale per il vettore R dovrà comparire con segni alternati + e – , in modo che il complesso delle equazioni presenti una certa simmetria matematica. Fermi mantenendo i termini ρm e Jm già introdotti da Franceschetti e comunque inessenziali (a valore nullo), a causa della inesistenza della carica

181

magnetica, non resta che introdurre una densità di corrente di massa Jk che si affiancherà alle densità di corrente J e Jm . In buona sostanza i termini nuovi che affiancheremo a quelli già presenti a destra del segno di uguaglianza nelle equazioni di Maxwell - nella forma con gli ∂R apici - saranno Jk e una sorta di densità di corrente di massa di spostamento . Bisogna ∂t anche tenere ovviamente conto della necessaria omogeneità dimensionale delle quantità fisiche che si sommeranno tra loro, per il che sarà necessario introdurre, oltre alla costante κ0 , anche un'altra costante λ0 , che ragioni di "simmetria fisica" fanno presumere di poter definire come: λ0 =

1 µ = 0 c ~ 30 Kg m2C-2s-1 , 4π ε 0 c 4π

ove c =

1

ε0µ0

è la velocità della luce nel vuoto ( µ0 indica, come usuale, la permeabilità

magnetica).

In definitiva, ecco come si presenterebbero le equazioni unificate ottenute per estensionesimmetrizzazione di quelle di Maxwell con l'introduzione del campo gravitazionale: 7) ∇ . D = ρ 8) ∇ . B = ρm 9) ∇ . R = ρmeq 10) ∇ × E = λ0(Jk + 11) ∇ × H = J +

∂R ∂B ) - Jm ∂t ∂t

∂D ∂R - Jk ∂t ∂t

12) ∇ × X = κ0(Jm +

∂B ∂D ) - κ0λ0(J ). ∂t ∂t

Dalle equazioni si vede come i tre termini di corrente, uno per ciascuno dei 3 campi, compaiono alternativamente nelle 10), 11) e 12) insieme ai termini differenziali dei tre campi R , D , B (che appaiono sotto forma di derivate parziali rispetto al tempo), con i segni più e meno in forma ciclica. Questa ipotesi di simmetrizzazione spiegherebbe anche l'anomala presenza del segno meno nelle equazioni già ampliate da Franceschetti con l'introduzione dei termini magnetici.

Non resta che verificare se: a) le equazioni producono effetti che non hanno a quel che si sa un equivalente fisico, nel qual caso il nostro discorso cadrebbe senz'altro; b) le equazioni generano effetti che hanno qualche rispondenza in fenomeni noti ma non ancora spiegati, o ne prevedono di ancora non noti che potrebbero però essere reali.

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In pratica non resta che verificare la "sostenibilità" del precedente sistema di equazioni nel mondo reale, dopo di che "divertirsi" a dedurne eventuali effetti pratici ancora sconosciuti.

Coerenza delle equazioni con fenomeni fisici osservati Cominciamo con considerazioni di carattere generale.

In assenza di correnti di massa e di variazioni del campo gravitazionale le equazioni classiche ∂R di Maxwell restano invariate poiché: Jk = 0 e =0. ∂t Ferma restando la costanza della massa nelle normali situazioni sperimentali, le variazioni possono esser dovute unicamente ad azioni dinamiche e quindi a movimenti di masse (flussi di massa).

Quali sono le masse in movimento, coinvolte nei fenomeni elettromagnetici?

Sappiamo che la corrente elettrica è dovuta ad un flusso di elettroni all'interno di campi elettromagnetici, di conseguenza un flusso di elettroni produce sia una corrente elettrica grazie alla carica dell'elettrone, sia una "corrente di massa", grazie alla massa dello stesso elettrone. Calcolando la divergenza della 11) , e ricordando che la divergenza di un rotore è sempre uguale a zero, si ha:

∂D ∂R ) - (∇ . Jk) - (∇ . ) = ∂t ∂t ∂ (∇ . R) ∂ (∇ . D ) = (∇ . J) + - (∇ . Jk) = 0, ∂t ∂t ∇ . (∇ × H) = (∇ . J) +(∇ .

la quale diventa, in virtù delle equazioni 7) e 9) : (∇ . J) +

∂ ρ meq ∂ρ - (∇ . Jk) = 0. ∂t ∂t

Passando all'integrale di superficie si ottiene: I+

∂ Qmeq ∂Q - Ik = 0. ∂t ∂t

In questo caso sembrerebbe negata la legge di conservazione della carica elettrica, che si esprime nella seguente formula: I = -

∂Q , ∂t

ma si ottiene una sorta di conservazione di "carica totale": 13)

I - Ik = -

∂ Q ∂ Qmeq + . ∂t ∂t

Ricordiamo inoltre che, essendo la massa dell'elettrone pari a: me = 9,1091 x 10-31 Kg , e il termine moltiplicativo 4πε0G pari a: 1,8544 x 10 -21 Kg–3m-1s2C2N , per la quantità totale di massa di elettroni che attraversano la sezione del conduttore nell'unità di tempo si ottiene un termine moltiplicativo dell'ordine di grandezza di un 10 -51 che, per quanto numerosi siano gli

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atomi all'interno di detta sezione, rende totalmente irrilevante da un punto di vista quantitativo il termine correttivo nella precedente legge di conservazione della carica totale.

Poniamoci, ora, nella ipotesi di assenza di cariche coulombiane in movimento (corrente elettrica), e di presenza di un campo magnetostatico. L'equazione di conservazione della carica totale prende adesso questa forma: 14)

Ik = -

∂ Qmeq ∂t

.

Ricordando ancora una volta il valore numerico della costante moltiplicativa 4πε0G , quando una massa di 1 Kg attraversa una superficie unitaria in 1 secondo, si otterrebbe una corrente di "massa equivalente" pari a 6,18 10-21 A, praticamente non misurabile. Questo conferma l'applicabilità del principio di conservazione della carica coulombiana come ottima approssimazione della equazione generale della conservazione della carica totale anche in presenza di masse in movimento.

Altra legge che parrebbe violata è quella della irrotazionalità del campo elettrico in un campo magnetostatico che si ricava integrando la 10) :

∫

E . ds = λ0Ik .

In buona sostanza si otterrebbe la previsione che una massa in movimento produce un campo elettrico perpendicolare alla direzione del movimento, e disposto con simmetria circolare intorno alla massa. Ovvero, che mettendo una massa in movimento attraverso una spira chiusa si produce un campo elettrico nella spira, e quindi una corrente.

L'osservazione fatta in precedenza, però, ci porta ad affermare che la irrotazionalità del campo elettrico in un campo magnetico statico resta sostanzialmente valida, cioè con buona approssimazione, fintantoché non entrano in gioco masse in movimento dell'ordine di 10 12 tonnellate, in grado di produrre, correnti di 1 micro Ampere.

In altre parole, ammettendo per un attimo che le equazioni siano valide, non si può ottenere corrente apprezzabile semplicemente facendo passare per esempio dell'acqua all'interno di un tubo.

Un problema serio è invece posto dalla 12) , che nega la irrotazionalità del campo gravitazionale (vedi 6) ) in presenza di campi elettrici e magnetici non statici, ferma restando la inesistenza di correnti magnetiche create da un monopolo magnetico, e quindi l'identità J m = 0 . La 12) prevede nuovi inattesi fenomeni fisici, perché, se è vero, come abbiamo appena visto, che gli effetti dei moti di masse su campi elettrici e magnetici sono sostanzialmente inapprezzabili, viceversa per quelli dei campi elettromagnetici sui moti delle masse (sul campo gravitazionale) sarebbe vero esattamente il contrario.

Effetti delle equazioni unificate sulla possibilità di creare un campo gravitazionale a partire da campi elettromagnetici Vediamo come si trasforma la 12) scrivendola in forma integrale: 15)

∫

X . ds = - κ0λ0 I + κ0

∂ ∂ (flusso di B) - κ0λ0 (flusso di D) . ∂t ∂t

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Supponiamo di voler realizzare un apparato elettromagnetico che sfrutti la 15) per generare un campo gravitazionale opposto a quello terrestre, in pratica un apparato elettromagnetico per la levitazione gravitazionale.

Considerando i termini al secondo membro, ci vengono offerte due possibili vie: 1 - Sfruttare il termine di corrente e quindi adoperare una corrente continua.

2 - Sfruttare i termini di flusso elettromagnetico e quindi adoperare generatori di corrente alternata in grado di generare campi elettromagnetici tempovarianti.

La prima soluzione parrebbe quella più abbordabile anche per la semplicità degli apparati composti da un generatore di corrente continua ed una bobina.

Sarebbe, infatti, sufficiente far circolare una corrente opportuna, in una spira circolare per produrre un campo gravitazionale orientato perpendicolarmente al campo della spira e, quindi, in grado di farla sollevare.

La presenza del termine moltiplicativo κ0λ0 , purtroppo, rende impraticabile questa soluzione.

Supponendo, infatti, di essere in presenza di campi elettrostatici, e considerando il campo X prodotto costante in intensità e direzione lungo il piano della spira (questa è in realtà solo una approssimazione, in quanto il campo gravitazionale è perfettamente verticale al piano della spira solo al centro di essa, mentre tende a ruotare intorno al conduttore quando ci si allontana dal centro) la 15) può essere scritta come segue: X

∫

ds = X 2πR = κ0λ0 I ,

da cui: X = κ0λ0 I/2πR .

A questo punto, ricordando che g = 9,8 m s -2 (ovvero N/Kg) è l'accelerazione di gravità media sulla terra, e supponendo di disporre di una spira di raggio R = 1 m , se ne ricava che la corrente necessaria per produrre il sollevamento sarebbe pari a: I = 6,28 x 9,8 / (30 x·4,306 x 10-10) = 4,76 109 Ampere , che è purtroppo un valore del tutto incompatibile con la dissipazione per effetto Joule che affligge i tradizionali conduttori, oltre che una corrente difficilmente generabile.

Il problema potrebbe forse essere risolto nell'ambito della tecnologia dei superconduttori, ma vogliamo vagliare alternative differenti e tecnologicamente più agevoli. Ripieghiamo, quindi, sull'uso di campi elettrici e magnetici tempovarianti, soffermando la nostra attenzione sul termine legato alle variazioni nel tempo del flusso magnetico. Anche in questo caso, per poter generare un campo X opposto alla direzione della attrazione gravitazionale terrestre, si può pensare di ricorrere ad una spira "magnetica" circolare di raggio r , e nuovamente supporremo X costante (indipendente cioè da ds , pur consci del fatto che questa approssimazione è valida solo nei pressi del centro della spira). Nell'attuale ipotesi il campo X ha una direzione ortogonale al piano della spira e dipende unicamente dal tempo, essendo indotto dal flusso dei campi elettromagnetici tempovarianti. Estraendo X(t) dall'integrale a sinistra della 15), tale termine diviene pari a: 2πr X(t) . A questo punto non resta che progettare la spira magnetica in grado di produrre le variazioni di campo che appaiono a destra della equazione 15).

Per generare un campo siffatto possiamo pensare di adoperare un solenoide toroidale avvolto su ferro. Questo accorgimento ci consente di "amplificare" l'effetto del termine µ0

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(permeabilità magnetica nel vuoto, che vale 1,2566 x 10 -6 m Kg C-2), che nel nostro caso va moltiplicato per un termine aggiuntivo µr , una costante pura che per il ferro ha un valore di circa 800. Indicheremo con µferr = µ0 µr il termine che sostituisce la permeabilità magnetica nel vuoto, per avvolgimenti su ferro. Vediamo subito perché un simile dispositivo potrebbe rispondere, in linea di principio, alle nostre esigenze. Ogni spira dell'avvolgimento genera, percorsa da corrente, un campo magnetico ortogonale alla spira. Possiamo avvolgere le spire seguendo il "cerchio magnetico" che desideriamo realizzare. Ciò che si ottiene è, appunto, una bobina a forma di toro circolare. Indichiamo con N s il numero di spire che formano la bobina, con R il raggio del toro e con r il raggio di ciascuna delle spire minori che avvolte formano il toro, e passiamo a calcolare il campo magnetico indotto dalla corrente I(t) .

Partendo dall'integrale della 11) , calcolato nella ipotesi che D ed ed R siano costanti, si ha:

∫

H . ds = I(t) .

Questa equazione è applicabile a ciascuna delle spire circolari che formano l'avvolgimento.

Le linee del campo H divengono, per simmetria, circolari e coassiali e quindi il campo scalare H complessivo indotto è pari a: H(t) = Ns I(t) / 2πr , da cui: B(t) = µferr H = µferr Ns I(t) / 2πr .

Se utilizziamo un generatore di corrente alternata con pulsazione ϖ0 si ottiene per la I(t) l'espressione sinusoidale: I(t) = I0 sin(ϖ0t) , e quindi: B(t) = µferr H = µferr Ns I0 sin(ϖ0t) / 2πr .

A questo punto torniamo alla 15). Sappiamo che con correnti ordinarie il primo termine di corrente, a sinistra, può essere trascurato; inoltre trascuriamo, per ora, anche la derivata parziale di D rispetto al tempo, che andrà comunque riportata in conto alla fine del calcolo, poiché questa componente nasce per induzione ogni qual volta si generano campi magnetici tempovarianti, ed è inseparabile da essi (con la conseguenza che il rendimento complessivo del nostro "motore antigravitazionale" cala considerevolmente, tenuto conto del fatto che il lavoro associato al generatore del campo gravitazionale verrà in parte dissipato dalla resistenza del conduttore ed in parte impiegato per la generazione del campo indotto ma indesiderato D ). Ecco la forma che prende l'equazione, ferma restando l'ipotesi di indipendenza di X(t) da ds : 2πR X(t) = κ0

∂ (flusso di B) . ∂t

Applicando ad essa il valore (scalare) di B(t) prodotto dal toro circolare si ottiene: 2πR X(t) = [κ0 µferr Ns I0

∂ sin(ϖ0t)] / 2πr . ∂t

Da qui si ottiene: 4π2 rR X(t) = κ0 µferr Ns I0 ϖ0 cos(ϖ0t) ,

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e quindi in definitiva: 16)

X(t) = κ0 µferr Ns I0 ϖ0 cos(ϖ0t) / 4π2 rR .

Per avere un'idea di come vanno quantitativamente le cose, supponiamo di utilizzare un toro di raggio R = 6 m , avente sezione circolare di raggio r = 0,005 m , e conduttori a sezione s = 0,001 m (sicché il numero di spire massimo ottenibile con un solo avvolgimento sarà: N s = 2πR / s = 37700 ). Un siffatto toro avrà un volume pari a: V = πr2 x 2πR = 2 π2 r2 R = 2,95 x 10-3 m3 , e una massa che si deduce dal valore precedente moltiplicandolo per la densità del materiale di composizione. Sebbene l'avvolgimento sia su ferro, mentre il materiale di conduzione sarebbe, in generale, di rame, supporremo per semplicità che tutta la struttura toroidale sia in ferro, sicché, indicata con Dferr la densità volumetrica di questo materiale, che considereremo pari a 9,7 103 Kg/m3 , la massa complessiva risulterà pari a M = Dferr V = 28,7 Kg .

Tornando al nostro punto, per sollevare il toro sarà necessario produrre un valore massimo di X(t) (che si ottiene considerando la condizione di picco del coseno, cioè quando questo raggiunge il suo valore massimo pari ad 1) pari al richiamato valore "critico" 9,8 N/Kg .

Possiamo ricavare quindi la necessaria frequenza di alimentazione partendo dall'espressione del campo prodotto: X = κ0 µferr Ns I0 ϖ0 / 4π2rR = 9,8 , la quale implica: ϖ0 = 2πf = 4π2rRX / κ0 µferr Ns I0 (f = frequenza) , ovvero: f = 2πrRX/κ0 µferr Ns I0 .

Ricorrendo ad una corrente di 1 Ampere si ottiene, per il generatore di corrente, che la frequenza di alimentazione necessaria per il sollevamento è di circa 110 Mhz. Ci sarebbe però un altro problema da risolvere. Essendo la corrente alternata di tipo sinusoidale, più che sollevarsi, il nostro veicolo sarebbe soggetto ad una vibrazione verticale di altissima frequenza, quale quella precedentemente stimata. L'alimentatore del sistema non può essere quindi puramente sinusoidale, ma andrebbe adoperata, semmai, una sinusoide raddrizzata con le "gobbe" troncate al primo quarto. L'operazione di "raddrizzamento" della sinusoide si può ottenere con l'uso di un ponte di raddrizzamento e di un filtro opportuno.

Ecco una immagine dell'apparato proposto:

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Si porrebbe, a questo punto, pure la questione dello spostamento dell'eventuale macchina volante nelle diverse direzioni. Una possibile soluzione sarebbe quella di costruire una cupola tale che le linee di forza del campo gravitazionale prodotto siano, punto per punto, ortogonali ad essa. Sulla cupola, poi, andrebbero alloggiati gli apparati per produrre il campo gravitazionale di compensazione. Un'idea potrebbe essere quella di ricoprire la cupola con una serie di solenoidi toroidali compositi di piccole dimensioni, ma si potrebbe anche tentare di utilizzare il campo elettrico, e quindi l'ultima componente della 15), approfittando inoltre del "piccolo" vantaggio offerto dal fattore moltiplicativo λ0 . La soluzione proposta consente di creare da un lato lo spostamento dell'apparato in qualunque direzione, dall'altro consente di riutilizzare i piccoli solenoidi toroidali per ridurre le vibrazioni del "velivolo", alimentandoli, magari, con una corrente sfasata di 90 gradi rispetto a quella che alimenta il solenoide toroidale principale. Ecco un'immagine dell'apparato proposto in sezione:

Non è difficile riconoscere, nella macchina, la classica forma a sfera schiacciata di un UFO, e non può, sempre rimanendo nel fantastico, non tornare alla mente l'apparizione dei primi di questi oggetti intorno agli anni 50. Il vero problema è che la frequenza di alimentazione sembra difficilmente compatibile con la tecnologia dell'epoca, quindi il mistero resta, anche se è interessante notare che questo tipo di apparecchio potrebbe produrre effetti molto simili a quelli che solitamente vengono associati agli avvistamenti di UFO, vediamone alcuni.

L'elevata frequenza genera correnti indotte, e quindi può provocare bruciature o carbonizzare

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composti biologici (piante, animali, etc.) che si avvicinino all'apparato in funzione, esattamente come accade in un forno a microonde. La gravità inversa prodotta dall'oggetto provocherebbe una forza repulsiva gravitazionale nella parte inferiore di esso, e quindi lo schiacciamento di superfici (ad esempio manto erboso) pur senza che il sistema vi si sia fisicamente poggiato. La parte superiore della sfera, invece, presenterebbe una forza gravitazionale attrattiva che produce una compressione dell'aria con conseguente riscaldamento, rendendo possibili anche fenomeni di luminescenza. La compressione dell'aria indotta nella parte superiore potrebbe a sua volta provocare fenomeni di diffrazione, rendendo vaghi i contorni dell'ipotetico veicolo.

Infine, il sistema può interferire con sistemi elettronici, provocando disturbi radio o inducendo correnti tali da distruggere gli strumenti, o bloccarne temporaneamente il funzionamento.

Possono, in questo caso, venire in mente i blocchi dei motori di normali autoveicoli, spesso segnalati nel corso di avvistamenti, a causa della interferenza per induzione elettromagnetica con le bobine degli spinterogeni.

L'esperimento Rainbow: possibile?

Visto che ci siamo già "screditati" abbastanza agli occhi del paziente lettore, arrivando a dare una "spiegazione" razionale alle fantasticherie ufologiche, perché non ritornare alla fantasia primitiva da cui eravamo partiti?

Veniamo, quindi, all'esperimento Rainbow che ci ispirò, quasi oltre 15 anni fa, le bizzarrie che abbiamo esposto. Da un punto di vista puramente teorico, disponendo i solenoidi su una sfera, anziché su una cupola, come per il famoso esperimento, si potrebbe generare un campo antigravitazionale centrato sul centro della sfera. Se, in linea di principio, i solenoidi sono alimentati ad alta frequenza e con intensità di corrente elevate, il campo antigravitazionale potrebbe provocare una deviazione della luce verso l'esterno del campo, e non verso l'interno come accade, ad esempio, nei pressi di un campo gravitazionale tradizionale ed attrattivo intenso quale quello di un buco nero.

Inutile dire che, proseguendo sulla via di speculazioni quasi fantasiose, ci sarebbero effetti anche sullo spazio-tempo. Sempre in teoria, mentre nei pressi di un campo gravitazionale attrattivo di notevoli dimensioni il tempo scorre più lentamente, in un campo antigravitazionale artificiale il tempo scorrerebbe più velocemente, facendo apparire "il mondo esterno" praticamente fermo. La stravaganza considerata consentirebbe lo spostamento della nave a velocità che per il mondo esterno sarebbero pressoché istantanee! Esisterebbero anche delle ulteriori particolari anomalie, dovute alla distanza dal centro della sfera che produce il campo. Infatti, il tempo, evidentemente, scorrerebbe più veloce man mano che ci si avvicina al centro della sfera, come dire in buona sostanza che l'interno della sfera viaggerebbe più velocemente della parte esterna della nave, con conseguenze difficili da immaginare.

Altro, straordinario, risultato sarebbe la possibilità di costruire una macchina del tempo che, vista la possibilità di generare campi gravitazionali inversi, potrebbe scorrere al contrario consentendo viaggi nel passato, e non solo quelli nel futuro già contemplati dalla relatività einsteniana!!

Soltanto un'idea bizzarra?

E' con mia somma meraviglia che, solo pochi giorni or sono, durante una delle mie peregrinazioni attraverso le autostrade telematiche, mi sono imbattuto in una sconcertante teoria, peraltro estremamente ben congegnata, e con basi logiche che vanno assai oltre la mia semplice idea di simmetrizzazione. Ebbene, la teoria espone risultati ed equazioni non molto dissimili da quelle illustrate in questo lavoro. Essa porta il nome del fisico tedesco Burkhard

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Heim (scomparso, purtroppo, il 14 gennaio del 2001), ed è reperibile in linea al seguente indirizzo: http://www.mufon-ces.org/docs/heimphysics.pdf , relativo al documento: The Physics of Burkhard Heim and its Applications to Space Propulsion, by Illobrand von Ludwiger, M.Sc., realizzato per la presentazione al primo Workshop Europeo sulla Field Propulsion, 20-22, Gennaio 2001, University of Sussex, Brighton, GB. Sintetizzarla in maniera corretta è pressoché impossibile, ma possiamo delineare le linee di fondo ed il percorso logico seguito da Heim. L'obiettivo che si è posto lo scienziato è stato quello di comprendere se le equazioni della Relatività Generale di Einstein potessero essere combinate e rese compatibili con quelle della fisica quantistica, adottando opportuni accorgimenti matematici ed in particolare una apposita matematica che fosse in grado di far transitare dallo spazio dei tensori della fisica dei sistemi macroscopici a quello della quantizzazione dello spazio-tempo, e quindi a ciò che Heim chiama spazio dei "selettori" per la fisica quantistica. Il tutto senza interruzioni o rotture, ma con un unico sistema di equazioni.

Ebbene, Heim non solo riesce nel suo intento, ma lo fa introducendo uno spazio ad 8 dimensioni ove, alle 4 tradizionali (3 per lo spazio ed una per il tempo) se ne aggiungono altre 4 virtuali. Uno spazio che potremmo definire "spazio delle configurazioni", ove sono allocate tutte le possibili forme della realtà, le dimensioni aggiuntive facendo riferimento al piano che descrive la probabilità dei cambiamenti di stato. Le equazioni spiegherebbero non solo la possibilità di considerare la Relatività e la Meccanica Quantistica come applicazioni particolari di esse, ma anche di desumere in maniera automatica, quali loro soluzioni, l'esistenza di 4 tipologie di particelle: fotoni, neutroni, cariche elettriche e gravitoni, di cui Heim calcola, sempre in base alle sue equazioni, il valore esatto delle rispettive costanti.

Ma non finisce qui. Le equazioni applicate allo cosmologia consentono di interpretare ciò che appare come espansione dell'universo quale effetto della espansione del metrone (quanto di spazio) e del cronone (quanto di tempo), e quindi di calcolare il momento iniziale corrispondente alla nascita dell'Universo (la teoria non prevede alcun Big-Bang).

Quello che, però, è più rilevante ai nostri fini, è la applicazione di questa teoria alla fisica dell'elettromagnetismo, che porta alle equazioni di seguito riportate:

Ove: Γ = campo gravitazionale µ = mesofield α = permettività gravitazionale nel vuoto (1/4πγ = 1.19 × 109 s²kg/m³) γ = costante di gravitazione universale ( γ = 6.67422 × 10-11 m³/s² kg) ß = 1/αc² (9.34 × 10-27 m/kg) c = velocità della luce (3 × 108 ms) je = densità di corrente elettrica jm = densità di corrente di massa .

Heim aveva lavorato, fino al 1954, presso il Max-Planck-Institut di Goettingen, che abbandonò a causa di un grave handicap che lo privò dell'uso degli occhi e delle mani. Tra il

190

1979 e il 1984 pose mano ad una voluminosa opera (699 pagine) in cui espose l'intera teoria.

Quando uscĂŹ il volume praticamente nessuno ricordava che Heim giĂ nel 1959 era divenuto famoso proponendo un nuovo sistema di propulsione astronautico.

----[Per una presentazione dell'autore si rimanda al suo articolo pubblicato nella prima parte di questo stesso numero di Episteme] sabato.scala@libero.it

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Recent Developments in the Relativistic Electrodynamics Controversy (Gianfranco Spavieri, Miguel RodrĂ­guez and Edgar Moreno) Abstract In this paper we consider the controversial facets of two tests that are supposed to show experimental evidence against the accepted standard electrodynamics based on special relativity. The first refers to the detection of longitudinal electromagnetic forces in current carrying conductors, and the second represents a modified version of the Trouton-Noble experiment for which a non-null result has been found. Although the first test is inconclusive, the positive result of the second, if it is really such, is surprisingly in agreement with standard electrodynamics. ***** 1 - Introduction Classical electrodynamics is in a slow but continuous evolution and some of the recent advances are the results of discussions that have been going on for decades. In recent times many papers have been published on themes related to the so called "electrodynamics controversy." This is a scientific controversy between physicists in favor of the standard relativistic interpretation of classical electrodynamics and physicists that favor an approach to electrodynamics based on coordinate transformations different from the Lorentz transformations and, thus, negate the validity of special relativity.

In this paper we consider, both from a theoretical and experimental point of view, two aspects of this ongoing controversy, namely: the detection of longitudinal forces on current elements [1-8] and an experiment of the Trouton-Noble type [10-16] which, supposedly, leads to a nonnull result, in contrast to the traditional view exposed in many textbooks.

Before going into the details, we would like to make a general comment on the reliability of the papers that deal with this type of conflicting aspects of fundaments of physics. As it has been remarked by several epistemologists and experts in the philosophy of science, most physicists assume spontaneously a partial position in these discussions. The remark is that some experimentalists are tempted to, and in fact do, try to arrange the experimental set up in such a way that the data are trimmed or slightly modified in favor of expected or desired results, which would corroborate their own visions or theories. Moreover, it is not uncommon to find out that theoreticians may have selected from the existing theory formulas or partial approaches that lead to a theoretical result in agreement with their vision, most of the times neglecting "unintentionally" other formulas or approaches that would lead to opposite or different results.

We believe that the majority of physicists deal with controversial issues with serious and frank attitude, so that the effects of "unintentional" modification of experimental data and manipulation of theoretical models is probably limited and, hopefully, do not alter significantly the objective physical results. Nevertheless, some of these controversies, which generally imply the waste of a lot of time, would not subsist if physicists were a little more scrupulous in their research. Moreover, some physicists, either in favor the official, standard view of accepted theories or not, assume generally a rigid and dogmatic attitude that often prevents discussion and advances. Sometimes this attitude prevents the research of issues that later are recognized as real fundamental unsolved problems of modern physics.

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With this in mind, we try to address in an objective way the two experimental topics mentioned above, being our impartiality somewhat assured because, although the predictions of opposing theories are clear, we are not completely in favor of the expected standard prediction.

Two groups of researchers performed recent experiments on these topics. The novelties of the experiments, which make them interesting from a theoretical point of view, are: - In the case of detection of longitudinal forces, a time varying current has been used [3], unlike other previous experiments where the current was steady-state [1-2, 4-6].

- In the case of the Trouton-Noble experiment, the parallel plate capacitor was not shielded from external electric fields [13], unlike previous experiments of this type [10-12].

2 - Advances in the Controversy of the Longitudinal Forces on Current Elements This is an old discussion that sets as opposing theories or formulas, describing the force acting a current element, the Ampere law and the Biot-Savart law.

The Ampere law reads

∆ Fm, n = − k

imin dmdn , ( rm, n ) 2

(1)

where im and i n are the currents flowing in the current elements of length dm and dn respectively, r is the distance between the two elements, and k is a dimensionless geometrical function that takes into account the direction of current in each element.

An important feature of this law is that the action and reaction principle holds for the interaction between two current elements. Moreover, besides the usual forces perpendicular to the current elements, this law predicts also the existence of longitudinal forces, i.e. forces acting on a current element in the direction of the current.

The Biot-Savart law reads

∆ Fm , n = im dm × B n ,

(2)

where Bm is the magnetic field due to current element dn , given by the Laplace formula

dB n =

rn , m µ (i n dn) × .

4π (rn ,m ) 3

(3)

For this law, the forces are always perpendicular to the current element. However, this law does not comply with the action and reaction principle between two current elements.

Nevertheless, both laws give the same result when the interaction is extended to the complete circuit and the action and reaction principle is not violated.

Several of the experiments that try to discriminate the two laws experimentally have been discussed in Ref. 4-5, 7. It has been remarked that the theoretical advantage of the Ampere law is that it complies with the action and reaction principle. Although some more refined discussion should be in order on this theoretical aspect, the final impression we have, from an experimental point of view, is that a point in favor of the Ampere law has not yet been made.

In this article we consider the results of a recent experiment by Graneau et al. [3] who claim to have proven the existence of electromagnetic longitudinal forces. Their experimental set up

193

consists of a closed circuit where a high intensity time-dependent current I is induced, as shown in schematically in Fig. 1. In this experiment, a capacitor is charged at a very high voltage and then discharged when connected to the electric circuit where a current I = I(t) is induced. A small section R of the circuit is isolated from the rest of the circuit by two air gaps, Gu and Gd, so that the rod R can move up and down if a net force acts on it in the longitudinal direction.

Graneau et al. observed that the rod moves, during their tests, and it reaches a height h that depends on the maximum intensity of the current and also on the difference between the lengths of the up and down gaps, Gu and Gd. Their data indicate that the net force, which makes the rod reach the height h, is zero for a symmetric set up, when Gu = Gd, while the force and the height h increases progressively up to a maximum value when, progressively, one sets Gd < Gu. Thus, Graneau et al. conclude that their experiment proves the existence of electromagnetic longitudinal forces and favor Ampere's law. An extended article refuting their conclusions has been recently submitted for publication [8]. Here we give some of the arguments used for the rebuttal and use this occasion to make some other comments about this controversy with the aim to provide suggestions for other tests of electrodynamics where time-dependent fields are used.

Qualitatively, our explanation of the results of Graneau et al. is the following. The net force exists but it is not of electromagnetic nature. When the current I of very high intensity is induced in the circuit, most of the power P = RcI 2 is dissipated via the Joule effect in the air gaps where the electrical resistance Rc is higher than in the rest of the circuit. The air in the gaps reaches a high temperature and pressure, generating a gas expansion, like a small explosion that acts on the inner surface of the mobile rod R. However, the air in the smaller gap Gd is relatively more confined than the air in the upper gap Gu. Molecules, radiation energy, electrons, etc., of the expanding ionized air, will bounce back and forth many more times between the inner walls of the gap Gd than of Gu, before they leave the gap. Thus the pressure exerted in the smaller gap is more effective than that in the larger gap. It is this pressure difference that generates the net upward force that pushes the rod at a height h.

The details and a quantitative description of this mechanism are given in Ref. 8 where it is shown that the dependence of h with the length Gd is in good agreement with the experimental data and in better agreement with the the experimental results than the predictions of the Ampere law, as calculated by these authors. Thus, we believe that the experiment here considered is not conclusive and cannot be taken as an experimental proof of Ampere's law.

Some considerations are in order here that can help to address the controversy on what are the real forces acting on charges or current elements.

The novelty of this experiment is that it is conducted in non steady-state conditions, since the current varies with time. In this circumstance, the vector potential A(t), associated with the time varying current, also varies with time. Since A(t) can be in the direction of a current element, the force â&#x20AC;&#x201C;q dA/dt = qE, where E is the induction electric field and q the charge associated to a current element, may also be in the direction of current elements.

Generally, the circuit is neutral so that besides the moving charge q there is also a stationary charge â&#x20AC;&#x201C;q in the current element, and there should be no net force. But, if the rod R accumulates a net charge during the extreme conditions of the test, a longitudinal force could be acting on R, even though it is probably small in this set up.

However, the interesting point in the case of time-dependent fields is that one realizes that, contrary to the usual steady-state conditions where the Biot-Savart law is generally confirmed, there is no mention in the literature of experiments dedicated to the detection of forces acting on charges or current elements due to time-dependent induction fields.

194

When the phenomenon of induction is applied to a closed loop we have many direct verifications of the law of induction, or Faraday's law, in terms of the emf,

emf =

∫E

⋅ d ,

induced in the loop, which has an integral form. In this common case, there are forces acting in the direction of the current but only the resultant on the closed loop is being tested in terms of the induced current or voltage difference. The differential force acting on a current element or a part of a loop is not being tested in the usual induction experiments.

Thus, what has not been tested experimentally is not only if these induction forces are the same for charges at rest or in motion (as the moving charges in a current element), but if the induction forces act at all in an isolated stationary charge that is not part of a closed circuit.

One reason why the experimental results for the last mentioned case are not obvious, even for standard relativistic electrodynamics, is that the action and reaction principle does not hold for the interaction between a coil producing a time varying magnetic field and an isolated charge (this is the so called Shockley-James paradox, solved in Ref. 9). Theoretically, there should be a force –q dA/dt acting on the isolated charge. However, the existence of a possible reaction force on the coil has been the source of controversial discussions [9].

There is a pragmatic reason why these problems related to time-varying fields are mentioned here. From an operational point of view, it may be easier experimentally to detect possible discrepancies with classical electrodynamics for isolated static charges than current elements.

In fact, a current element is mainly a theoretical concept that is difficult to realize experimentally, as all the objections and drawbacks of the experiments on longitudinal forces performed so far has shown. While an isolated charge is a theoretical concept realized experimentally in many set ups, such as the experimental proof of Coulomb law, and it should be easier to handle without ambiguities.

Thus, our suggestion and belief is that the electrodynamics controversy may achieve more interesting and definite results if it shifts its attention to the possible tests of electromagnetic interactions with time-dependent fields of the type mentioned above.

3 - A New Experiment of the Trouton-Noble Type With the same spirit that motivated the mentioned papers [4] and [5], we believe that it is worth reconsidering here one of the tests of classical electrodynamics, the Trouton-Noble (TN) experiment, that has been recently discussed in the literature.

The outcome of the TN experiment has been considered a null result for decades. Trouton and Noble wanted to verify that a charge moving with respect to the ether frame where the Maxwell equations were valid, would create a magnetic field. In order to check this hypothesis, they suspended a charged capacitor to a thin thread. Since the Earth (and the capacitor) was supposed to be moving with respect to the frame of the ether, the magnetic field produced by one of the charges of the capacitor in motion would act, via the Lorentz force, on the other charge producing a torque and an observable rotation of the apparatus.

The experiment was first performed by TN [10] and later by Chase [11], and more recently and with a high sensitivity by Hayden [12]. The results of all these experiments indicate so far that the effect sought by TN does not exist.

However, recently Cornille [13] has claimed that he performed a TN experiment with positive result and gives a number of reasons why the previous experiments failed while his succeeded. This result is surprising because it seems to defy the generally accepted interpretation of the TN experiment and of the standard, relativistic interpretation of classical electrodynamics.

195

In the present section we show that a test of the Faraday law in differential form can be related to an experiment of the TN type. Furthermore, we clarify the experimental limits of the original TN experiment and of that performed by Cornille. In a future paper we consider another test of the Faraday law in differential form and point out an interesting and unique experimental consequence of the validity of the conservation laws in electrodynamics.

Without considering here Cornille's theoretical arguments in detail, we have noticed that Cornille's experimental set up differs from the others because he did not shield the suspended condenser from external electric fields. He also mentions that the magnetic field of the Earth cannot produce a torque because the charges of the capacitor are at rest in the laboratory frame of the Earth.

We show that, theoretically and contrarily to the current belief, in specific experimental conditions an experiment of the TN type, consisting of a suspended charged capacitor, may succeed. In fact, according to the standard interpretation of Faraday's law of induction, a positive result is theoretically possible if the effect of the small magnetic field of the Earth on the capacitor is taken into account.

However, the foreseen non-null result refers to the action of the external magnetic field of the Earth on the TN capacitor, which is actually rotating about the Earth axis in its diurnal rotational motion. It does not refer to the effect originally sought by TN and other theoretical effects considered by Cornille.

Furthermore, the experiment of the TN type here considered, may provide a definitive quantitative test of the old theory of magnetic field lines ''cutting,'' which supposedly has been disproved qualitatively by the Kennard [14] experiment.

In the final part of the paper we indicate the experimental conditions that lead to a positive result for an experiment of the TN type and comment on the experimental result of Cornille.

4 - The Standard Description of the Faraday Disk The Faraday disk, as shown in Fig. 2, consists of a conducting disk rotating about its symmetry axis and connected to an electric circuit AECR with one end (A) on the axis at the center of the disk and the other end (R) in the form of a sliding contact touching the external circumference. When a magnet is placed near the rotating disk with its magnetic pole aligned along the disk axis, an induction current flows in the circuit.

If the magnetic field B is uniform near the disk of radius R rotating with angular frequency ω, the electromotive force is given by 1 emf = ∫ E ⋅ d l = ∫ ( v × B) ⋅ dl = wR 2 B i 2

(4)

In many textbooks, result (4) is deduced from the integral form of Faraday's law taking into account the change of the magnetic flux as the material segment AR rotates in the presence of the field B. The integral form of Faraday's law cannot tell where, along AECR, the emf is induced.

However, considering Faraday's law in differential form, the expression v×B represents the induction, effective field Ei seen by the charges co-moving with the disk along the segment AR. It is a consequence of the validity of the Lorentz force F=E+q v×B, written in a reference frame S, that indicates that the charge moving with velocity v in the presence of B and with E=0, experiences the field Ei=F/q= v×B. According to the transformations of the electromagnetic fields of special relativity, an observer in a reference frame S' instantaneously co-moving with a point of the disk experiences the fields B´≈B and E´≈ v×B. The observers of both frames S and S' agree that the emf is induced in the radial path of the disk and the description of the effect is essentially the same for S and S'. The same result is

196

obtained if the magnet is rotating with the disk or if a rotating conducting magnet alone is used as a Faraday disk. In fact, according to the standard relativistic interpretation of electrodynamics a cylindrical magnet can be thought of as made of a cylindrical current distribution, and the current and field produced by the current is the same even if the current loops rotate about the symmetry axis.

Historically, the field lines of B were considered to have a precise physical reality. The potential difference generated across the radius AR was interpreted as due to the cutting of the magnetic field lines by the rotating metal. In the term qv×B, the velocity was interpreted as that of the charge with respect to the field lines, and not as the velocity of the charge relative to the reference frame where the magnetic field is measured.

In the case of a Faraday disk formed by a rotating magnet, in the pre-relativistic interpretation, Faraday's hypothesis of 1851 -- in which he visualized the magnetic lines as fixed to the magnet and rotating with it -- was assumed. In this case, the lines will thus be cut by the external branch ECR and the emf is not induced in the disk but instead in the stationary part ECR of the electric circuit. In this interpretation v represents the velocity of the ''cutting'' field lines at the position of the ECR. Measurements of the induced voltage and/or current cannot discriminate between one theory or the other since in both cases the generated intensities are the same. In 1917 Kennard [14] achieved a breakthrough when he suppressed the ECR branch and was capable of measuring an induced potential difference along AR when the whole system rotated as a unit. Kennard's experiment consisted of a cylindrical capacitor and a coaxial solenoid. The induced electrostatic charge separation was measured by inserting an electrometer by means of two leads located along the axis. One of the lead was connected to the inner part of the capacitor, the other was connected to a radial wire reaching the outer part of the capacitor. When Tate [15] in 1922 reviewed the whole problem, he acknowledged Kennard's result and the implied disproof of the theory of rotating lines of force.

Without negating the validity of Kennard's experiment, we point out some of its limitations.

First of all the apparatus consisted, as in the case of the Faraday disk, of two parts in relative motion: the measuring device, or electrometer, at rest; and the rotating capacitor in motion.

What is being measured is always a potential difference between the two parts and not the local field. The inner part of the capacitor had finite dimensions and one cannot exclude that, if the flux lines are rotating, they may induce a potential difference in the stationary part of the electrometer. Furthermore, the results are necessarily qualitative because of the difficulties of graduating the electrometer and eliminating additional electrostatic effect due to the air drag produced by the rotating parts.

In an ideal experiment the measuring device should be co-moving with the rotating apparatus (magnet or solenoid) and measure the local electric field intensity, so that these objections no longer apply. This ideal situation is achieved with the set up of an experiment of the TN type that exploits the Earth rotation, as described in the sections below.

5 - The Effect of the Magnetic Field of the Earth The magnetic field of the Earth (Fig. 3) is usually approximated by the equivalent field produced by a magnetic dipole placed at the center of the Earth of intensity m o=8.1×1025 gauss⋅cm3. Correspondingly, the magnetic field on the surface of the Earth varies from 0.3 to 0.6 gauss depending on the latitude.

The magnetic dipole is not aligned with the axis of rotation with which it forms an angle α≈14°, corresponding to a distance of about 1000 miles between the geographic and the magnetic pole. The radial component mosinα is quite smaller than the axial component mocosα, being sinα/cosα ≈ 0.22. In the following we consider first the effect of axial component and then show that, for our purposes, the radial component has no effect and can be neglected.

197

Let us consider the component aligned with the Earth axis with a dipole moment intensity of m=mocosα. To all respects, the Earth can be considered equivalent to a rotating magnet so that the results of Sec. 2 valid for the Faraday disk can be applied here.

What is of interest here are the perpendicular and tangential components of B to the Earth surface. Taking the z-axis of frame S aligned with m, the components of the field B at a given latitude and longitude of the vector r are given by

B=

3 r ( r⋅ m ) r

5

−

m r

3

(5)

By means of Eq. (5), one can find the field components that, because of the symmetry, do not depend on the longitudinal or azimuthal angle φ, but depend on the latitude θ . In analogy with the interpretation of the Faraday disk, a charge fixed on the Earth and rotating with it in the presence of the field B will feel the effective electric field Ei.=F/q=v×B. We consider now the effect of the small radial component m r=mosinα of the magnetic dipole.

In the rest frame S, the radial component mr rotates with angular velocity ω. At a point r in space the magnetic field due to mr is a time-varying field and, by Maxwell's equations there must be also an induction electric field. In order to find this electric field, one can consider a moving inertial reference frame S' instantaneously at rest with a point rotating with the same angular velocity ω. We use special relativity but neglect retardation effects and relativistic corrections of order higher than v/c. In S' the magnetic field Br´≈ Br produced by mr is constant and there is no electric field. Transforming the fields one finds that the electric field in S is given by -v×Br. The Lorentz force due to mr acting on a charge fixed on the rotating Earth, is F=qE+qv×Br =q(-v×Br+ v ×Br)=0. Thus, the radial component mr does not have a net effect on a charge at rest on the Earth.

The main difference between the effect of m and mr, is that m generates a constant magnetic field in S, while mr generates a constant magnetic field in S'.

In conclusion, a charge fixed on the rotating Earth feels only the effect of the field B due to m, i.e. it experiments a field Ei.=F/q=v×B. 6 - An Experiment of the Trouton-Noble Type in the Magnetic Field of the Earth Let us consider now a charged capacitor suspended by a thin elastic thread of torsion constant k as in the case of the Trouton-Noble experiment. The capacitor is generally described as two charges of opposite value q placed at the ends of an insulating rod and separated by a distance d, as shown in Fig. 4.

In the following we assume the standard interpretation of electrodynamics which foresees a null result for the effect sought originally by Trouton and Noble. This was supposed to be a torque due to the self-action of the charges moving in the ether and generating a magnetic field with their motion.

What we look for in the present experiment is the effect of the external magnetic field of the Earth on the moving charges. As discussed in the section on the Faraday disk, in the frame S the sought effect is due to the Lorentz force qv×B, in the frame co-moving with the charge the effect is due to the existence of the electric field qv×B. In order to detect this electric field, shielding screens around the capacitor must be avoided, as in the case of Cornille's experimental set up.

With respect to frame S, the velocity v of the charges is in the West to East direction. The only torque on the capacitor about the axis of suspension is due to the component Bp of the magnetic field perpendicular to the Earth surface that produces a force F=qvBp lying on the plane of v and d, tangent to the Earth. The resulting torque is

198

[ (

)]

τ = r× q v× B p = qvB p dcosϕ

,

where ϕ is the angle formed by the vectors v and d.

This torque generates a rotation of the capacitor that tends to set d perpendicular to v. At the position of equilibrium the capacitor has rotated by an angle ε such that τ=kε. In order to verify that this angle is detectable with an apparatus of the Trouton-Noble type, we express the charge on the capacitor, for a parallel-plate capacitor, as q=CV and C=εoS/d. The result is that, when cosϕ = 1,

ε =

ε o SV ( vB p ) k

.

(6)

In order to estimate ε, we consider a location near the equator where the tangential velocity is greater, for example in Venezuela at 8° above the equator corresponding to θ=82° in Eq. (5´).

In this case, with the radius of the Earth given by r=6.37×106m and a velocity of v=ωrsinθ=445m/sec near the Equator, the perpendicular field component turns out to be Bp=0.17gauss directed toward the centre of the Earth and Ei=v×B≈ 7.5×10-3V/m. With a potential difference of V=2×104Volt, a plate surface S=1m2 and a torsion constant k=108 kg⋅m2/s2, the torsion angle turns out to be of the order of ε≈0.13 radians≈7.5°, which is easily observable.

7 - Conclusions We have considered two aspects of the electrodynamics controversy.

The first aspect refers to the detection of longitudinal forces acting on current elements. We discuss the experiments by Graneau et al. and point out some weakness in the experimental set up that make it unreliable for this test.

However, an interesting feature of the experiment performed by Graneau et al. is that timedependent fields have been used. This feature reminds us that there are no tests of the elementary laws on charges and current elements and that Faraday's law of induction has been tested with great accuracy but only in its integral form, on closed loops.

Consequently, our suggestion is that the electrodynamics controversy should be directed toward testing the elementary forces relevant to the discussions on the Shockley and James paradox.

The second aspect refers again to the test of the Faraday law in differential form. We have shown that the effects of the magnetization produced by the rotating Earth can be described in analogy with those produced by a rotating magnet. Thus, an apparatus of the TN type should lead to a non-null result and can be used to detect the small induction electric field Ei=v×B seen by an observer at rest on the Earth surface and co-moving with it in its diurnal rotational motion with a tangential velocity v=ω×r.

This induction electric field is analogous to the local field supposed to be generating the emf observed in a closed electrical circuit in the Faraday disk. Therefore, this experiment can be used as a test of the Faraday law in differential form and as a quantitative test for the localization of the emf, which has been already qualitatively verified by Kennard.

The non-null result reported by Cornille for his TN experiment -- with a high voltage of 40×103V -- seems to corroborate the existence of the small induction electric field Ei However, there are still some difficulties.

First of all, Cornille's result is qualitative, as he observed a rotation of the apparatus tending to align along the velocity v, but did not measure the torque. He also states that the rotation is

199

unchanged by reversing the potential difference and concludes that the TN effect exists. If we discard the existence of the effect originally sought by Trouton and Noble, an explanation of the effect observed by Cornille can be attributed to an electrostatic induction of objects near the capacitor, which does not depend on the sign of the potential difference.

In conclusion the experimental evidence for the localization of the emf is still uncertain and at most qualitative. However, the experiment described in this paper represents a theoretical improvement and its realization should be able to settle the question of localization -- and the questions raised by Cornille's experiment -- in a quantitative and definite way.

Acknowledgments This research was made possible by a grant from the CDCHT (C-1015-00-05-B, ULA, MĂŠrida, Venezuela).

References 1.

P. Graneau, Phys. Lett. A 97, 253 (1983)

2.

T.E. Phipps and T.E. Phipps Jr., Phys. Lett. A 146, 6 (1990).

3.

N. Graneau, T. Phipps Jr., and D. Roscoe, Eur. Phys. J. D 15, 87 (2001).

4.

G. Cavalleri, G. Spavieri, and G. Spinelli, Eur. J. Phys. 17, 205 (1996).

5.

G. Cavalleri, G. Bettoni, E. Tonni, and G. Spavieri, Phys. Rev. E, 57, 1 (1998).

6.

P. T. Pappas, Nuovo Cimento B 76, 189 (1983).

7.

Cavalleri G., Spavieri G. and Tonni E., Hadronic J. 21, 459 (1998).

8. G. Cavalleri and G. Spavieri, submitted to Eur. Phys. J. (2001).

9.

Y. Aharonov, P. Pearle, and P. Vaidman, Phys. Rev. A 37, 4052 (1988); G. Spavieri, Nuovo Cimento B 109, 45 (1994).

10.

Trouton F.T. and Noble H.R., Proc. Royal Soc., 72, 132 (1903).

11.

Chase C.T., Phys. Rev., 28, (1926).

12.

Hayden H.C., Rev. Sci. Instruments., 65, 788 (1994).

13.

Cornille P., Galilean Electrodynamics, 9, 33 (1998).

14.

Kennard E., Phil. Mag. 33, 179 (1917).

15.

Tate J., Bull. Nat. Res. Council, 4, 6 (1922).

16.

L. Nieves, M. Rodriguez, G. Spavieri, and E. Tonni, Nuovo Cimento B 116, 585 (2001).

Figure Captions Fig. 1. Scheme of the electrical circuit used by Graneau et al. for the detection of longitudinal electromagnetic forces. The mobile part of the circuit R moves up when a strong, impulsive electric current flows.

Fig. 2. Scheme of the Faraday disk picturing the magnetic flux lines generated by the magnet.

In the Faraday disk the emf is induced along the rotating material segment AR of the circuit.

Fig. 3. Scheme of the magnetic field lines of the Earth. The Earth magnetization can be represented by a magnetic dipole placed at the centre of the Earth.

200

Fig. 4. A Trouton-Noble apparatus is suspended to a thin elastic thread. Due to the rotational motion of the Earth, the charged condenser moves with velocity v in the presence of the external magnetic field B. The Lorentz force F=qvĂ&#x2014;B acts on the charges Âąq and tends to rotate the condenser until d is perpendicular to v.

----FIG. 1

201

FIG. 2

202

FIG. 3

FIG. 4

----Centro de Astrofísica Teórica, Facultad de Ciencias, Universidad de Los Andes Mérida, 5101 - Venezuela spavieri@ula.ve [A presentation of the first two authors can be found in Episteme N. 3]

203

Dynamic Space Converts Relativity Into Absolute Time And Distance (Tuomo Suntola) Abstract A confusing feature in the theory of relativity is the use of time and distance as parameters in explaining the constancy of the velocity of light and the reduced frequencies of atomic clocks in fast motion and in high gravitational field. It is well known that a radio signal passing a mass center is delayed compared to a signal from same distance through free space. Instead of stating that the velocity of the signal were reduced the theory of relativity explains that time close to mass centers flows slower thus saving the basic assumption of the theory, the constancy of the velocity of light. Same is true for atomic oscillators and the characteristic absorption and emission frequencies of atoms, an atomic clock loosing time when in fast motion is not considered as running slower but as experienced slower flow of time.

A key demand of a physical theory is its capability to create an understandable picture of the reality we observe. Instead of just introducing mathematical expressions for observations, a physical theory should explain the logic behind the phenomena observed. The old Ptolemy astronomy worked well for calendar and eclipses but failed in serving as a basis for a physical view of celestial motions. A key in Copernicus' findings was the realization of the observer's state in the system - instead of defining the observer's state as the origin at rest Copernicus identified the Sun as the origin of the planetary system with Earth orbiting and rotating like any other planet. Such a structure gave basis for a physical approach of motions in the system thus opening a new era for the understanding of the celestial mechanics and the laws of nature.

The Dynamic Universe approach takes a further step in reorienting the observer. The observable three-dimensional space as whole is considered as a closed spherical structure with its dynamics determined by a zero energy balance between gravitation and motion in the structure. Such approach links local phenomena to the state and motion of whole space and gives physical explanations to several postulates like the velocity of light, the rest energy of matter and the Mach's principle. It also explains the dependence of the velocity of light on the gravitational environment and the dependence of the ticking frequencies of atomic clocks on the state of local motion and gravitation - not by distorting time and distance coordinates but in absolute time and distance.

***** 1 - Space as the surface of a 4-sphere Many physicists have noticed the striking equivalence between the total rest energy of all mass in space and the gravitational energy of space estimated from Newton's gravitational energy as E â&#x2030;&#x2C6; GMÎŁ2/R where R = c/H is the Hubble radius. For further analysis of the total gravitational energy we need to assume certain geometry of space. A natural solution is a three-dimensional surface of a four-dimensional sphere. Following the ideas of Ludwig Schläfli, Georg Riemann and Ernst Mach, Einstein, Ref. [1] proposed such geometry in 1917.

Einstein was looking for static space, which lead to the need of the cosmology constant to prevent shrinkage of the structure. Further, the fourth dimension was already reserved for time in the theory of relativity just completed. As the result, the spherical space was rejected.

204

Combining the idea of space as the surface of a 4-sphere to the mystery of the equality between the gravitational energy and the rest energy of mass in space suggests that space as the surface of a 4-sphere is in motion at velocity c in the direction of the radius of the 4sphere so that the energy of motion related to mass in space moving at velocity c along the 4radius is written like the energy of light as E = cp = c⋅MΣ c = MΣ c2 (see Figure 1).

E”(m)

F’(g),t − R4

m

R" M" − F”(g)

R4

E”(g)

MΣ = 2ρ π R4 2

3

Figure 1. The tangential shrinking force, F'(g),t, due to the gravitation of uniformly distributed mass in spherical space is equivalent to the gravitational effect, F"(g), of mass equivalence M" at distance R" from mass m along the 4-radius of the structure.

The sum of the total energies of motion and gravitation in space is zero.

A detailed mathematical analysis taking into account the four-dimensional geometry in the expression for the gravitational energy allows the zero-energy balance between motion and gravitation to written in form M Σ c02 −

GGE M Σ2 = 0 R4

(1)

where GE = 0.776 is a geometrical factor resulting from the integration of the gravitational energy throughout the three-dimensional surface of the 4-sphere, Ref. [2].

When solved for the velocity of space, c0, in the direction of the radius of the structure we get c0 = ±

GGE M Σ GM " = ± R4 R"

(2)

which means that for maintaining the zero energy balance in space the velocity of expansion or contraction along the 4-radius is linked to the gravitational constant, total mass in space and the actual length of the 4-radius. For a mass density 5 ⋅10−27 [kg/m3], which is 0.55 times the Friedmann critical mass, and the 4-radius of space R4 = 14⋅109 light years, the numerical value of c0 in equation (2) is equal to c0 = c = 300 000 km/s. The latter form of equation (2) applies the mass equivalence M" of space at distance R" in the fourth dimension, in the direction of the 4-radius of three-dimensional space (see Figure 2). When applied to mass object m equation (1) means that the rest energy of matter can be explained as the energy of motion due to the expansion of space along the 4-radius.

The buildup and release of the energy of matter in space can be described as a zero-energy process from infinity in the past through singularity to infinity in the future. In the contraction phase mass obtains its velocity against the release of gravitational energy like in free fall and in the expansion phase the energy of motion obtained in the contraction is converted back to the gravitational energy.

205

dM

R" M"

D

x,y,z m Im

Figure 2. The integrated gravitational effect of all the mass in space on a mass object m can be described as the gravitational effect of mass M" at distance R" along the imaginary axis inside closed space.

In the expansion phase, the radial motion of space works against the gravitation of the structure, which means that the radial expansion velocity is gradually diminishing. The relative reduction of the expansion velocity in the present state of the Universe is about ∆c0/c0 = 4⋅10−11 /year. It turns out that the frequencies of atomic clocks and the characteristic wave numbers of the spectral lines of atoms are directly proportional to the internal momentum due to the motion of space at velocity c0. Accordingly, the reduction of the velocity of light is not detectable in measurements based on the readings of atomic clocks.

Energy of motion ∞

time

−∞

contraction

∞

expansion

−∞

Energy of gravitation

Figure 3. Contraction and expansion of space and the corresponding evolution of the energies of motion and gravitation. In the contraction phase, the 4-radius of space goes from infinity to zero. In the expansion phase, after singularity, the radius increases from zero back to infinity. Zero total energy is preserved through the entire process.

206

2 - The fourth dimension The shocking message of equations (1) and (2) is that the velocity light appears as the velocity of all mass in the fourth dimension. Same message is hidden in the line element in Lorentz coordinates or Minkowski metrics which in local homogeneous space can be expressed as

( ds )

2

= − ( cdt ) + ( dx ) + ( dy ) + ( dz ) 2

2

2

2

(3)

or in vector form as ds = i cdt + dx + dy + dz

(4)

where c instead of dt is expressed as a vector in the fourth dimension, mathematically shown as the imaginary direction. Following the concept of space as the three dimensional surface of a 4-sphere, c in equation (4) does not mean motion in space but motion of space, i.e. motion that all matter at rest in space is subject to according to equation (2). Accordingly, the rest momentum of a mass object in space is p 4 = i mc 4

(5)

i.e. momentum in the fourth dimension which, when summarized to a momentum p in a space direction gives the total momentum ptot relevant with the total energy of an object moving in space Etot = c4 ptot = c4 pr2 + ( mc4 )

2

(6)

Equation (6) shows the total energy of an object in the same format as given by the theory of special relativity, however, without the use of the Lorentz transformation as a correction of the coordinates. Equation (6) describes the total energy as the result of the orthogonal sum of momenta due to the motion of space and the motion in space.

In fact, motion of space at the velocity of light along the radius of curvature is implicitly given in the Hubble law and the uniform expansion of space, which were not known at the time the theory of relativity was formulated.

3 - Motion in spherical space Observing that any motion in spherically closed space is central motion relative to the mass equivalence of space in the fourth dimension, the gravitational acceleration in the fourth dimension is reduced due to central acceleration (Figure 4). The effect can be expressed as a reduction of work done by the object against the gravitation of the mass equivalence of space in the fourth dimension. The effect can be expressed in terms of a reduction of the internal mass mI responding to the gravitational interaction with the total mass in space mI = meff ( 1 − β

2

)= m

1− β

2

(7)

The reduction of the internal mass reduces the momentum of the object in the fourth dimension and, accordingly the "excitation" of the energies of motion and gravitation. It can be shown that such situation results in a reduction of the characteristic frequencies of atomic oscillators, i.e. the frequency of atomic oscillators moving at velocity β = v/c is reduced by factor 1 − β 2 as fI = f0 1− β

2

(8)

where f0 is the frequency of the oscillator at rest in the local energy frame. Equations (7) and (8) give direct physical meanings to the Lorentz factor - not as a correction of time coordinate but a factor reducing the internal energetic response of a moving object to the gravitation of

207

the total mass in space on the object. In terms of inertia this means that the buildup of kinetic energy when accelerating an object to a velocity in space involves the work done in reducing the gravitational energy due to all mass in space.

Im 2

FC=mv /R” v

F"i(a) = χmradc /R” 2

v=c

Fg =−GmM”/R” =−Eg/R”

2

R" R”

F"g = −χmradc /R” 2

M”

Figure 4. (a) As central motion relative to the center in the fourth dimension, motion in space reduces the gravitational effect of the total mass described by mass equivalence M" in the fourth dimension.

Figure 4. (b) For an object moving at a velocity equal to the velocity of space in the fourth dimension the gravitational effect of the total mass in space is fully counterbalanced by the centrifugal acceleration.

4 - The effect of mass centers on the local velocity of light The idealized picture of completely symmetric spherical space assumes that mass is uniformly distributed all over the space. When mass is cumulated into mass centers in space the conservation of total gravitational energy demands that the "smooth" surface of an ideal fourdimensional sphere is tilted to form dents in the fourth dimension around mass centers in space. In tilted space also the direction of the fourth dimension is turned relative to the direction of the expansion, accordingly, locally the velocity of space in the fourth dimension is reduced in proportion to the tilting (see Figure 5).

In a local gravitational frame the famous equation E = mc2 shall written in form Eδ = c0δ mc

homogeneous space c φ

c0

dr M

φ dr0

c0

(9)

Figure 5. In the vicinity of a mass center local space is tilted by angle φ relative to homogeneous space moving at velocity c0.

Accordingly, the velocity of space, c, in the local fourth dimension is c = c0 cosφ .

208

where c is the local velocity of light in the gravitational state denoted by the gravitational factor δ and c0δ is the velocity of light outside the local gravitational frame, in the apparent homogeneous space of the local frame. The local velocity of light can be expressed in terms of the local gravitational state as  GM  GM   c = c0δ cos φ = c0δ ( 1 − δ ) = c0δ  1 −  ≈ c0δ  1 − rc 2  rc c 0 0δ  

(10)

where φ is the tilting angle of local space and δ the gravitational factor as expressed in terms of the gravitational constant G, M the mass of the central mass of the gravitational frame at distance r from the location of the object studied.

Factor mc in equation (9) has the meaning of momentum in the local fourth dimension. The kinetic energy of free fall in a local gravitational frame is gained against a release of the rest energy of the falling object through the reduction of the local velocity of light.

As a consequence of the reduction of the momentum in the fourth dimension the locally obtainable maximum velocity in space, the local velocity of light, and the frequencies of internal atomic processes are reduced. Motion in space reduces the frequencies of internal atomic processes through the reduction of internal mass, mass centers in space reduce the frequencies through a reduced velocity of light in tilted space. Combining effects of motion on the internal mass of an object and the effect of reduction of local velocity of light, the characteristic frequencies of an atomic oscillator moving at velocity β in gravitational state δ in a local gravitational frame can be expressed as fδ , β = f 0δ ,0 ( 1 − δ

)

1− β

2

(11)

where frequency f0δ,β is the frequency of the oscillator at rest in the apparent homogeneous space of the local gravitational frame.

Local tilting of space and the reduction of the velocity of light near mass centers have several interesting consequences. Light or radio signal passing a mass center is delayed due to the lengthened path and reduced velocity. Also, the path is bent due to the local deformation of space. A further consequence of the local deformation of space is that the main axis of elliptical planetary orbits is subject to a rotation observed as a shift in the perihelion of the orbit.

5 - The system of cascaded gravitational frames Real space consists of cascaded gravitational systems such as our planetary system in the solar system, the solar system in the Galaxy, and the Galaxy in the local galaxy group.

Following the zero energy principle, in cascaded gravitational systems the local velocity of light can be related to the velocity of light in apparent homogeneous space around the local dent and, finally, to the expansion velocity of hypothetical homogeneous space in the fourth dimension (see Figure 6). This also means that in a gravitational frame like the Earth gravitational frame the zero reference for the local velocity of light is locked to the shape of the local dent, the zero reference follows the orbital motion of the Earth around the Sun, i.e. the reference at rest "the local ether" for the propagation of light in the Earth gravitational frame is the Earth centered non-rotating frame (or Earth Centered Inertial frame in the language of the general theory of relativity). Based on the present knowledge of the gravitational systems Earth is bound to (the Solar system, Milky way and the local galaxy group), the local velocity of light on the Earth is about 1/10 6 (one per million) lower than the velocity of light in hypothetical homogeneous space where all mass were uniformly distributed.

209 Im0δB

the apparent homogeneous space of the MB frame Re0δB

ImδB=Im0δA

Re0δA

ImδA m MA

MB

the apparent homogeneous space of the MA frame

Figure 6. Apparent homogeneous space of the MA frame around mass center MA follows the direction of space in the MB frame as it were without the MA center.

The assumption we made of space as a closed surface of a four dimensional sphere contracting and expanding by maintaining zero total energy leads to a number of phenomena we are used to know as relativistic effects. As a major difference to the theory of relativity we do not need to use the coordinate quantities, distance and time as parameters to explain the phenomena.

In dynamic space, the effects of motion and local gravitation on internal atomic processes like the ticking frequencies of atomic clocks can be understood as consequences of the motion and local gravitation on the energetic state of the objects. More than that, we can understand why the velocity of light is the maximum velocity obtainable in space and how the inertia of mass linked to the total mass in space.

We do not need to assume that time were different due to gravitational field to understand the delay and bending of light near mass centers or the gravitational red- and blueshift of atomic clocks and electromagnetic radiation. We can honor the coordinate quantities as constant measures in all observations. The velocity of light is not a constant but a function of the local gravitational state.

In a complete form, taking into account the cascaded gravitational frames the equation for the rest energy of an object shall be written as Eδ = mc02 ( 1 − δ

n

) ∏  ( 1 − δ i ) i= 0

1 − β i2  

(12)

where m is the mass of the object, c0 is the expansion velocity of space. Gravitational factors δi describe the effects of the gravitational states of each gravitational frame in its parent frame and factors βi = vi /ci the motions of the local frame in the parent frames. On the Earth, the local velocity of light can be estimated to be c ≈ 0.999999 c0. Taking into account the effects of the cascaded system of gravitational frames the frequency of atomic oscillators can be expressed as n

fδ , β = f 0 Π  ( 1 − δ i ) 1 − β i2  i= 0  

(13)

where f 0 is the frequency of the oscillator in hypothetical homogeneous [see equation (11) as reference].

210

6 - Expansion of space occurs everywhere By linking the energies of motion and gravitation through the zero energy principle, the spherically expanding space allows (or demands) the expansion of space also to occur within local gravitational systems. In the Earth − Moon system this means that out of the 3.8 cm annual increase in the Earth to Moon distance 2.8 cm is due to the expansion of space and only 1 cm due to the tidal interaction.

In cosmological scale the propagation of light follows a spiral path, characterized by equal velocities in the fourth dimension with the expansion of space and the propagation observed in space (see Figure 6).

Figure 6. At cosmic distances the propagation path of light appears as a spiral in four dimensions.

p=h0/λ ⋅c R4=R4(t)

The precise geometry of space and the defined propagation path of light in spherical space allows the derivation of the Hubble law and the redshift versus magnitude dependence without arbitrary parameters needed in the standard cosmology model. The Hubble law obtains the forms z=

D R4 1 − D R4

and v =

D c R4 0

(14)

where the optical distance of the object, D, is the integrated tangential component of the light path from the object to the observer, which is the distance traveled by light in space.

Inherently, equation (14) is consistent with the definition of the redshift in the general theory of relativity.

The energy flux of an object with redshift z can be expressed as F( obs ) F( e)

=

1 z ( z + 1) 2

(15)

corresponding to magnitude versus redshift relationship m = m0 + 5log z + 2.5log ( z + 1)

(16)

Equation (16) gives a perfect match to the observed redshift − magnitude dependence of supernovas as shown in Figure 7. Accordingly, recent confusion regarding the redshift versus magnitude observations becomes solved without any new assumption or parameter, the prediction derived from the dynamic spherical space is shown as the solid curve in Figure 7, also showing recently published observations on supernovas.

211

apparent magnitude 26

Figure 7. Apparent magnitude as a function of redshift in the range z = 0.01 to 1. The dots show observations reported by Perlmutter et al. , Ref. [5].

22

2

F/F0 = 1/[z (1+z)]

18

14 0.01

0.1

redshift (z)

1

7 - Doppler effect and gravitational redshift of electromagnetic radiation The combined gravitational shift of atomic oscillators and the Doppler effect of electromagnetic radiation in a particular gravitational frame has the form f A( B ) = f B

( 1 − GM ( 1 − GM

rA c 2 ) 1 − β

( 1 − β B vˆ B ⋅ rˆ ) rB c 2 ) 1 − β B2 ( 1 − β A vˆ A ⋅ rˆ ) 2 A

(17)

Equation (17) can be derived from the classical Doppler effect by taking into account the effects of gravitation and motion on the frequencies of oscillators.

In the general theory of relativity the Doppler equation corresponding to equation (17) has the form, Ref [3], f A( B ) = f B

( 1 − β B vˆ B ⋅ rˆ ) rB c 2 − β B2 ( 1 − β A vˆ A ⋅ rˆ )

1 − 2 GM rAc 2 − β 1 − 2 GM

2 A

(18)

In the Earth gravitational frame the difference between equations (17) and (18) is too small to be detected (for example, in the famous Scout D experiment, Ref. [4], the difference between equations (17) and (18) is of the order 10−18.

When related to the frequency of the transmitter, fA, equations (17) obtain the form of the classical Doppler equation f A( B ) = f A

( 1 − β B vˆ B ⋅ rˆ ) ( 1 − β A vˆ A ⋅ rˆ )

(19)

where the effect of the velocities of the transmitter and receiver βA and βB are velocities in the local rest frame.

8 - Discussion The Dynamic Universe approach is an "energy based" description of observable reality instead of the "metrics based" description given by the theory of relativity. Unlike the theory of relativity, the Dynamic Universe is derived starting from structure and zero energy balance of whole space and then, by conserving the energy balance in the system, derived into local phenomena. Such approach relates all local phenomena to the energetic state of whole space, which can be found to result in the effects generally referred to as "relativistic effects". The DU approach re-establishes the classical meanings of time and distance, which as coordinate

212

quantities, are not used as parameters in explaining observations. The DU approach gives precise predictions to phenomena covered by the theory of relativity and the standard cosmology model. In addition, the DU approach explains the origin of inertia and the Mach's principle, the nature of mass as the substance for the expression of energy, and the physical mechanisms of the effects of motion and gravitation on the frequencies of atomic oscillators.

It also describes the buildup and release of the rest energy of matter in the contraction and expansion of space in the zero-energy process of spherical space from infinity in the past to infinity in the future, Ref. [2].

References [1] Einstein, A., Kosmologische Betrachtungen zur allgemeinen Relativit채tstheorie, Sitzungsberichte der Preussischen Akad. d. Wissenschaften (1917) [2] Suntola, T., The Dynamic Universe, A New Perspective on Space and Relativity, Suntola Consulting Ltd., ISBN 951-97938-6-0 (2002), www.sci.fi/~suntola [3] Baker, M.L., Jr., Astrodynamics, Academic, New York (1967) 218 [4] Vessot, R.F.C., Levine, M.W. et al., Phys. Rev. Letters, 45, 26 (1980) 2081 [5] Perlmutter, S. et al., 1998 AAS Meeting Jan 1998, Washington DC

----Tuomo Suntola, Dr. Tech.

Senior Scientific Advisor Fortum Corporation POB 100, 00048 FORTUM, Finland http://www.sci.fi/~suntola tuomo.suntola@fortum.com Tuomo Suntola was born in Finland in 1943. Helsinki University of Technology, M. Sc. (1967), Ph. D. (1971), Scientist at State Research Centre, VTT, (1971-1973). Development of humidity sensor for Vaisala Oy (Humidity measuring instruments based on Humicap찾 sensors are still world market leaders in humidity sensing and monitoring). Chief Scientist Instrumentarium Oy/Lohja Corporation (1974-1987). Development of Atomic Layer Epitaxy, ALE, for manufacturing of electroluminescent thin films. Development of flat panel display product and production machinery, implementation of the technology into commercial activity. Managing director of Microchemistry Ltd, a research company in Neste Group (1987-1997). Development of solar cell technologies, extension of the use of Atomic Layer Epitaxy to the manufacturing of heterogeneous catalysts and a research tool for surface chemistry. Direction of the ALE technology and machinery to semiconductor applications, start up of business activity on Atomic Layer Deposition ALD for semiconductor manufacturers. Microchemistry Ltd's ALD business was merged into ASM

213

(Holland) in 1998. ALD technology has become a main stream technology for nanoscale semiconductor devices, (e.g. Applied Materials, Veeco, IPS, Genus).

Senior Scientific Advisor and R&D Fellow, Fortum Corporation since 1997.

Docent at Physics Department of Tampere University of Technology since 1975.

Lectures on semiconductor physics 1972-78. Member of the Finnish Academy of Technology, TTA since 1983, board member 1988-93. Board member of the Mentor Program since 1999. Deputy board member in the Foundation of Technology in Finland since 1991. He holds patents and has published widely in the fields of material science, thin film technology, and surface chemistry.

[See even the presentation of Dr. Suntola's book which is published in the first Section of this same number of Episteme]

214

Nature of Energy, Light, and Einstein's Light-Principle in Special Theory of Relativity (Paramahamsa Tewari, B. Sc. Engg.)* Introduction With the discovery of positron (1932), a unique phenomenon of annihilation of matter (electron and positron) was observed. In this process, both the particles lose their mass, charge, and existence, producing annihilation-radiation, that is, light. An essential fact revealed through annihilation is that light is the last phenomenon of energy-effect before electron and positron lose their basic properties. Therefore, in order to understand the nature of light produced, an exact knowledge on the nature of charge and mass, and their distribution in the structure of the particles is essential, so as to gain deeper insight of the physical process of conversion of mass and charge into light, and to avoid any erroneous conclusion in the interpretation of this phenomenon. Further, light produced by thermal radiation is also considered emitted by orbital electrons in atoms, though, the structure of the electrons is not affected in this process. Light is some form of energy; and energy, from mass-energy equation, is expected to have proportionate mass. Therefore, understanding the origin of mass and charge in the electron structure is the first crucial step in determining the real nature of energy and the annihilation-light.

Apart from the basic properties of light, that is energy-content, wavelength and frequency, the process of its transmission in absolute vacuum is equally important. In post relativity era, space medium, when considered without electromagnetic fields, is believed an empty extension (void) and, yet, light is supposed to be somehow transmitted in this void of nothingness. Such an assumption presupposes that the properties of mass, inertia, charge, and energy, possessed by matter, are independent of spatial reality, that is, the energy constituting matter is not derived from space. But, a comprehensive theory that explains creation of mass, inertia, charge and energy, say, in electron-structure; and that pinpoints the very source of universal energy and its fundamental nature, is nonexistent in contemporary physics.

In this article, creation of electron from space, postulated to be fluid and nonmaterial in my earlier works [1,2,3] has been first described; mass, charge, energy and basic fields in the electron structure and the medium of space are briefly analyzed and defined; and from the observed conversion of mass and charge in the annihilation process, nature of the annihilation-light has been determined. With the new physical picture of the annihilationlight, shown here to be the most fundamental light-effect in the universe, conceptual errors in the current understanding of the nature of light have been pinpointed. Einstein's lightprinciple in special theory of relativity has been examined for its correctness.

Mass and Charge of Electron The property of mass of electron has been shown [1,2,3] to originate from the medium of space - postulated to be a nonmaterial medium with fluidity, incompressibility, continuity, homogeneity, mass-less ness, and zero-viscosity. That is, none of the properties, except fluidity, possessed by matter, exists in space. The only property of the fluid-medium of space (hereafter, referred as "space") is a limit to its velocity of flow and also to the angular velocity of rotation (Ď&#x2030;) when circulating in a vortex. Fig.1 shows an irrotational vortex of space which has opened up at the center into a dynamically stable spherical void due to the postulated limiting Ď&#x2030;, which is also the maximum velocity gradient, c/r e, where "c" is the limiting flow

215

of space (maximum velocity-field), and "re" is the radius of the spherical interface enclosing the void.

A diametrical cross section of the vortex (Fig.2) shows an inward maximum accelerationfield c2/re; this inward radial acceleration of space prevents dilation of the vortex and results in dynamic stability. The vortex described above is the electron structure.

216

The mass of electron is defined as volume-integral of space-velocity within the interface, just prior to the creation of electron; and can be derived (Fig. 1) considering a differential element of volume: dV = (π re2 sin2 θ) re dθ, since, space, equivalent to this volume, is forced out at velocity ω re sin θ during the creation of void when the speed of space in circulation reaches c, and angular velocity becomes ω. Mass of the elemental volume from above definition: dM = dV (ω re sin θ). Integral over the spherical volume within the interface gives, θ varying from 0 to π me = (4π/3) re3 c.

(1)

Mass has the dimension of [L4/ T], and in CGS unit, it has been derived3: gram = 8.6 x 106 cm4/s.

(2)

Charge of electron is defined as the surface integral of space velocity on the spherical interface. Considering the elemental surface: dA= (2π re sinθ) re dθ, and charge on it: dQ = [(2π re sin θ) re dθ] ω re sin θ. Integrating over the whole interface, θ varying from 0 to π qe = (π/4) 4π re2 c.

(3)

The charge has the dimension of [L3/T], and in CGS unit, CGSE = cm3 /s.

(4)

With the use of (1), inward gravitational field (g) due to mass of electron at a radial distance r from the electron center has been derived1,2,3

217

g = (k/4πc) me / r2

(5)

2

where k is 1/s .

With the use of (4), inward electric field (E) due to charge of electron at a radial distance r from the electron center has been derived1,2,3 E = -c2 re2 sin2 θ / 2 r2.

(6)

Basic constants derived [1,2,3] are: Coulomb's constant, with electron as the unit of charge, is c/4π; dialectic constant of vacuum: ∈ = π / 2c; permeability-constant: µ0 = 2 / πc; electron's intrinsic angular momentum: L= (4/5) me c re; magnetic moment of electron: µ = (3/4) qe c re; Planck constant1 for electron: h = (4/5) me c re. All these constants show proportionality to c, which quantitatively proves the postulated universality of c.

Energy in Electron Structure Qualitatively, most basic state of universal energy is defined as "dynamic space in linear, accelerating, or circulating motion".

The central void at the electron center is field-less and hence energy-less (Fig. 3a), whereas, as per the modern concept of electron - a point-mass and a point-charge - energy is distributed all the way up to the center (3b).

The latter leads to the following serious problems:

218

(a) energy in the electrostatic field of an electron becomes infinite at r = 0; (b) electron can emit and absorb energy.

With the central void at the electron center, minimum value of r is r e, and not 0; thus avoiding the integration of energy to reach an infinite value. Also, the energy-less center of electron cannot emit energy (photons); neither can it absorb energy, because, the interface of the electron with space-circulation at limiting speed, is impervious to all external interactions.

The distribution of energy in the structure of a stationary electron starts from its interface and spreads throughout the universal space as gravity and electrostatic fields. During motion, acceleration, or rotation of electron around a center, relative to space, the gravitational and the electrostatic energy is seen [1,2,3] as electromagnetic energy or light (discussed later).

Energy of Electron Creation Refer to Fig. 1. As explained earlier, a differential element of disc with volume: dV= π re2 sin2 θ re dθ, has mass: dM = dV (ω re sinθ) = c π re3 sin3 θ dθ. The area at the interface of the elemental disc, 2π re sin θ re dθ, is subjected at each point to an inward radial acceleration field: af = (ω re sin θ) 2 / re sinθ = c2sin θ / re, where c = ω re. Supposing, the elemental disc collapses under the above inward acceleration-field to zero radius. The work done in this process will be: dE = dM af (re sin θ) = (c π re3 sin3 θ dθ) (c2 sin θ / re) (re sinθ) = π re3 c3 sin5θ dθ.

Integrating over the whole interface where θ varies from 0 to π E = (4/5) [(4π/3) re3 c] c2, which, from mass-equation (1), becomes E = (4/5) me c2.

(7)

The 'work done' is the energy produced due to the displacement of the inward acceleration field from the interface to its center; this energy fills up the void, and should be equal to the energy required to create the void at the electron center. Thus, the energy required for the creation of electron from (7) is (4/5) me c2.

Medium of Space, and its States Fig. 4(a) shows the most basic state of space-a static non-viscous fluid, incompressible, continuous and mass less. This is the most basic substratum of the universe, existing eternally.

In Fig. 4(b) dynamic space is depicted. The flow-velocity of space is termed as velocity-fieldthe most fundamental field, which produces all energy fields (Fig. 4c), that is, gravity, electrostatic, magnetic, nuclear, and electromagnetic. The solar system exists in the universal dynamic space with fields and matter (Fig. 4c) created by the galaxy.

219

Creation of Electron The process of creation2 of electron is shown in Fig. 5.

220

In a space vortex (irrotational) when the angular velocity of rotation reaches the limiting Ď&#x2030;, space breaks down into a spherical void due to being subject to the highest velocity gradient c/re, as discussed before. The radial outward flow of space, creating the interface, takes place at the limiting speed c, and halted after a time interval r e /c, because that is the maximum volume of the spherical void possible for dynamical stability. Since the fluid space is incompressible, a spherical shell of radial width re, with outward pressure3 in it, is created concentric with the interface (void), and is transmitted in the universal space at the limiting speed c, thus energizing the universe gravitationally. Due to the incompressibility of space, at a sphere of radius r, there will be actual displacement (radial) of space points (Fig. 6), which will create gravitational potential there proportionately. This potential will exist as long as the void exists at the electron center.

221

Annihilation Process There can be two electron vortices, with their velocity fields (in between them), opposite in direction, or in the same direction (Fig. 7a,b).

There is only one fundamental particle [1,2,3], electron, which, looked from the other end of its axis, is a positron. Positive and negative charges are relative concepts. Electrical attraction

222

between an electron and a positron can be determined from (6) from which Coulomb's equation has been derived [1,2,3]. Qualitatively, the unidirectional velocity fields between an electron and a positron (Fig.7a) cause attractive electrical force drawing the particles together.

In this process, the spherical interfaces of the particles can be imagined to finally superpose each other (Fig. 7c); thus stopping the oppositely directed space-circulations around their interfaces, and leading to the collapse of their central voids and annihilation of the particles.

Consequently, as experimentally observed, light is produced.

Fundamental Nature of Light It is evident that the void-interiors of the electron and positron, being energy-less, cannot emit any kind of energy (photon). The energy (velocity and acceleration fields) in the vortex structure of these particles pervades the whole universal space before annihilation; and following annihilation, the process of dying (reducing to zero) of the electromagnetic and gravitational potentials of the particles, initiating from their superposed interfaces, is seen as a pulse, or a single shell of light (Fig.8).

When the interfaces of the particles superpose, there is only one spherical-void common to both; space flows radially at its maximum speed c into the void (Fig. 8); the duration of collapse, â&#x2C6;&#x2020;t = re / c. During this time interval, a shell of radial width, â&#x2C6;&#x2020;t c, that is, (re/c) c = re, is formed, and transmitted outward at speed c relative to space. The transmission of the shell is a process that de-energizes the space medium, erasing for all the time the gravitational and electrostatic potentials that were created at the time of creation of the (now non existent) electron and positron. The spherical shell produced due to dying of potentials-a process of deenergizing of space substratum consequent to the electron/positron annihilation-is the fundamental light.

The gravitational field of electron is radial and uniformly distributed on its interface (Fig.9).

223

Therefore, the effect of light due to dying-gravitational-potential will have spherical symmetry. Whereas, the maximum electrostatic fields of these particles, is confined mostly to the diametrical plane at right angles to the axis of rotation (Fig.1); hence, maximum effect of light produced due to dying-electrostatic-potential will be confined within this plane.

Wavelength and Frequency The wavelength of annihilation light (Fig.8) is equal to the electron radius. This light, with a single shell, cannot have the concept of frequency applicable to it. In case there are several annihilations taking place at a point, one after the other, without absolutely any time gap between the successive annihilations, then the frequency can be defined as the nos. of shells formed in unit time. Also, if the time for the formation of a single shell is â&#x2C6;&#x2020;t, then frequency f can be defined as: f = 1/â&#x2C6;&#x2020;t, keeping in mind, however, that this mathematical operation does not mean that the single light-shell has the property of frequency as per the conventional definition of frequency mentioned above. When light is produced due to atomic vibration (Fig.10), the frequency of light is determined by the nos. of atomic oscillations in unit time, assuming that the oscillations are continuous [2,3].

224

Fig. 10 The shell of light produced in annihilation, as well as a light -shell produced in atomic vibration have their centers fixed with the source (assumed stationary relative to space), while the wave front with a fixed wavelength (radial) is transmitted at speed c relative to space. In

225

the modern concept of light, the photon, postulated as a "packet of energy", is understood to have its center moving at speed of light relative to the source. It is not clear as to how the concept of frequency is related with a photon; though, physical picture is not possible, perhaps, a photon wobbles transverse to its line of motion, a number of times say, f, in a unit time, while traversing at speed c relative to the source. And, if that is the possible physical picture, then, "f" will have meaning for a photon (with indivisible energy quantum, hf) only after it has traveled for a unit time having wobbled f times! Again, the specific characteristic of a photon that determines its wavelength remains obscure. Though, it is well known that the classical concepts of wavelength and frequency are inapplicable for a photon in quantum physics, in the absence of a physical picture, there occurs a serious conceptual error, leading to a mathematical discrepancy in the very basic relationship between energy and frequency in the Planck energy equation as pointed out below.

Planck Energy Equation Based on the concepts of Maxwell-Hertz, that electromagnetic (light) energy is given off from electrical oscillators, Planck believed that the orbiting electrons inside the atoms of a glowing solid-emitter radiated electromagnetic waves in different quantities, the frequency being determined by the vibration of the oscillator. The classical picture was revised by Planck based on his observed experimental fact when he assumed that an oscillator, at any instant, could have its total energy (potential, kinetic) only as an integral multiple of the energy quantity hf, where h is a universal constant (experimentally determined) and f is the frequency of vibration of the oscillator. Thus, the light energy can be absorbed or emitted in an indivisible quantum of magnitude hf. Planck energy equation is: E = h f.

(8)

It can be also written as E / f = h.

(9)

It is seen from (9) that "h" is the energy associated with one oscillation of the vibrator, on the following basis.

It has been shown elsewhere [2,3] that a time varying gravitational potential at the surface of an atom produces light (Fig. 10); and that one shell of light produced due to atomic vibration has energy close to the experimentally determined value of h. Though Planck believed that the oscillator emits its own energy (kinetic, potential) possessed by it structurally, by deriving h from the varying gravitational potential in space external to the oscillating atom (Fig.10), a new fact has been brought to light: that the "least energy" produced (in each shell of light) is " E / f". Therefore, the quantity "h f" is, actually, the energy contained in f-numbers of successive light- shells produced by the oscillator in unit time, and cannot be an "indivisible quantum" of light-energy available at an instant, which Planck assumed.

Further, as stated earlier, the structures of the oscillators, either electrons or atoms, are not suited to absorb or emit energy-a serious misconception continuing since Maxwell's theoretical conclusion that oscillations of electric current leads to a loss of energy from the system in the form of electromagnetic waves. The modern concept that heat and light energy get detached from the oscillating atoms is corroborated in the following: "4â&#x20AC;Śthe collisions between atoms and molecules in a gas are said to be perfectly elastic. Although this is an excellent approximation, even such collisions are not perfectly elastic; otherwise one could not understand how energy in the form of light or heat radiation could come out of gas." But such a concept of energy absorption and emission is basically wrong with the vortex structure

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of electron and atom. Even in 'oscillating electric current', the electrons cannot part with their structural energy (the velocity field in the vortex).

The intrinsic angular momentum of electron derived from its vortex structure: L = (4/5) m e c re; substituting the values of me and re, it is found [2,3] to be 7.5 times less than the Planck constant. However, for an average atom, Planck constant computed is close to the experimentally determined value [2,3].

The dimensions of h are that of angular momentum-same as the angular momentum of electron given above. Though, the angular momentum of electron is 7.5 times smaller than the accepted value of the Planck constant, the nearness of the two values may lead to a guess that the orbital electrons in the atoms are indeed the electric oscillators that produce light, as imagined by Planck and others, and as is also the prevalent concept. In this conjecture, however, following difficulty arises.

An atom shows overall electrical neutrality in the region beyond the orbital electrons, where only the gravitational field of the atom should exist. On account of this, h has been computed theoretically with the considerations of the time-varying potential of gravitation alone [2,3].

This is not to say that a charged atom will not produce light; rather the value of h obtained from an assembly of charged oscillating atoms should be different, and so also the nature of light (frequency, wavelength) produced.

Since the structure of light is shown to consist of successive shells, it can be said that light energy exists in quanta, where quanta is defined as "energy in each shell"; whereas, the kinetic energy of a moving body, which is proportional to the velocity of the body that can continuously vary, can not have quanta of energy. Any generalization coming out of Planck energy equation, and leading to the concept that all forms of energy occur in quanta, is therefore erroneous.

Black Body Radiation In a hollow cavity, the equilibrium distribution of electromagnetic radiation energy, experimentally obtained, shows that at low frequency the energy is proportional to f 2, while at high frequency there is an exponential drop. Whereas, the theoretical energy distribution as per Rayleigh-Jeans law gives excessive energy for higher frequency, such that if integrated over all frequencies the total energy becomes infinite. Though, classical mechanics places no limit to the frequency of the mechanical oscillators (atoms), a limit to the oscillator's frequency is imposed by the motion of the fluid-space submerging the atomic vortices (oscillators). The displacement of the atoms from their mean positions displaces space, which has a limiting speed c. If an average radius of atoms is taken as taken as 1.5 x 10 -8cm, the displacement of an atom on either side of its mean position up to a length equal to the radius will involve total displacement relative to space as 3x10 -8cm. Time required for the fluid space to move up to this length at its maximum speed is: 3x10 -8cm/(3x1010cm/s) = 10-8s. The nos. of light shells produced in one second due to this atomic oscillation will be 10 18/s, which is the frequency of the light produced. Thus, maximum frequency of the oscillators in thermal radiation, excluding X-rays and gamma, should be limited to about 10 18/s. It can therefore be inferred that the exponential fall of energy distribution in cavity at higher frequencies is due to the reaction from space at higher oscillation frequencies. The classical concept that to determine the total energy within a cavity (black body radiation), integral has to extend over all the frequencies is based on a misconception that atoms oscillate in the void ness (reaction less) of space and hence there can be no limit to their frequency of oscillation.

Explaining Photoelectric Effect - Einstein's Error In the vortex structure of atom (Fig.11), the vortices of the orbital electrons, interlocked with the velocity fields of the atomic vortex, are carried round the nucleus as explained earlier.

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As is well known, the outer orbital electrons, if interacted with light of appropriate wavelength, are released in photoelectric effect. It is now believed that the photo- electrons absorb energy from the incident light for their release, and also for the kinetic energy that they possess. On this phenomenon, the following new aspects are to be taken into account.

As stated before, absorption of energy by an electron is, structurally, impossible. The orbital electron, already in circulating motion, possesses kinetic energy due to the velocity field of the atomic vortex. This energy is computed: The nuclear radius of an average atom is, r n = 2.37 x 10-9 cm. Like an electron, the nucleus too has its axis of rotation and, hence, the maximum electrostatic field is confined in a circular vortex in a plane (more or less), at right angles to the axis of rotation. In the irrotational vortex, space-circulation velocity falls inversely as the radius of rotation. In the electron vortex, in the diametrical plane transverse to the axis of rotation, c re = constant. Applying this relationship also on the nuclear surface, c r e = u n rn

(10)

where un is the maximum tangential velocity of space on the nuclear surface in the diametrical plane at right angles to the axis of rotation. Substituting in (10) the known values of c, re, and rn = 2.37 x 10-9 cm, we have un = (3x1010) 4x10-11 / 2.37x10-9 = 5x108 cm/s.

(11)

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This velocity, as stated above, falls in the atomic vortex (around the nucleus) inversely as the radius of space rotation. Assuming the radius of rotation of the outermost orbital electron to be 10-8cm, the space circulation-speed, which is also the tangential-velocity of the orbital electron, will be v = un (2.37x10-9cm) / 10-8cm =(5x108cm/s) 2.37x10-1 =1.2x108cm/s.

(12)

The kinetic energy of the orbital electron is E kin = (1/2) me v2 = (1/2) 10-27 (1.2x108) 2 = 7.2X10-12 erg.

(13)

The experiments show that the kinetic energy of the photoelectrons is about 8x10 -12 ergs, which is so very close to the value obtained above (13). It is thus seen that Einstein mistook the source of the kinetic energy of the photoelectron, thinking that it came from the incident light; whereas, the reality is that the velocity field in the atomic vortex projects the electron after the incident light has triggered its release, as explained below.

Production of light due to oscillation of an atom has been mentioned before (Fig.10). We shall analyze here the displacement of an atom during its oscillation, and the radial flow of the surrounding space. An atomic nucleus, composed of independent electronic voids, closely packed, approximates to a "spherical hole" in space, central with the atom. The atom, during displacement equal to its diameter, leaves a "hole" in its previous location. This "hole" is filled due to radial flow of space at speed c, through the light's first wavelength λ, which gets formed. The time taken for this flow across the wavelength is λ/c; and the acceleration of space is c / (λ/c), which is c2/ λ. Each successive wavelength, formed due to the oscillations of the atom, possesses the above inward acceleration-field across it (radial). Now suppose that the spherical wave front of one of these shells, during its transmission, meets an orbital electron of an atom. The orbital velocity v of this electron, is derived from the atomic vortex which subjects it to an inward acceleration v 2 / r, where r is the radius of its rotation. The electron is held by electrical force, created by the above inward acceleration towards the nuclear center. The acceleration field c 2/λ, within the wavelength of the light shell that meets the orbital electron of the atom, is also inward, that is, towards the light source. For the electron to be released from the atomic vortex, the above two acceleration fields must be equal and opposite. Thus, c 2 / λ = v2 / r Or

λ = c2 r / v2.

(14) (15)

Substituting the values: v = 1.2 x 10 8 cm/s obtained above (12); r = 10-8 cm; c = 3x1010 cm, the value of λ comes to, 6.25x10-4 cm, which corresponds to the cutoff frequency of, 3 x 10 10 / 6.25x10-4, that is, 0.48 x 1014 cycles/s. (For metallic sodium, the threshold frequency is about 5x1014 sec-1). Considering the approximate nature of the assumptions on the orbital radius of electron, and the radius of an average size of nucleus, with which the space-circulation velocity around the nucleus and the orbital velocity of the electron were calculated; any better result from (15) to conform to the experimentally obtained value of threshold frequency is unlikely. For, the orbital radius of the electron, if supposed to be 10 -9cm, rather than 10-8cm, the thresh hold frequency calculated from (15) will be closer to the experimental value.

The additional information given by (15) is as follows. In atomic vortex, the velocity field falls inversely from the nucleus center; and therefore, the inner orbital electrons will have higher speed of rotation. On release by the incident light shell, these electrons will possess higher kinetic energy. It is seen from (15) that for higher value of the electron's speed v, the wavelength λ is smaller. It is thus concluded that with higher frequency of the incident light,

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the photoelectrons released will show higher kinetic energy. This is an experimentally observed fact.

The above analysis shows that the concept of the photon-nature of light, with an indivisible quanta of energy possessed by each photon, is a case of the most serious misconception, which led Einstein (who was a believer in the emptiness of space, as evident from the formulation of special theory of relativity) to wrongly treat light-energy, hf, as the instantaneous value (when in reality, this energy is produced and accumulated in unit time); because this way, the kinetic energy of the photoelectrons, as observed experimentally, could be explained without going deeper into the structure of the atom (that became known later about 1912 through Rutherford's experiments) to determine whether the photoelectrons have any other source in the atomic structure that imparts kinetic energy to them at the time of their ejection from the atoms.

Though, Planck integrated together the energy of f nos. of shells erroneously, he still believed that light energy is distributed uniformly over an expanding set of wave fronts. In contrast, Einstein conceptualized that the energy of light is not distributed evenly over the whole wave front, as the classical picture demanded; rather it is concentrated or localized in discrete small regions. With the help of both these energy integration and concentration operations, the right order of magnitude of the kinetic energy of the photoelectrons, as observed experimentally, could be achieved at an instant in the quantity hf .

For better understanding of the physical significance of the "indivisible quanta", we take the following example: Consider the case of a light source producing successive spherical wave pulses or spherical shells of light with frequency f, say 10 15/s and wavelength 3x10-5cm. In one second, the energy produced by f nos. of shells will be hf, that is 6.62x10 -27 erg s x 1015/s = 6.62x10-12erg. Now, if it is desired to make the energy "hf" indivisible, then the independent shells produced successively in one second become indistinguishable, and the new imaginary wavelength of this light will become: 位f = (3x10-5) cm x 1015 = 3x1010cm; while the frequency will be one, that is, only one wavelength of this large width of 3x10 10cm will be produced in one second. The quantum physics will accept the energy of this new shell of light as calculated above, but not the new wavelength and frequency. It will accept the energy content of this new shell of light for explaining the photoelectric effect; and will reject the wavelength and frequency because the hidden inconsistencies in the photon model will come to the fore.

Without any physical picture, clarity and meaningful explanations, some of these ambiguous conceptions on the fundamental nature of light laid foundation to quantum physics.

Shortest Wavelength of Light As is known, in positronium, the electron and positron circle each other, till annihilation; this happens due to interaction of their vortices. At the final instant preceding annihilation, the rotation of the particles will reach the limiting speed c, because this is the speed that space has on the interfaces of the particles. In (15) the value of v will be equal to c. Also the distance between the centers of the particles being 2re, the value of r in (15) will be 2re. Substituting these values in (15), the shortest possible wavelength of light is 位s = c2 (2re) / c2 = 2 re = 2 (4 x 10-11 cm)= 8 x 10-11 cm.

(16)

The shortest wavelength of light in the universe is produced consequent to the annihilation of electron and positron.

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Interaction of X-rays with Atoms High-speed electrons, projected inside a vacuum tube and stopped by its walls produce Xrays. Here, each electron on impact and almost instantaneous-rebound leaves a "spherical hole" of the size of electron-void at the point of its contact with the wall, to be filled in with the space flowing nearly at speed c. This process is somewhat similar to the light produced during annihilation because, here too, the potentials in space associated with the electron at the instant of impact, die away, producing (which is seen as) X-rays. From each point of electron's contact with the wall, a spherical shell of light expanding at speed c will arise.

Though the energy distribution on the wave front of the shell will fall inversely as the square of the radius of the expanding shell; yet, this shell after transmitting for some distance and with depleted energy-density on its wave front, on meeting an atom of a metal, releases an electron possessing kinetic energy almost equal to the kinetic energy of the first electron that produced the X-ray pulse. Indeed, the principle of energy conservation cannot explain this phenomenon because the same is not relevant here. Recognizing that light has the nature of successive shells, and in each shell, across the wavelength, exists an "acceleration field" of constant magnitude independent of the energy density in the wave front; the release of the electron, as discussed earlier in the case of the photoelectric effect, is attributable to this acceleration field, rather than to the energy density in the X-ray's wave front. If however, the explanation is sought with the idea of energy exchange between the X-ray and the ejected electron, this effect is most puzzling. In the words of Sir William Bragg: 'It is as if one dropped a plank into the sea from a height of 100 feet, and found that the spreading ripple was able, after traveling 1000 miles and becoming infinitesimal in comparison with the original amount, to act upon a wooden ship in such a way that a plank of that ship flew out of its place to a height of 100 feet.' Yet this effect was not utilized to support the wave nature of light. It was argued that the X-rays when passed through a gas, ionize only few molecules, and had the rays had the wave-property many more molecules should be ionized since the wave will meet all the molecules. This argument does not hold good with the shell nature of light; because, the acceleration-field in the X-ray shell has to be in opposition to the acceleration field of the orbital electron, that is, both the opposing acceleration fields must be in line for effective nullification of the electron's bond in the atomic vortex; which requires that the orbital electron, at the instant when it meets the light-shell (wave front), should be moving tangential to it. Obviously, such a disposition of the light shell and the electron can be only in rare encounters and, hence, the numbers of the ionized molecules with one shell of light are expected to be limited. Thus it is seen that wave nature (or more precisely shell nature) of light can explain the ionization of gases by the X-rays satisfactorily.

Bohr's Theory of Atomic Radiation As per classical electromagnetism, electric charges in acceleration will radiate energy, and hence the orbital electrons in the atom will lose energy due to which the emitted radiation should continuously change. However, the existence of sharp spectrum lines, are not in accord with the above prediction of the classical theory. As a solution to this problem, Bohr postulated different 'energy states' for an atom, such that when it falls from a higher to the lower energy state, it emits a photon with energy hf as per Planck's energy equation.

As discussed before, in the space vortex structure of the atom and electron, the orbital electrons have already their fixed orbits. These electrons, carried by the vortex around the nucleus, can neither lose any energy (structural, potential or kinetic) due to orbital motion, nor change their orbits due to strong bond created by the velocity fields in between the nucleus and the electrons; because 'losing energy' by an electron signifies 'losing part of its vortex structure'. Further, these electrons make negligible contribution to the gravitational potential

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of the atom that, as seen before, produces light due to its time variation [2,3]. Moreover, the basic error of Bohr lies in the application of the concept of Planck's indivisible energy quanta hf, in equating the same with the differential energy between the two energy states, composed of the sum of the kinetic energy of the orbital electron and the electrical potential energy of the proton-electron system; this is because, as mentioned before, the energy 'hf' is the quantity produced in a unit time, whereas, the energy released due to difference between two energy states of Bohr (even if the energy states are supposed to exist) is instantaneous.

The Compton Effect Compton's experiments are said to confirm that photon is a concentrated bundle of energy.

The experiment consisted of a beam of X-rays of known wavelength falling on graphite block. He measured the intensity of the scattered X-rays with respect to their wavelength. His conclusion is that the X-rays are not waves but several photons each with energy, "h f". A photon, in his experiment, collides with a "free" electron in the graphite block, like the collision of billiard balls. He treats in his mathematical analysis the "free electron" as the one, which is not bound with the atom of the graphite block, and is at rest. The collision of photon, assumed with a free electron, has the following implication.

As is well known, X-rays can damage molecules and ionize gases; and like in photoelectric effect, will extract electrons bound in atoms. In the latter case, even if the outermost orbital electron is released, its own kinetic energy in the atomic vortex, as discussed before, will be about 10-11erg. By assuming the collision of the X-ray with a "stationary" electron, the initial kinetic energy of the electron prior to its release from the atom has been neglected. In any case, one cannot assume that the X-ray interacts only with a "free and motionless" electron.

This kinetic energy of about 10-11erg will be larger for the inner orbital electrons, which rotate at greater speed. For, an inner orbital electron, with an average speed of three times the speed of the outermost electron, will increase the above kinetic energy to about 10 -10erg. The quantity of energy, accounted in Compton's experiment against the kinetic energy of the recoil electron, is about the same order of magnitude; the concept behind is that the electron's recoil energy comes from the energy of the incident X-ray photon. If an X-ray of frequency 10 17 is used during the experiment, its energy as per Planck energy equation will be; hf = 6.6x10 -27x 1017 = 6.62x 10-10erg, which is not far from the above figure of the kinetic energy of the ejected electron that it would have had in the vortex of the atom due to its rotation prior to the release. On account of neglecting the initial kinetic energy of the released electron, and matching this figure with the indivisible energy quanta, Compton's conclusions on the photon nature of X-rays become erroneous. The misinterpretation of Compton experiment - that Xrays is not of wave but photon-nature - led to a misleading picture of photon, both qualitatively and quantitatively.

Another misconception in the above experiment is to believe that a bullet-like photon after striking an electron rebounds with a reduced frequency. Evidently Compton believed that a single photon has a frequency; that it oscillates, perhaps, across its line of motion. As stated earlier, frequency for light would be meaningful only if it is defined as the numbers of waves, photons or shells, produced per unit time. But, in case of a single photon, its wavelength is not known in a physical way except for the mathematical expression c / f, which leads to an imaginary large wavelength of 3 x1010cm, and a single frequency, described earlier.

Compton's interpretation of his experiment together with the basic concept of relativity that all kinds of energy should have mass, made photon to possess hypothetical mass, momentum and inertia, while the most fundamental cause for its observed uniform motion at the constant speed of light remained unknown.

From the relevant literature, it is seen that Compton's arguments to assign momentum to a photon run as follows: As per the classical wave theory of light, if a body fully absorbs the energy E from a parallel beam of light, then a linear momentum E/c is transferred to the body.

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Based on this Compton, using Planck Energy equation E= h f, derives momentum, p, for an individual photon p = E / c = h f / c = h / 位.

(17)

But the "radiation pressure" on a body is otherwise explainable by the interaction of light shell with the gravity field of atom without absorption of light energy [4]. The classical physics is equally wrong in the concept of absorption and emission of light energy. Further, the use of Planck Energy equation makes a single photon to possess enormous energy, that is, 10 16 times the actual energy, if we use light of frequency 10 16/s, because in reality, the energy of a single shell of light is, 6.62x10-27erg, as determined by Planck Constant.

It is seen that the concept of "energy quanta" misguided Compton too (after Einstein and Bohr) in the interpretation of his experimental results.

Constancy of the Speed of Light in Special Theory of Relativity Einstein postulated that different observers, moving at uniform velocities relative to each other and to a source of light, should find their measurements of the speed of light to be the same, provided they use a defined reflection procedure. Let us suppose that light consists of several particles of energy (energy-as conventionally interpreted today, such that there is little difference at quantum level between matter and energy) say, electrons with properties of mass and momentum, being projected from a light source at random in all directions so as to form a uniform spherical distribution. The observers can choose any one of these particles for the test. A particular observer, moving in the same direction as his chosen particle, will find its speed different from the measurement of the other observer who is moving against the motion of the particle, as per classical relativity. Similarly, if light is imagined as a swarm of photons, each with mass, momentum and kinetic energy (as believed to day), being emitted from the source at random without any constant interval between the two successive photons from the same atom, the Galilean relativity will indeed be applicable, similar to the above-cited example of the shower of electrons; and the two observers will measure different velocity for the same photon. But, as shown before, the structure of light is that of successive shells of mass-less energy with a constant time-interval between the fronts of the adjoining shells emitted from each atom, as determined by the atom's vibration. It's the time-interval of emission between the successive shells that determines the frequency of light; whereas, in the earlier example of the photon-model of light, the frequency of light is a mere mathematical quantity, E/h, having no relationship with the timings of emission of the two successive photons from the same atom. It is this haziness on the physical picture of the frequency and wavelength of a photon that leads to misinterpretations of the results of several experiments devised to check the above postulate of special relativity. The following simple analysis, almost trivial, supports constancy of light-speed measurements by different observers in relative uniform motion postulated by Einstein.

In Fig.12 a source of light S (stationary with respect to space) from which a single spherical shell of light, produced consequent to the annihilation of an electron and a positron located in S, is transmitted at a constant speed c relative to the medium of space.

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When the wave front of this shell meets the eye of an observer O, who is also stationary relative to the static space, let him record this instant assuming that his time is the same as that of any other observer (universal time) who may even be in motion relative to space. Let him also record the instant when the tail end of the shell passes away from him. If λ is the radial width of this light-shell (wave length of this shell of light is r e, equal to the electron radius), then, from the ratio of λ and the time difference between the above two instants, say t 1, the observer can calculate the speed of light from the relation c = λ (1/ t1) = λ / t1

(18)

because, light-effect is postulated to be transmitted within the wavelength at constant speed c relative to the stationary space. Let S produce similar shells in succession such that the tail end of a shell coincides with the front of the following shell. If the nos. of shells received by O in unit time is f, he will calculate the distance covered by f nos. of shells in unit time as fλ, and time duration as ft1. With the ratio of these two quantities he will get the value of c, same as before. It is seen that the measurement of the light velocity across one wavelength is the same as across any of the successive wavelengths, provided the successive shells are similar with no interruptions in between. Now let O move with a uniform velocity v relative to the static space towards S, and record his timings across one shell. Because his velocity relative to the light shell now is v + c, time elapsed across one shell will be

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t2 = λ / (c + v)

(19)

which is shorter than t1 measured earlier. The moving observer's eye interacts with the lighteffect within the approaching shell for a shorter duration now and, hence, he sees the wavelength as: λm = length through which the light effect is transmitted in time t2 = c t2 = c λ/ (c + v).

(20)

The nos. of shells meeting the eye of the observer in unit time from (19) will be fm = 1 / t2 = 1 / [λ / (c + v)] = (c + v) / λ.

(21) The moving observer can now determine the light speed from (20) and (21) as: Speed of light = λm fm = [c λ / (c + v)] (c + v) / λ = c.

(22)

From (18) and (22) it is seen that the observer, in moving as well as stationary states, finds that the speed of light is constant; and he reaches this conclusion without sacrificing the traditional concept of time.

In the well-known experiment of Sagnac, a beam of light is split into two halves that travel around closed identical paths (reflected through mirrors) in opposite directions, and combined again in a detector to examine their interference pattern. The rotation of the apparatus produces shift in interference fringes as a function of the angular velocity. From (20) and (21) the reflecting mirrors along one path, rotating opposite to the light beam, will 'see' shorter wavelength and, proportionately, more of light-shells in unit time (frequency); while the mirrors rotating in the same direction as the light beam in the other path, will see longer wavelength and lesser nos. of the light-shells in the same time interval. On account of this, the wavelength as well as the frequency of the two beams reaching the detector will be different and, consequently, a shift in the interference fringes will occur. The product of the wavelength and the corresponding frequency for each path of the beam remaining the same, the mirrors placed in the two paths (observers) will find the same value of the velocity of light. Therefore, on rotation of the apparatus, appearance of the shift in the interference fringes in Sagnac's experiment should not be taken to mean that the light has different speeds (relative to space) along the two paths.

The above interpretation of Sagnac experiment can be confirmed by increasing the nos. of the reflecting mirrors in each path; in which case the shift in the interference pattern should increase.

The effect of light at a space point involves creation of light shell there from the already existing gravitational potential at that point, and its further transmission. This process repeats continuously as the light shell traverses each point in space. In the various experiments, set up to determine the light speed, only transmission aspect of light is taken into account, neglecting the process of the formation of the wavelength-the radial spread of light. That is why a "ray" of light, supposed to be continuously issuing forth from the source, is erroneously supposed to have instantaneous reflection from a mirror, and also instantaneous interaction with the eye of the observer; as if the wavelength is zero. Due to this misconception, it does not become apparent that a moving mirror reflects light of wavelength different from what it receives; and a moving observer too sees light of wavelength different from what he sees the same light to be, when stationary relative to space.

Considering Einstein's treatment of special relativity, in the moving frame of reference (with respect to the stationary one) the reflecting mirror for the light signal located at the X- axis,

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should also be moving at uniform velocity like the observer; the ray of light (replaced by annihilation light source, sending out light-shells one after the other) from the origin of the axes towards the +X axis in this frame of reference will be reflected by the moving mirror at an increased wavelength and decreased frequency, as shown above; and the observer, because of his motion opposite to the reflected ray, will find the wavelength of this light decreased and the frequency increased proportionately. In the stationary frame of reference, the stationary observer receives the reflected ray of the same wavelength as that of the ongoing ray. Thus, the observers in both the reference frames find the reflected ray having the same wavelength. Since their time is the same as the universal time, the nos. of shells per unit time, that is the frequency of the light ray, will be equal for both of them; hence, they get the same velocity of light irrespective of the motion of the moving observer.

Fresenel, around 1820, postulated ether-drag in a moving material medium and increase in light velocity on account of this. His ether-drag is close to the velocity-field that gets associated with the moving molecules of matter-responsible for momentum [2,3].

Transmission of light along the motion of the medium will increase the wavelength, whereas, it's opposite direction will decrease it. As the respective frequencies also will proportionality change, the velocity of light in both the directions of light will remain the same. This subtle aspect, that despite changes in wavelengths the speed of light will be the same, had not been taken note of. Fizeau's experiment to measure speed of light in flowing water detected changes in speed because he based his conclusion on fringe-shift that will occur when unequal wavelengths are superposed.

In the assumed void-ness in space of 20 th century physics, which provides no explanation to the creation of matter and fields, speed of light too has no medium, either for its creation or for transmission; in fact in a medium of nothing ness, matter and light cannot exist. Therefore, if the velocity of light measured by different observers in uniform relative motion with respect to each other has to be the same as postulated in special theory of relativity, the spatial-reality and shell-nature of light require recognition. With this proposed conceptual shift on the basic nature of the absolute vacuum and the nature of light, the relativistic concepts involving changes in length and time dependent on the motion of the observers will become redundant.

Light speed is Independent of the Motion of the Source Consider an electron with its vortex structure. At any point in space, the velocity field and its radial distance from the vortex center will determine the magnitudes of its gravitational and electrostatic potentials [1,2.3]. As discussed earlier, a displacement of the electron's center will produce changes in the potentials; such changes will occur during electron's motion, either uniform are accelerating. The equalization of potentials due to self-action of space takes place at speed c with respect to space. Therefore, considering motion of electron at ordinary velocity, it can be assumed that the field structure of electron retains its original symmetry of distribution as before in static state.

Let an electron and a positron, moving together at ordinary speed, under go annihilation.

After collapse of the electron-void during annihilation, it loses mass, charge, and its existence; but, since the entire field distribution can not die instantly, the light shell produced continues its transmission relative to space with the point of annihilation as its center, independent of the speed of the particles prior to the instant of their annihilation. The point of annihilation and the surrounding field structure get fixed relative to space subsequent to the annihilation.

On similar arguments it will be seen that light produced during atomic vibration is transmitted at speed c relative to space due to self-action of space to equalize the potential gradients.

Further, since light shells are mass less entities, not emitted from within the electron or atom in the light source, they cannot carry the momentum of the source (light-producing particles, atoms and electrons in the constitution of the moving source of light).

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Time Dilation The traditional concept of time was revised in special relativity. Though it has been shown above that with the shell-nature of light, the postulate of relativity on invariance of the speed of light in different frames of reference is supported, the following thought experiment reveals the fallacy of the often-quoted arguments5 in support of time dilation.

Fig.13 shows a platform in uniform motion with two observers A and B on it, and another stationary observer C on the ground.

The relativist's view is that 'if the observer A lights a match-stick creating a flash, the observer B sitting opposite to him will think that the flash has directly come to him along the route PQ, whereas, the observer C will see the path along PQ 1, since, during the time the flash has reached him, the platform has reached to a new location P1 Q1 R1 S1. The path of the flash does not look the same to the two observers B and C. Since the flash is moving with A, it seems to B taking a longer path; and if the speed of light is to remain the same, the longer path must seem to take longer time: time must pass faster for C'. The misconception on the nature of light in the above statement is the presupposition that "the flash is moving with A".

But is the flash really moving with the observer A? It has been shown above that the speed of light is independent of the motion of the source. Hence, the uniform motion of A cannot be imparted to the flash of light that he creates by striking a match. To further pinpoint the relativistic misconception on the motion of the flash along with A, let us suppose that A has with him an electron and a positron that undergo at some instant annihilation. As explained in the earlier section, the point of annihilation along with the field structure of the particles will

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get fixed in space, while the observers A and B will move on. Supposing, B can see the point of annihilation P even prior to the instant when the light shell consequent to annihilation reaches him, he will see that P is shifting to his left due to his own motion (relative to space) to the right along with the platform; and by the time B reaches Q1, he will see that the light shell has taken the route PQ1 to reach him; PQ1 is the same length as seen by C. Therefore, the assumption of the relativist that the flash of light is moving with A is erroneous. Further, if the stationary observer C stands at D, where PQ1 = PD, the light shell will reach both B and C at the same instant.

It has been shown that the new concepts of 'time dilation' and 'simultaneity' are clearly superfluous in special theory of relativity, since, the invariance of the speed of light in different frames of reference in relative uniform motion follows otherwise from its very basic nature.

Conclusion The ether was declared superfluous in special relativity without identifying and providing a substitute for a universal entity, which could create cosmic energy and matter. And in the absence of a basic theory of matter that alone can reveal the genesis of material properties (mass, inertia, charge), and the associated energy-fields including electromagnetic, any generalization that the laws of nature are invariant in respect of all inertial systems will certainly lead to a highly complex theorization, just as special relativity has come to be. But, despite that, discarding photon model of light, and with a nonmaterial fluid space, Einstein's Light-Principle-that the velocity of light is invariant in respect of all inertial system, is vindicated with the shell-nature of light, which light in reality is.

Notes *

Former Executive Director (Nuclear Projects), Nuclear Power Corporation, India.

1

It has been shown that Planck constant is not a universal constant; and, theoretically, each atom has a Planck constant with slight difference in magnitude. Electron too has a Planck constant.

2

Creation of electrons and positrons take place in the interiors of the stars and the galactic center, where space circulations reach the limiting speed.

3

The word "pressure" is used in material fluid; for fluid-space another appropriate word is to be coined.

4

The Feynman Lectures on physics, Feynman,Leighton, Sands; Vol. 1, page 10-9.

5

"The Clock Paradox", Dr. J. Bronowski, Scientific American, February 1963, Vol. 208, No.2. pp.

134-144.

References 1. P. Tewari, (1982), "Space is the Absolute Reality", Proceedings of ICSTA, International Publishers, East-West , Niederschocklstr, 62, 8044 Graz, Austria.

2. P. Tewari, (1995), Beyond Matter - A Comprehensive Theory of the Material Universe, Editor: Wolfram Bahmann, Feyermuhler Str, 12, D-53894 Mechernich.

3. P. Tewari, (1984, 1996), Beyond Matter, Crest Publishing House, G-2, Ansari Road, Darya Ganj, New Delhi - 110 002.

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4. P.Tewari, (2000), "Conceptual Error on the Fundamental Nature of Light-Phenomenon in classical electrodynamics, led to the Complexities in Quantum Physics", Journal of New Energy, Vol.5, No. 1.3084 E.3300 South, Salt Lake City, Utah 84109-2154.

----Paramahamsa Tewari was born on January 6, 1937, and graduated in Electrical Engineering in 1958 from Banaras Engineering College, India, and held responsible positions in large engineering construction organizations, mostly in Nuclear Projects of the Department of Atomic Energy, India. He was also deputed abroad for a year at Douglas Point Nuclear Project, Canada. He retired in 1997 from his position as Executive Nuclear Director, Nuclear Power Corporation, Department of Atomic Energy, India, and is the former Project Director of the Kaiga Atomic Power Project. Fundamentals of physics attracted Tewari's imaginations right from the early school and college days. Over the last two decades his new ideas on the basic nature of space, energy, and matter have concretized into definite shape from which a new theory (Space Vortex Theory) has emerged. The theory reveals the most basic issue of relationship between space and matter precisely pinpointing that space is a more fundamental entity than matter. The physical significance of mass, inertia, gravitation, charge and light are revealed by extending the analysis in the theory beyond material properties and into the substratum of space, which again is broken down into fieldless voids, thus showing the limit to which a physical theory can possibly reach. The real universe is shown to be opposite to the current concepts of concrete-matter and empty space. The books that he has authored on Space Vortex Theory are: The Substantial Space and Void Nature of Elementary Material Particles (1977); Space Vortices of Energy and Matter (1978); The Origin of Electron's Mass, Charge Gravitational and Electromagnetic Fields from "Empty Space" (1982); Beyond Matter (1984). He has lectured as invited speaker in international conferences in Germany, USA, and Italy on the newly discovered phenomenon of Space Power Generation. For the practical demonstration of generation of electrical power from the medium of space, Tewari has built Space Power Generators that operate at over-unity efficiency, thereby showing that space medium indeed is the source of generation of basic forms of energy. http://www.tewari.org/ ptewari1@sancharnet.in [See even the presentation of Dr. Tewari's book which is published in the first Section of this same number of Episteme]

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On the Space-Vortex Structure of Cosmic Bodies (Paramahamsa Tewari, B. Sc. Engg.)

1. As per the recent recorded data on the solar wind close to the surface of the sun, the wind velocity varied from a minimum of about 380 km/s to the maximum of about 500 km/s, giving an average of 440 km/s [ http://soho.nascom.nasa.gov/ ; 48 hours of solar wind data on 10 July 2002]. While the sun rotates axially at a peripheral speed of about 2 km/s at the equator in the plane at right angles to its axis, the reason for so high a wind velocity is briefly explained with the principles of space vortex theory.

RenĂŠ Descartes, the great French philosopher and mathematician, in his Vortex Theory, postulated around the middle of the 17th century that the solar system is a large vortex of ether (space) that he defined to be a "property less" fluid. And in this vortex, the planets were carried along their orbits with no relative motion between them and the surrounding ether.

"He firmly denied that the earth moved (relative to the neighboring space medium), and asserted that it was carried along with its water and air in one of those larger motions of the celestial ether which produce the diurnal and annual revolutions of the solar system" [Pioneers of Science; Sir Oliver Lodge; Dover Publications, INC.]. His above concept was powerful enough to protect him against any possible persecution by the church which, unlike Galileo, did not occur. That Descartes was right in his principles is clear from the fact that in addition to the explanation and derivation of the most basic phenomenon of surface gravity of the sun and the planets, the genesis of the solar wind close to the sun's surface can also be computed with the principles of Space Vortex Theory (SVT) which has postulates very similar to the Cartesian Philosophy.

In my paper "On Planetary Motion caused by Solar Space Vortex" [Journal of New Energy, Vol. 3, No. 2/3, August 1998], Kepler's third law was derived, showing that the orbital speed of a planet is inversely proportional to the square root of the distance from the sun's center. If v is the orbital velocity of a planet whose orbit is at a distance r from the sun v = k / (r)1/2

(1)

where k is a constant of the solar space vortex.

Substituting the known value of the orbital speed of the planet Mercury (it can be any other planet also) and its distance from the sun in (1), k is determined. Now, using this value of k, and substituting in (1) the sun's radius for r, it is calculated in the paper referred above that: v = 436.7 km / s. This shows that in the near hood of the sun's surface, its gaseous matter will be subjected to a maximum average velocity of 436.7 km / s, due to fluid-space circulation around the sun in the solar space vortex. The above computed value is so very close to the recorded data (440 km / s) mentioned above.

The existence of the solar space vortex and the reality of the space-circulation gets proved (in the earlier paper) by deriving the surface gravity of the sun as: g s = v2 / Rs, where v is the space velocity calculated above, Rs is the radius of the sun and gs is its surface gravity. The value of 274 m / s2 obtained through the above calculations is exactly the same as accepted to day.

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It is most unlikely that through any other contemporary physical theories so accurate quantitative results and physical explanations revealing the genesis of the solar wind can be had.

2. The Space Vortex Theory deals with the fundamental structural relationship between the universal matter and the space of the universe.

Postulating the medium of space as a nonmaterial fluid, with a limiting flow and rotation when in vortex motion, it is shown that the universal matter cannot exist, or be created, in the absence of a dynamically real (energetic) space, as the only source of primordial energy. A circulating fluid-space creates energy and matter as its own vortices. The following are some essential aspects of this theory.

- The most fundamental state of energy is an accelerating volume of the fluid-space.

- The electron is identified as the only fundamental particle of matter - an irrotational vortex of space with a limiting speed (speed of light relative to the absolute vacuum) of rotation.

- The property of "mass" (introduced in the Newton's laws of motion) of electron is shown to be due to a discontinuity in the energy distribution (field-less-void) in its vortex-structure at the center, rather than due to some kind of densification and continuous distribution of energy at the electron's center, as generally supposed currently. The property of inertia exhibited by matter follows from an "inward acceleration field" from the circulating-space acting towards the electron-center due to the existence of the central void in its structure.

- The most fundamental field is "velocity field" defined as the velocity of a fluid-space-point, when space is in linear or circulating motion. The "charge" and "mass" of electron are shown proportional to the limiting value of this velocity field. The direction of spin in the electron's space-vortex determines the nature of electric charge; positive are negative.

- A "gravitational potential" in space is created with the breakdown of the fluid-space in the electron's vortex-structure during its creation. Thermal radiation (light) from a vibrating atom is caused in space by a time-varying gravitational potential of the atom-only remotely connected with the orbital electrons in the atom as believed today.

- All the universal constants, presently known, have been derived with a single universal constant (speed of light) and the electron radius.

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- Surface gravity of the Earth, the Sun and the other planets, has been theoretically derived with a hitherto unknown formula in celestial mechanics.

- A new electrical repulsive force operating between the Sun and the planets that maintains stability of the planets in the solar system has been found. The orbital radii of the planets have been accurately determined with a new equation that uses this electrical repulsive force.

- The constancy of speed of light as measured by different observers in relative motion is supported (special relativity), while time dilation is concluded to be superfluous.

- A serious misconception on the basic nature of light and, consequently, inappropriate use of Planck constant in photoelectric effect and atomic structure, are shown to be the cause that led to the present complexity and incomprehensibility of the quantum physics.

- An unambiguous proof of the operation of the electrical forces of repulsion and attraction among cosmic bodies has been provided recently with the observation of the colliding galaxies; It was predicted that if two galaxies are drawing closer and closer, then this would be due to an electrical attractive force, and for that to exist, the galaxies in question must have opposite directions of their spin.

- A decisive proof of generation of output electrical power more than the input has been achieved in a new system of power generation, thus showing a clear cut violation of the Lenz's law (law of conservation of energy).

If indeed this pair of galaxies are drawing closer, then their spin directions will be opposite; the attractive force will be electrical (in addition to gravity).

It would be of interest to know precisely the spin directions, as this will prove the existence of electrical forces too between cosmic bodies.

3. This last comment is concerning the recent press news from NASA on the picture of colliding galaxies (NGC 4676) sent back by the Hubble Space Telescope's new camera.

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You can see above a picture enlarged from the NASA website (from http://antwrp.gsfc.nasa.gov/apod/ap990722.html). They are spinning in opposite directions in support of the predictions contained in my article "On Planetary Motion caused by Solar Space Vortex" [Journal of New Energy, Vol.3, No.2/3, Summer/Fall,1998].

[See http://antwrp.gsfc.nasa.gov/apod/colliding_galaxies.html for more pictures.]

It was brought out in this article that the planets and the sun, due to their axial spin, will possess electrical charge, and will therefore be subjected to electrical repulsive forces between them. The stability of the planets in the solar system was analyzed taking this new electrical repulsive force into consideration.It was also generalized that all cosmic bodies, includig galaxies, possessing axial spin will have electrical charge. Cosmic bodies with similar direction of spin will repel; whereas, with opposite directions of their spin, will attract electrically. The formula for the quantitative determination of the electrical forces was also given in the article.

It thus follows that the force of attraction between the pair of galaxies reported by NASA, if these are drawing closer and closer, is an electrical attractive force, and the galaxies must necessarily have opposite directions of their spin.

It is added that the modern celestial mechanics takes no account of the electrical forces between the cosmic bodies.

It would be of interest to know if the spins of these galaxies are indeed opposite; that will prove the existence of the new electrical force discussed in my above article.

----[A presentation of the author can be found at the end of his previously published paper]

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Louis T. More: Prophet of the 20th Century (Theo Theocharis) Strange Rapprochment "Belatedly ... a strange rapprochement is under way between the forces of religion and science." (Peter Stanford, "Science meets God half way", The Sunday Times News Review, p.

3.9, 27 October 1996.)

As I have been pointing out since 1977, and as I shall show below, this rapprochement is a debut-de-siècle [beginning-of-century] matter, not a fin-de-siècle [end-of-century] affair. <<The Chief Rabbi [of the UK] Dr Jonathan Sacks [has said]: "I don't think there would have been a single social observer in the year 1900 who would have predicted that religion and religions would be as strong in the world today and, indeed, even in the liberal West, as they are.">> (John Tusa, "They said God was dead - why won't he lie down?", Church Times (UK), 8 November 1996, pp. 12-13.)

Prophet But at least one "social observer", Louis Trenchard More, who of course had to be knowledgeable in all the subjects that matter, came very close to making this prediction not much later than 1900 - specifically in 1912. The understanding shown in 1912 by L. T. More, ("The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370-371, 1912) is so deep, the insight so visionary, and the prescience so profound, that the following relevant passage deserves to be quoted in full: <<Both Einstein's theory of Relativity and Planck's theory of the Quanta are proclaimed somewhat noisily to be the greatest revolutions in scientific method since the time of Newton.

That they are revolutionary there can be no doubt, in so far as they substitute mathematical symbols as the basis of science and deny that any concrete experience underlies these symbols, thus replacing an objective by a subjective universe. The question remains whether this change is a step forward or backward, into light or into obscurity. It is held, and apparently rightly, that the revolution effected by Galileo and Newton was to replace the metaphysical methods of the schoolman by the experimental methods of the scientist. Now the new methods might seem to be just the reversal of that step, so that, if there is any revolution in thought, it is in reality a return to the scholastic methods of the Middle Ages.>> (Louis Trenchard More, "The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370371, 1912.)

Mysterianism In his regular column "Hard drive" in the London Daily Telegraph weekly supplement Connected, Peter Cochrane is described thus: "Peter Cochrane holds the Collier Chair for the Public Understanding of Science and Technology at the University of Bristol." In the opening paragraph of his "Bricks in an unreal city" (Hard drive, 10 February 2000), Peter Cochrane wrote with evident admiration: <<Richard Feynman was ... a founding father of our most

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fundamental atomic understanding. One of my favourite Feynman key pronouncements is the shrewd: 'I think we can safely assume that no one understands quantum mechanics.'>> In fact Richard Feynman was the best known living scientist in the world from the 1960s until he died in the 1980s. Moreover, the curious "no one understands quantum mechanics" viewpoint articulated in the very last year of the 20th century by a Professor for the Public Understanding of Science and Technology at a leading University has been the standard viewpoint of establishment science and philosophy throughout the 20th century. I recognised the stark and gross inconsistency pointed out here from the very beginning of my scientific studies in the 1970s when I also devised my standard rebuttal: "A theory that no one understands is not scientific but hopelessly mystic." (Theo Theocharis "Men of [Surreal] Ideas", The Listener, 4 May 1978.)

Science Re-Enslaved by Religion "The 17th century is better remembered as the time that science liberated itself from theology." (Malcolm Povey, "In need of perspective", Financial Times, 20 June 1994, p. 26.)

Prediction: The 20th century will be better remembered as the time that science re-enslaved itself to theology.

----[A presentation of the author can be found in Episteme N. 4] theotheocharis@ic4life.net

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Ultimate Creative Ignorance (Theo Theocharis) I supply here independent support to the important argument involved in the title of Foster Lindley's (tfl0@msn.com) "Creative Ignorance" (Human and Ecological Risk Assessment, Vol. 7, No. 6, pp. 1593-1601, November 2001). It is useful to quote these passages that explicate the label "Creative Ignorance": "The probabilist converts cognitive uncertainty into physical uncertainty. â&#x20AC;Ś As the probabilist presents his failure to differentiate as a discovery about the nature of reality, it is a creative use of ignorance."

It is not only the probabilist who "converts cognitive uncertainty into physical uncertainty".

Every professor of physics everywhere does the same, and more (ie worse). The so-called Heisenberg's Uncertainty Principle was devised (in the 1920s) in order to codify a certain measumental inaccuracy. It was converted right away into physical uncertainty. Not much later, it was converted again - this time into some new convoluted combination of physical/cognitive certainty/uncertainty: the physicist knows (with certainty?) that the physical entities featuring in Heisenberg's inequality really fluctuate, but (at least for the time being) within the restricted bounds permitted by Heisenberg's inequality.

This last conversion is best debunked as follows: Creation of the Universe: According to current cosmological thinking, a(n already existing) quantum of energy (obeying the again already existing law of Heisenberg's Uncertainty Principle) transformed itself into matter which somehow inflated itself to the presently known Universe. One is bound to ask: Which proposition is more believable?: (i) The Universe was created by an all-mighty God; (ii) The Universe was created by a tiny quantum fluctuation.

On careful reflection, the latter does not give sufficient credit to Heisenberg, so it must be rephrased thus: (ii)' The Universe was created (some 15 billion years before Heisenberg's birth) by an uncertainty in Heisenberg's knowledge.

There have been debates in physics and philosophy forums as to whether the act of observing creates the observed entity, but is there one professor of physics anywhere who has ever repudiated these other (now seventy year old) moronic abuses of elementary Aristotelian logic?

----[A presentation of the author can be found in Episteme N. 4] theotheocharis@ic4life.net

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What the Global Positioning System Tells Us about the Twin's Paradox (Tom Van Flandern) Abstract. In the GPS, all atomic clocks in all reference frames (in orbit and on the ground) are set once and stay synchronized. We can use this same trick to place a GPS-type clock aboard the spacecraft of a traveling twin. That clock will stay synchronized with Earth clocks, allowing a clear resolution of the twin's paradox in special relativity - why the traveler expects to come back younger, and why the stay-at-home twin is not entitled to the same expectation.

Background In a previous article [1], I described how the Global Positioning System (GPS) is a marvelous laboratory for testing relativity because the orbiting and ground atomic clocks have differing gravitational potentials and high relative speeds. Their precision is such that the predicted relativistic clock corrections are confirmed to within a fraction of a percent. However, initial expectations based on special relativity were that clocks in different reference frames should have different readings and rates. Yet the Global Positioning System is designed in such a way that, after the individual clock rates are adjusted once pre-launch for the predicted relativity effects, all satellite clocks in all orbits remain in synchronization with one another and with all ground clocks without need for further consideration of relativity corrections, with the exception of one small correction needed for the slight non-circularity of the orbits.

The previous article concluded with a discussion of what this means for Einstein's special relativity (SR), and for the competing Lorentzian relativity (LR) theory. The comparison favors LR as the simpler theory describing the relativity of motion.

As history buffs may know, the Lorentz Ether Theory (LET) [ 2] appeared a year before Einstein's 1905 publication of SR. Of course, LET incorporated both the relativity principle (taken from Poincare, but it was first formulated about a generation earlier) and the Lorentz transformations that bear his name. The essential new element introduced by Einstein the following year was the equivalence of all inertial frames, thereby eliminating the need for the luminiferous ether. This first postulate of SR makes the Lorentz transformations reciprocal; i.e., they work equally well from any inertial frame to any other, then back again; so it has no meaning to ask which of two identical clocks in different frames is ticking slower in any absolute sense. The second postulate of SR makes the speed of light independent of not only the speed of the source (which is also true generally for waves in any medium, including luminiferous ether), but also independent of the speed of the observer (which is a feature unique to SR).

Today, many physicists and students of physics have acquired the impression that these two postulates have been confirmed by observations. However, that is not the case. In fact, none of the eleven independent experiments verifying some aspect of SR [1] is able to verify either postulate. It is now widely believed that no experiment is capable of verifying these postulates even in principle [3], because they become automatically true by convention if one adopts the Einstein clock-synchronization method, and they become just as automatically false if one adopts a different synchronization convention such as the "universal time" postulate of Lorentz. Of interest here is the point that the GPS uses the latter synchronization convention for pragmatic reasons, as I will shortly explain.

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So is the difference between SR and LET then purely cosmetic? No, it is not cosmetic at all. It is true that both SR and LET explain all existing electromagnetic-based experiments and, in that sense, would remain viable theories of the relativity of motion. But the difference between them is much more than aesthetic. In addition to a great difference in practicality for use in systems such as the GPS (in favor of LET), the two theories differ about whether or not material bodies can exceed the speed of light in forward time. In SR, that is proved impossible because time ceases to advance for any entity traveling at the speed of light. By contrast, in LR, no speed limit for material bodies exists. It is true that speed relative to the preferred frame causes electromagnetic-type clocks (which include all ordinary mechanical, biological, and atomic clocks) to slow, meter sticks to contract, and the momentum of bodies to be increased by the relativistic factor Îł = 1 1 â&#x2C6;&#x2019; v 2 c 2 just as in SR. But in LR, time, space, and the matter content themselves are not affected. (Here, v is the speed of the body and c is the speed of light.) So the question of which theory better represents nature is of major importance to the future of physics, which is presently invested in the belief that speeds faster than light in forward time are not possible.

Today, our concepts of the "luminiferous ether" are considerably different than they were in Lorentz's day. It is now widely recognized that the local gravity field serves as the "preferred frame" of LET. With this alteration from Lorentz's original concept but without any change in the math or structure of the theory, LET has now become known simply as "Lorentzian relativity" (LR). Although LR has no intrinsic speed limit, it recognizes the innate difficulty of material bodies composed in part of electrons, while propagating in luminiferous ether, being able to exceed the wave speed of that ether, the speed of light. LR treats this as analogous to a propeller-driven aircraft exceeding the speed of sound without any outside assists, such as from gravity. A force that cannot itself propagate faster than light cannot propel material bodies faster than light.

Of critical importance to choosing the model that best represents nature, none of the eleven independent experiments testing SR verify frame reciprocity or distinguish SR from LR. In fact, historically, de Sitter, Sagnac, Michelson, and Ives concluded from their respective experiments that SR was falsified in favor of the Lorentz theory. 1 Indeed, the GPS itself is a practical realization of Lorentz's "universal time", wherein all clocks remain synchronized despite being in many different frames with high relative speeds. However, subsequent re-interpretation of SR allowed that theory to survive these objections.

This "magic" is envisioned to happen by virtue of each clock in the system being synchronized to an imaginary clock in the Earth-centered inertial (ECI) frame, instantaneously co-located with the moving clock, and assumed to be in a gravitational potential equal to that at sea level at Earth's poles. (Note the "coincidence" that the magic makes use of the Lorentzian preferred frame, the local gravity field.) This trick makes the clock rates all the same as they would have been if they were at rest in the ECI frame and in a constant potential field. This is all very nice, but hardly what Einstein envisioned when speaking of two clocks in relative motion, one at a station and one on a passing train. How simple special relativity would have become all these years if physicists had realized that all they had to do was reset the clock rates so they all ticked at the same rate as the reference clock in the local gravity field!

The converse is also true. Suppose we did not change the clock rates before launch, but instead let them tick at their design rates in accord with whatever speed and potential they experienced in orbit. Now, suppose we tried to Einstein-synchronize the system of clocks.

Satellite and ground clocks would tick at different rates. And if we tried to work in any local,

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instantaneously co-moving inertial frame, the corrections needed to synchronize with each orbiting clock would be unique to that observer's frame and different from moment to moment because both clocks are accelerating. The practical difficulties of operating the system would be virtually insurmountable. What we would gain by doing that is constancy of the measured speed of light in all inertial frames. But because all clocks are now re-synchronized to just the ECI frame in the GPS, the speed of light is constant in that one frame, and the invariance of the speed of light in other inertial frames is of no practical value.

In a recent article, Ashby [4] claimed that the clock-epoch correction term (also called "time slippage" term) in the Lorentz transformations, vX c 2 (see Eq. below), can be dropped even when its value is large, but he is very vague about why. However, this particular term is the only difference of consequence between Einstein synchronization of clocks in different inertial frames and Lorentz synchronization of clocks to an underlying "universal time". And the GPS system has been designed to use Lorentz synchronization, for which one frame, the local gravity field or ECI, is special; not Einstein synchronization, wherein clocks tick at their natural rates and all inertial frames are equivalent. By itself, this does not prove LR "right" or SR "wrong". But the practical difficulties for GPS of not changing the natural rates of clocks pre-launch, or with the use of SR for any frame but the Lorentzian preferred frame, are very great. If a ring of satellites (A, B, C, …, Y, Z) circled the Earth in a common orbit, and each satellite tried to Einstein synchronize with the next in sequence, then when Z tried to complete the circuit by Einstein-synchronizing with A, the corrections required would lead to time readings for A different from the starting readings, making closure impossible.

Introducing the twins The "twin's paradox" is an illustration of the complexity of SR's interpretations of nature.

Suppose two identical twins start out at some common instant. One remains on Earth. The other (the "traveler") is on a spacecraft headed for Alpha Centauri (AC) four light-years away at 99% of the speed of light, for which speed the time dilation factor is γ ≈ 7 . (We choose a large value of γ so that the effects of the relativity of motion will be large and obvious, not subtle.) Upon arrival at AC, the traveler turns back to Earth at the same speed (or is replaced by a traveler already headed toward Earth of identical biological age at the moment they pass, to avoid need for an acceleration). The round trip requires slightly over 8 years Earth time; let's say 98 months to be specific. This is path 1 in Figure 1. When the twins are reunited, the Earth-bound twin is 98 months old, and the traveler is 14 months old (a factor of 7 less).

Figure 2.

The traveling twin's journey to Alpha Centauri (AC) begins at Earth (E).

Upon arrival, the traveler can return to Earth by any path (1), continue on to Beta Centauri (2), or circle Alpha Centauri (3).

That much is a clear prediction of SR. Note especially that no accelerations need actually occur at the beginning or end of the journey, nor even in the middle if we do the "twin replacement" trick. That is consistent with cyclotron experiments showing that

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accelerations as such, even as great as 1019 g (where g is the acceleration of gravity at sea level), have no effect on clocks [5]. At each stage of the journey where an event occurs, comparisons can be made without ambiguity between adjacent points, one in each of the inertial frames containing the clocks or twins to be compared. Despite the fact that many textbooks discussing the twin's paradox treat accelerations as essential, that is illusory.

Accelerations are unbounded in size, and in principle can be done in an instant, allowing no local time to elapse in any relevant frame. Accelerations (as distinct from velocities) and forces (as distinct from potentials) do not change local clocks, clock rates, or biological aging.

Now we come to the paradox part: Why isn't the traveler entitled to claim that the spacecraft remained at rest and the Earth traveled away at 99% of the speed of light, then turned around and came back? From that perspective, the original traveler would argue that the Earth-bound twin should be the younger one. We will examine the rather different answers to that question offered by SR and by LR. The traveler takes along a GPS clock Let's more closely follow what is happening to our two twins. Imagine that the inertial frame of reference containing Earth and AC is filled everywhere with synchronized clocks at rest, so that any traveler can always look out a window and read what time Earth-frame people think it is. See Figure 2. And let the traveler take a "GPS clock" along on his journey, along with an unadjusted "normal" clock. The GPS clock is preset in rate before the journey so that, once placed aboard the spacecraft, it will remain synchronized in epoch and rate with clocks on Earth, just as real GPS clocks do. Then the on-board GPS clock will always give readings identical to the nearest Earth-frame clock visible outside the spacecraft window. This instant ability to compare traveler's time in his own frame with time everywhere in the Earth-AC frame will prevent paradoxes from arising.

Figure 2.

From the Earth-frame, all stationary clocks are synchronized, and all clocks moving with the spacecraft are not. From the spacecraft, the situation is reciprocal. However, the on-board GPS clock always agrees with the Earth-frame clock immediately outside the spacecraft window. Š

Now let's examine the journey details. When the traveler's journey begins, the onboard native clock ticks slower than the GPS clock by a factor of seven. But isn't that already an asymmetry present at a stage where there is simply a relative motion, and no way to decide which twin should be aging slower? LR answers simply "yes" because the frame of the local gravity field is the preferred frame in which clocks tick fastest, and time in all other relatively

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moving frames passes more slowly. But SR offers the opposite answer. And understanding that answer is the key to understanding SR. SR is a mathematical theory built around the Lorentz transformations. Let the time T be the reading on a clock fixed in the Earth frame; and let X be the relative location in the Earth frame of a clock fixed in the spacecraft frame moving at speed v relative to the Earth frame. Let t be the time reading on the natural clock in the traveling spacecraft, and x be the relative location of Earth in the spacecraft's frame. In that frame, Earth passes the spacecraft with a speed − v . As before, the Lorentz time dilation/length contraction parameter is γ , having a value of 7 when v = 0.99c . So in general, the relation between the Earth-frame clock and the spacecraft-frame clock is: t = γ ( T − vX c 2 ) x = γ ( X − vT )

Because the relationships are reciprocal (all inertial frames are equivalent in SR), the inverse relations (with v → − v ) must also hold: T = γ ( t − vx c 2 )

X = γ ( x − vt )

Now let's compare time in the two frames. First, let an observer at a clock fixed on Earth watch time on the spacecraft clock. Then the observer is looking at a point X = vT .

Substituting that into eq. , we get the unsurprising result that x = 0 , meaning that the spacecraft clock remains fixed at the origin of its own coordinate system. And from the time transformation, using the definition of γ , we get t = T γ , which restates the well-known prediction of SR we cited above that the spacecraft clock will appear to the Earth observer to be ticking γ = 7 times slower than the Earth-fixed clock.

That much is routine. But before we leave the Earth frame, let's do one more calculation. Suppose the spacecraft frame is likewise filled with clocks everywhere, Einsteinsynchronized with each other. Because all such clocks are at rest relative to one another, they can simply exchange light signals and assume that the light takes equal time for the uplink and downlink portions of its round trip. Then the average of the transmission and reception times on one clock must agree with the signal reflection time on the other clock by definition of "Einstein synchronization". Now, from the Earth frame, let's peer into the spacecraft frame at the point X = 0 , the fixed location of the Earth observer. From Eq. , we now have t = γ T .

The meaning of this relation is that the Earth observer sees a succession of spacecraft-frame clocks parading by, and time on the succession of clocks goes by γ = 7 times faster than Earth time.

You read that right. According to SR, at the same time that each and every clock in the spacecraft frame is seen by the Earth frame to tick γ = 7 times slower, time in the spacecraft frame on a succession of passing clocks is passing by γ = 7 times faster than Earth time. To repeat this essential point, in any inertial frame with a relative motion, all individual clocks tick slower but overall frame time moves forward at a faster rate. Such is the effect of the vX c 2 term in the transformation. The time difference between clocks in different frames is a function of the different rates they tick at and of the "time slippage" effect, whereby time is a function of location in any relatively moving frame. In SR, this would remain true even if we used the GPS trick and eliminated the rate differences between clocks. In general, the time slippage effect dominates the effect of a changed clock rate for any clock in a frame with

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relative motion. (N.B. Time is everywhere the same when viewed from within an inertial frame. But it is everywhere different in that same frame from the perspective of any other frame with a relative motion because of time slippage.)

It is worth studying the points in the preceding two paragraphs because, while mathematically permissible, they defy our intuitions and are what makes relativity such an unintuitive theory.

The traveler looks back at the Earth twin Now let's switch to the spacecraft frame and look back at the Earth-frame clock at x = vt using Eq. . Then we get X = 0 and T = t γ . So the spacecraft clock sees the Earth clock ticking γ = 7 times slower than itself. Substituting x = 0 , we get T = γ t : the spacecraft twin sees Earth-frame clocks streaming by outside his window with time elapsing on a succession of them at γ = 7 time faster. So both effects, relative clock rates and frame time from time slippage, are reciprocal and symmetric between the two frames.

And that is SR's answer to the symmetry challenge we posed at the outset of the spacecraft's journey. Both LR and SR predict that the spacecraft's clocks will appear to tick slower than all Earth-frame clocks as viewed by Earth-frame observers. But SR (only) predicts that the situation looks reciprocal and symmetric for observers in the spacecraft frame looking at clocks in the Earth frame. The traveler is therefore not surprised by the behavior of the GPS clock on board, which correctly records a combination slower clock rate plus a fast time slippage for the Earth frame, and stays in agreement with the Earth-frame clocks passing by just outside the spacecraft window.

Now consider the traveler's arrival at AC, when the spacecraft turns around or is replaced by a spacecraft heading Earthward at the same speed. Neither the natural clock nor the on-board GPS clock changes rate or reading significantly during the turn-around.

However, before the turn-around, the Earth-frame clocks say four years (actually, 49 months) of Earth time have elapsed since the journey began, and the spacecraft natural clock says seven months of spacecraft time have elapsed. But the spacecraft infers that only a single month has elapsed back on Earth because a single clock in another frame is affected only by clock slowing, not time slippage; whereas the spacecraft agrees that 49 total months have elapsed at AC because the journey began with a 48-month time slippage for AC and added one more month during the journey. As usual, time slippage corrections (where applicable) dominate clock readings in other frames.

We now come to the crux of the resolution of the paradox, which seems paradoxical only in SR. The traveler has inferred that only one month has elapsed back on Earth since his journey began, so by spacecraft-frame reckoning, Earth time is just one month later than the actual departure time. For example, if the journey commenced in 2000 January, when the traveler arrives at AC, the on-board GPS clock reads 2004 February; but the traveler infers that Earth clocks still read 2000 February. Because of the finite speed of light, the traveler can see Earth only as it was, not as it is now, and therefore cannot check this inference by direct observation. According to SR, all these clock-reading inferences are not just illusions, but reflect the real, physical time for each frame involved. So at the same time and place that an AC resident infers that Earth time is 2004 February, the spacecraft traveler infers it is 2000 February - a four-year difference; and both are correct for their respective frames.

Then the spacecraft turns around. Nothing changes locally. But inferences about remote time change greatly because of time slippage, which now has the opposite sign. Now

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the traveler infers that Earth time is 2008 February - four years into the future instead of the past. As a consequence, the traveler will again infer that only one month of Earth time will elapse during the return journey, and all participants agree that Earth time upon the traveler's return will be 2008 March. The traveler arrives back younger (14 months old) than the stayat-home twin (98 months - over 8 years old). According to LR, this is because the traveler had a high speed relative to the preferred frame, the local gravity field; and there never was any symmetry between the two frames. But according to SR, the elapsed time is a combination of slowed aging and time slippage effects, the latter changing discontinuously when the direction of the traveler changes.2 The Earth twin thinks the traveler should naturally age slower because his clocks run slower. And the traveler thinks the Earth twin should naturally age faster because the time slippage effect dominated the slowed aging effect when that twin turned around. Note that the traveler could have taken any path whatever as long as the spacecraft speed relative to the Earth frame remained 0.99 c . Then at every instant along the journey, the traveler's biological age will be a factor Îł = 7 less than the elapsed time on the on-board GPS clock, which will agree with the Earth clocks upon return.

Indeed, the spacecraft could have simply continued in a straight line past AC and on to Beta Centauri (BC), say (for purposes of this example only), 8 light-years from Earth. Then there was no turn-around event, but the traveler is still just 14 months old on arrival, and twins born on BC at the same time the Earth twin was born (according to Earth-frame clocks) will still be 98 months old. And the traveler will infer that the BC twins started out 96 months old at the journey's beginning, and aged just two months during the journey. So clearly, neither the turn-around event nor any acceleration is essential to the result; and the SR resolution of the paradox retains its symmetry and the equivalence of all frames.

Hence, from the traveler's perspective, wherever the spacecraft goes in any direction without changing speed relative to the Earth frame, it will encounter Earth frame clocks with more elapsed time than on the natural clock aboard the spacecraft (but with the same elapsed time as for the on-board GPS clock). But the traveler will infer that all clocks in the Earth frame are always ticking slower than the natural spacecraft clock, and beings in the Earth frame are always aging more slowly than the traveler. Everything encountered can be explained by a combination of clock rate changes and time slippage. The traveler cannot infer that the Earth-bound twin will be the younger one upon the spacecraft's return because Earth experienced a time slippage event (whether sudden or gradual), rapidly aging everyone on Earth during the traveler's journey. That time slippage event is no different in character than the one that a hypothetical twin on Beta Centauri would experience if the traveler continued on past AC without a turn-around event.

The traveler takes different paths What we have just described are careful and correct inferences of SR as applied to the twin's paradox. This also shows the essentially mathematical nature of the theory, because it does violence to what we fondly call "common sense". The most important point to note carefully is that the theory is internally consistent, and no mathematical contradictions can be found no matter how the transformation equations are manipulated, or how many frames or twins are introduced. The next important point to note is that SR makes demands on our credulity that LR does not. Let's examine why.

At the point of turn-around on the original journey from Earth to AC, the traveler's inferences about time on Earth changed suddenly. Instead of the physically unrealistic instant

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turn-around, let's assume the spacecraft "orbits" around AC to perform the turn-around. (To stay at a safe distance from the star at the same speed, this would require propulsion, not just gravity.) This can still take a time short enough to be neglected, especially at such a high relative speed. So the traveler's spacecraft changes from headed away from Earth and inferring the Earth year is 2000, to traveling toward Earth and inferring the Earth year is 2008.

Again, SR says this is real, physical time, and not an illusion.

So before commencing a journey back to Earth, let's suppose the traveler orbits AC several times. Then each time the traveler heads away from Earth in that orbit, Earth time drops back to 2000; and each time the traveler heads toward Earth, inferred Earth time becomes 2008. The Earth-year is intermediate for intermediate orbital positions. Now the significance of repeating this situation several times is that, as Earth time goes to 2008, many people will have died and others will be born. And on each occasion that Earth time reverts to 2000, some of the dead will be resurrected and some living young children in 2008 will cease to exist in 2000. Note that while all this is happening according to SR, the on-board GPS clock representing LR's "universal time" continues to insist that Earth time is the same as spacecraft time and AC time: 2004 everywhere. In SR, effects of this type are never observable because they "lie outside the observer's light cone", hidden from direct view by the finite speed of light. Nonetheless, SR insists that such changes affect real, physical time and are not mere illusions, because the viewpoint of each inertial frame is just as valid as that from any other frame.

Conclusions In LR, one reference frame (the local gravity field) is preferred; and speed cannot affect time, but only the rate of ticking of mechanical, electromagnetic, or biological clocks. However, just as we do not assume that time has been affected when the temperature rises and causes a pendulum clock to slow down, LR says that changes in clock rates are changes in the rates of physical processes, and do not affect space or time. So by carrying an on-board GPS clock on the spacecraft, we are offered a clear choice between models: Earth time can be what SR infers it is, or it can be what the GPS clock says it is. In the former case, SR works, but leads to heavy-duty complexities and fantastic inferences about the nature of time at remote locations. Moreover, the proof that nothing can travel faster than light in forward time stands intact. In the latter case, LR works with great simplicity and in full accord with our intuitions about the universality of the instant "now". And the speed of light is no longer a universal speed limit because time itself is never affected either by motion or by gravity.

Aside from these practical difficulties with the use of SR in the GPS, Einstein's special relativity is also under challenge in a more serious way from the "speed of gravity" issue, because the proven existence of anything propagating faster than light in forward time (as all experiments indicate is the case for gravity) would falsify SR outright [ 6, 7]. So it is entirely possible that reality is Lorentzian, not Einsteinian, with respect to the relativity of motion. In that case, physics may have no speed limit when the driving forces are gravitational or electrodynamic rather than electromagnetic in nature. And that may be the most important thing that the GPS has helped us to appreciate.

Notes [1] T. Van Flandern, "What the Global Positioning System tells us about relativity", in Open Questions in Relativistic Physics, F. Selleri, ed., Apeiron, Montreal, 81-90 (1998). Also available online at <http://metaresearch.org>, "cosmology" tab, "gravity" sub-tab.

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[2] H.A. Lorentz, Lectures on Theoretical Physics, Vol. III, "The principle of relativity for uniform translations", Macmillan & Co., London, 208-211 (1931). Contains summary of and citation to original 1904 paper.

[3] H. Erlichson, "The rod contraction-clock retardation ether theory and the special theory of relativity", AJP 41, 1068-1077 (1973).

[4] N. Ashby, "Relativity and the Global Positioning System", Phys.Today May, 41-47 (2002).

[5] Bailey, J., Borer, K., Combley, F., et al., "Measurements of relativistic time dilation for positive and negative muons in a circular orbit", Nature 268, 301-305 (1997).

[6] T. Van Flandern, "The speed of gravity - What the experiments say", Phys.Lett. A 250, 1-11 (1998).

[7] T. Van Flandern and J.P. Vigier, "Experimental repeal of the speed limit for gravitational, electrodynamic, and quantum field interactions", Found.Phys. 32(#7), 1031-1068 (2002).

1

De Sitter argued that the forward displacement of starlight (aberration) depended on absolute, not relative, speeds because both components of a double star, each with some unique velocity, had the same aberration. Sagnac argued that the fringe shifts expected but not seen in the Michelson-Morley experiment are seen if the experiment is done on a rotating platform. Michelson argued in the 1925 Michelson-Gale experiment that the Earth was just such a rotating platform. Ives argued that ions radiated at frequencies determined by absolute, not relative, motion because they had to pick a specific frequency to radiate at. In each case, a complex-but-now-familiar SR explanation could account for the same observed results.

2

We note in passing that the effect that SR expects accelerations or frame changes to have on remote clocks would constitute an instantaneous action at a distance, a violation of the causality principle.

Acknowledgments The author thanks the Meta Research Board and members for financial support, with a special thanks to Tim Seward. The artwork in Figure 2 is Copyright (2002) by Boris Starosta, <http://starosta.com>.

----Tom Van Flandern received his Ph.D. degree in Astronomy, specializing in celestial mechanics, from Yale University in 1969. He spent 20 years at the U.S. Naval Observatory, where he became the Chief of the Celestial Mechanics Branch. In 1991, Tom formed a Washington, DC-based organization, Meta Research, to foster research into ideas not otherwise supported solely because they conflict with mainstream theories in Astronomy. Tom is editor of the Meta Research Bulletin, which specializes in reporting anomalies and evidence that does not fit with standard theories in the field. During the past few years, he has also been a Research Associate at the University of Maryland Physics Department in College Park, MD, and a consultant to the Army Research Laboratory in Adelphi, MD, working on improving the accuracy of the Global Positioning System (GPS). North Atlantic Books is the publisher of Tom's 1993 book, Dark Matter, Missing Planets and New Comets. A second edition was published in 1999. As with his research papers, the book is critical of many

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standard models in astronomy, such as the Oort Cloud, the Dirty Snowball, and the Big Bang theory. Tom also organizes the Eclipse Edge Expeditions to optimal solar eclipse viewing sites. During his career as a professional research astronomer, Tom has been honored by a prize from the Gravity Research Foundation; served on the Council of American Astronomical Society's Division on Dynamical Astronomy; taught astronomy at the University of South Florida and to Navy Department employees; been a consultant to NASA's Jet Propulsion Lab; and done several spots for the "Project Universe" series that continues to air occasionally on public TV. Meta Research <tomvf@metaresearch.org> http://metaresearch.org/

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REPRINTS

257

Sulle attrazioni newtoniane di origine idrodinamica (Emilio Almansi) 1. In un liquido omogeneo, indefinito (praticamente abbastanza esteso in tutte le direzioni), si abbia un numero qualunque di corpi C , C' , C'' , ... , i quali subiscano rapide variazioni di forma, od anche solo di posizione, tali che il fenomeno presenti, nel suo insieme, un periodo θ piccolissimo.

Quando siano verificate certe condizioni che accenno più avanti, avviene che, per ogni corpo, la forza risultante delle pressioni che il liquido esercita sugli elementi della sua superficie ha, in un intervallo di tempo multiplo di θ , un valor medio corrispondente all'attrazione che su quel corpo eserciterebbero gli altri, se i corpi del sistema possedessero certe masse m , m' , m'', le quali si attraessero secondo la legge di Newton.

Questo interessante fenomeno, ed altri analoghi, furono per la prima volta studiati, in casi particolari, sia dal lato matematico, sia sperimentalmente, dal prof. C.A. Bjerknes.

L'argomento è stato poi ripreso, ed ampiamente svolto in un suo corso di lezioni, dal figlio prof. V. Bjerknes(1).

I procedimenti analitici da me seguiti in altra Nota(2), permettono di arrivare al risultato nel modo più semplice e generale.

2. Supporremo che nel movimento indotto nel liquido la velocità sia ovunque continua, derivi da un potenziale ϕ , e si annulli all' infinito; che i pesi delle particelle liquide siano trascurabili; che la densità sia uguale ad 1 .

Denotiamo con (F) la forza che al tempo t agisce sopra un corpo C del sistema. Essa può decomporsi (Nota preced.) in due forze (F0) ed (F) . Le proiezioni X0 , Y0 , Z0 sopra gli assi coordinati della forza (F0) sono derivate esatte rispetto al tempo di funzioni periodiche col periodo θ : onde il valore medio (in un intervallo multiplo di θ ) della forza stessa - vale a dire la forza che ha per proiezioni i valori medii di X 0 , Y0 , Z0 - è nullo. Noi trascureremo questa forza (F0) .

Le proiezioni della forza (F) sono

X=

∫

σ

 1  ∂ϕ 2  ∂ϕ 2  ∂ϕ 2 ∂ϕ ∂ϕ ∂ϕ ∂ϕ     dσ  +  + +  +   α − ∂x ∂y ∂z ∂x  2  ∂ x   ∂z   ∂y  

,

ecc., rappresentando σ la superficie del corpo, ed α , β , γ i coseni della normale esterna(3).

Il potenziale di velocità ϕ presenta, in ogni istante, tutti i caratteri del potenziale newtoniano di masse µ , µ' , µ'' , ... distribuite negli spazi S , S' , S'' , ... occupati dai corpi.

Infinite distribuzioni dànno luogo, nello spazio esterno, allo stesso potenziale ϕ : noi supporremo di fissarne una. Verremo così a definire la funzione ϕ anche negli spaz! S , S', S'' , ... Supporremo che essa risulti, in ciascuno di questi spazi, finita e continua insieme alle sue derivate prime e seconde. Attraversando le superficie dei corpi, la funzione ϕ e le sue derivate prime non dovranno subire discontinuità. La densità ρ relativa a questa distribuzione di masse ideali sarà: ρ=

− 1  ∂ 2 ϕ ∂ 2ϕ ∂ 2 ϕ  + +   .

4π  ∂ x 2 ∂ y 2 ∂ z 2 

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Ciò posto, trasformiamo, nella espressione di X , l'integrale esteso a σ in un integrale esteso allo spazio S limitato da σ . Otterremo:  ∂ 2ϕ ∂ 2ϕ ∂ 2ϕ  ∂ ϕ + dS .

X = -∫ S  2 +  ∂ y2 ∂ z2  ∂ x  ∂x Poniamo X1 =

∂ϕ ∂ϕ ∂ϕ , Y1 = , Z1 = , ∂y ∂x ∂z

e teniamo conto della espressione di ρ . Avremo: X = 4π

∫

S

X 1 ρ dS

e, analogamente, Y = 4π

∫

S

Y1 ρ dS , Z = 4π

∫

S

Z 1 ρ dS .

Queste formule possiamo interpretarle dicendo che la forza (F) relativa al corpo C è, in ogni istante, quella stessa che si avrebbe se le masse ρdS si attraessero secondo la legge di Newton, e la costante dell'attrazione fosse uguale a 4π .

Parimente si potrebbe dimostrare che i momenti rispetto agli assi coordinati delle pressioni esercitate dal liquido sugli elementi di σ sono uguali ai momenti delle forze 4πX1ρdS , ecc.

3. Supponiamo, ora, che le mutue distanze fra i corpi C , C' , C'' , ... siano grandissime rispetto alle loro dimensioni lineari. Denoti P un punto fisso, che si trovi costantemente nello spazio S occupato da C . Così per gli altri corpi C' , C'' , ... , consideriamo i punti fissi P' , P'' , ...

Nelle formule precedenti noi possiamo ritenere che X1 , Y1 , Z1 siano le derivate del potenziale ϕ , dovuto alle sole masse esterne µ' , µ'' , ... (la resultante delle mutue azioni che si esercitano tra le masse elementari ρdS di uno stesso corpo essendo identicamente nulla).

Invece di X1 , Y1 , Z1 scriviamo X1 + δX1 , Y1 + δY1 , Z1 + δZ1 , intendendo ora che X1 , Y1 , Z1 siano le derivate, nel punto P , del potenziale ϕ , calcolato come se le masse µ' , µ'' , ... fossero concentrate nei punti P', P'' , ... Ponendo δX = 4π

∫

S

δ X 1 ρ dS , ecc.,

avremo: X = 4πX1µ + δX , ecc. Ammettiamo che la forza di componenti δX , δY , δZ sia trascurabile rispetto alla forza di componenti 4πX1µ , 4πY1µ , 4πZ1µ (ciò che potrà non avvenire; per es., se µ= 0). Potremo allora ritenere X = 4πX1µ , ecc. Onde, detta r la distanza costante PP' , e posto f = 4π

µµ ' r2

la forza (F) risu1terà, in ogni istante, dall'attrazione (f) dovuta al corpo C' , e delle altre analoghe dovute agli altri corpi.

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Le masse µ , µ' , ... si possono esprimere molto semplicemente mediante i volumi S , S' , ... dei corpi corrispondenti. Si ha infatti: −1 4π ∫

µ =

σ

∂ϕ dσ ∂n

.

∂ϕ è uguale alla componente, secondo la normale esterna, della velocità di un ∂n punto di σ , se diciamo ora dS l'incremento che subisce, nel tempo dt , il volume S , sarà E poichè

ds = dt

∫

σ

∂ϕ dσ ∂n

,

e, perciò, µ =

− 1 dS .

4π dt

Analogamente sarà µ' =

− 1 dS' . Onde, ponendo 4π dt

1 dS dS ' , 4π dt dt

q= avremo f =

q : r2

dalle quali formule vediamo che se in un certo istante i volumi S , S' sono ambedue crescenti od ambedue decrescenti, e quindi q > 0 , la forza (f) è realmente un'attrazione; altrimenti, è una ripulsione.

4. Il valor medio (F') della forza (F) , quindi ancora della forza (F) , in un intervallo multiplo di θ , o uguale a θ , sarà la risultante della forza (f') di grandezza f' =

q' , r2

ove q' è il valore medio di q , e delle analoghe relative agli altri corpi. Avremo dunque: θ

1 1 qdt = q' = ∫ θ 0 4π

θ

dS dS ' dt . dt dt θ 0

∫

Facciamo ora un'ipotesi più particolare intorno al modo di variare dei volumi S , S' , ecc.: supponiamo cioè che si abbia S = S0(1+hε) , ecc.,

260

ove S0 ed h rappresentano due quantità costanti per il corpo C , ε una funzione del tempo, periodica con periodo θ , uguale per tutti i corpi. Se poniamo m = hS0 , m' = hS' , sarà:

dS dε dS' dε = m , = m' . E, perciò, dt dt dt dt

θ

mm' dε 2 dt ( ) q' = ; 4π ∫0 dt θ quindi f' = k

mm' , r2

essendo 1 k = 4π

θ

dε

∫ ( dt ) 0

2

dt . θ

In questo caso, dunque, attribuito alla costante dell'attrazione il valore dato dall'ultima formula, si ha una perfetta analogia tra la forza (F') e le attrazioni newtoniane delle masse ideali (costanti) m , m' , ...

5. Nella formula S = S 0(1+hε) , noi possiamo sostituire ad ε una funzione lineare di ε , con che verranno solo a variare le costanti S 0 ed h . Potremo allora fare in modo che il massimo e il minimo valore della funzione periodica ε siano +1 e -1 . Diciamo S 1 ed S2 i valori corrispondenti di S (notando che, se la costante h è negativa, S 1 rappresenterà il valor minimo di S ). Si avrà S1 - S2 = 2hS0 = 2m ; quindi 1 (S1 - S2) .

2

m =

Le masse m vengono così ad essere le semi-differenze fra i valori estremi dei volumi dei corpi. t Quanto alla costante k , osserviamo che, se s'introduce la variabile τ = , si ha θ 1 dε dt dε dτ = , = , θ dt θ dτ k =

1

θ

2

1 4π

θ

dε

∫ ( dτ )

2

dτ .

0

Di qui vediamo che per una determinata funzione ε(τ) (per esempio, se t ε = sen 2πτ = sen 2π ) la costante dell'attrazione è inversamente proporzionale al θ quadrato del periodo.

261

(1) Fields of force, Columbia University Press. New-York, 1906. Vedasi anche la Memoria di W. Voigt, Beiträge zur Hydrodynamik, Gött. Nachr., a. 1891.

[NdR - A proposito della relazione tra i Bjerknes qui citati, e il C.J. Bjerknes autore sia di due articoli in questa sezione di Episteme, sia del libro presentato nell'apposita rubrica della I Parte, si veda appunto la detta recensione.]

(2) Sopra le azioni le quali si esercitano fra corpi che si muovono o si deformano entro una massa liquida, Rendiconti della R. Accad. dei Lincei, dicembre 1913. [Riporteremo tra breve qui di seguito il paragrafo introduttivo di questo lavoro.]

(3) Nella Nota preced. le X ed X 0 di questa Nota sono chiamate X1 ed X2 ; la quantità sotto il segno d'integrazione nella espressione di X ( X 1 ) è denotata con -H . La espressione di H è data a pag. 537.

-----Questo lavoro è stato pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1914, Vol. XXIII, 1° Sem., pp. 287-291. ***** Riteniamo al solito di fare cosa utile ai lettori offrendo loro il paragrafo introduttivo dell'articolo di cui alla precedente Nota 2, che apparve sempre sui Rendiconti della Reale Accademia dei Lincei, 1913, Vol. XXII, 2° Sem., pp. 533-544.

Meccanica. - Sopra le azioni le quali si esercitano fra corpi che si muovono o si deformano entro una massa liquida. Nota del Corrisp. E. ALMANSI. 1. È noto che due sfere immerse in una massa liquida sufficientemente estesa in tutte le direzioni, aventi i loro centri in due punti fissi dello spazio, e raggi periodicamente variabili intorno ad un valor medio, al quale si conservino sempre vicinissimi, esercitano una su l'altra un'azione attrattiva o repulsiva, secondochè le loro pulsazioni hanno la medesima fase, o fase opposta.

Parimente, se, restando costanti i raggi delle sfere, i centri si spostano sopra una retta, oscillando intorno a due punti fissi, le due sfere si attraggono o si respingono a seconda che i loro centri hanno, in ogni istante, velocità rivolte in senso contrario, o nello stesso senso.

La trattazione analitica dei problemi di questo tipo, pur supponendo, come io supporrò, irrotazionale il movimento del liquido, e trascurabili le forze di massa, incontra difficoltà le quali, fatta eccezione per un numero limitatissimo di casi (tra cui quelli accennati), sono da ritersi insormontabili.

Se però ci si contenta di determinare i caratteri generali del fenomeno, di stabilire, per esempio, se fra due corpi, in date condizioni di movimento, si esercitano azioni attrattive o repulsive, rinunziando alla loro valutazione quantitativa, si arriva con facilità, in tutti quei casi che più interessano, allo scopo prefisso. È appunto la trattazione del problema così ridotto quella che io qui mi propongo(1). [...]

(1) Sul problema delle sfere pulsanti o oscillanti, ved. W. Voigt, Beiträge zur Hydrodynamik, Gött. Nachr., a. 1891.

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Unforgettable, unforgivable, Stefan...

(Si veda anche la foto con cui si apre il Reprint di Omero Speri e Piero Zorzi nella I Parte di questo stesso numero/See also the photograph which appears in the Reprint by Omero Speri and Piero Zorzi in the first Part of this same number)

Marinov: Annus Horribilis (The Story of) A Payed Advertisement Published by Nature (Stefan Marinov) The year l996 will be an earthquake year for conventional physics: many formulas in the textbooks will be changed, many century-old dogmas will be renounced and many saints will be de-sainted. This radical change had to begin tens of years ago but the lack of glasnost in physics all over the world has delayed it and instead to have evolutional step-by-step reformations and several lighter earthquakes, now there will be a tremendous one. Vous l'avez voulu, Georges Dandins!

By my half-a-century experimental and theoretical work I showed the following (see references in my 16 books, 60 refereed papers, 8 paid advertisements and numerous papers and editor's comments in the journal DEUTSCHE PHYSIK edited by me): 1. The principle of relativity is wrong. Indeed, I rneasured three times optico-mechanically and once electromagnetically the Earth's absolute velocity. Its magnitude is 350 km sec -1 wlth equatorial coordinates of its apex δ = -20° , α = 12h (approx.).

2. The principle of equivalence is wrong. Indeed, my interferometric "coupled mirrors" experiment which was carried out during a year showed that when the laboratory's acceleration was kinematic (acceleration with respect to distant stars), the laboratory's velocity changed, while when it was dynamic (gravitational attraction by the Earth) there was no change.

3. The energy conservation law is wrong. My machines MAMIN COLIU and VENETIN COLIU which work with zero, or near to zero, Lenz effect, and SIBERIAN COLIU which

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works with anti-Lenz effect violated this law. Only because of lack of money I could not close the energetic cycle in the first two, but the third one was not expensive and I could run it as a perpetuum mobile. The day when I shall present this machine at a press-conference will be the start-day for the earthquake.

4. The Lorentz equation is wrong. If there are two electric charges q , q' moving with velocities v , v' and the vector-distance from q' to q is r , according to the Lorentz equation the force with which q'v' acts on qv is given by the following Grassmann formula fG = (µ0qq'/4πr3){(v.r)v' - (v.v')r}.

(1)

Numerous experiments done by other authors (Hering's experiments are from the beginning of the century!) and by me showed that the force acting on qv can be not only transverse to its velocity, as required by (1), but also longitudinal. Any rational man when seeing at least one falsifying experiment rejects the respective formula (Popper), however for thousands and thousands of Betonköpfe [heads made with ferro-concrete!] even hundred experiments were not enough. In the photograph [not included in the original] there is one such falsifying experiment which (as well as the other) can be carried out by children: A cylindrical magnet is cut along one of its axial planes and the one half is turned up-down (the magnetic forces themselves do the rotation). Around this magnet, there is à trough filled with mercury in which the copper ring which can be seen at right swims (the children take salt solution and suspend the ring on threads). After sending current of some tens of amperes from the battery at left, which is regulated by the rheostat, the ring begins to rotate. That's all!

5. The Lorentz-Marinov equation is the right one. As according to (1) f'G is not equal and oppositely directed to fG , I obtained Marinov formula by the most simple and natural symmetrization of (1) (take into account that r = -r') fM = (fG - f'G)/2 = (µ0qq'/8πr3){(v'.r)v + (v.r)v' - 2(v.v')r} .

(2)

Proceeding from (2), and assuming Φ ≠ 0 , ∂A/∂t ≠ 0 , I obtained by the most simple calculations that the force with which an electric system acts on a test charge q moving with velocity v is f/q = -gradΦ - ∂A/∂t + v×B + vS = Elor + v×B + vS ,

(3)

where Φ, A are the electric and magnetic potentials generated by the system at the point of the charges location, Blor = rotA is the Lorentz magnetic intensity, Swhit = -divA/2 is the Whittaker magnetic intensity and Bmar = -(µ0/8π) ∫

q'(v×v')(r.v)/v2r3 ,

Smar = -(µ0/8π) ∫

q'(v.v')(r.v)/v2r3 ,

(4)

are the Marinov vector and scalar magnetic intensities. B = Blor + Bmar is called vector magnetic intensity and S = Swhitt + Smar is called scalar magnetic intensity. (3) is called the Lorentz-Marinov equation. If neglecting the last term and under B we understand Blor we obtain the Lorentz equation which I call the Lorentz-Grassmann equation. That's the whole theory!

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6. The angular momentum conservation law is wrong. My Bul-Cub machine with interrupted current and rotating Ampere bridge with interrupted current rotated under the action of internal forces only. Marinov's formula allows violation of the angular momentum conservation law as the magnetic forces with which two charges interact are equal and oppositely directed but may not lie on the line connecting them.

7. It is impossible to violate the momentum conservation law in electromagnetism. Obvious conclusion from Marinov's formula.

8. Displacement current does not exist. For closed circuits both Grassmann and Marinov formulas do not allow violation of the momentum and angular momentum conservation laws as the first terms in (1) and (2) contain total differentials. As conventional physics believes in the displacement current of Maxwell, it accepts that all currents always are closed. I showed by numerous experiments that there is no displacement current (neither in vacuum nor in dielectrics) and one can interrupt the circuits by the help of condensers. At the age of 15 I understood that displacement current is a phantasmagoria and presented to my teacher in Sofia the following objection: "If the displacement current between the plates of a condenser acts with magnetic forces on other currents, then according to Newton's third law the other currents must act with magnetic forces on the displacement current and set it in motion. But how, comrade teacher, can vacuum be set in motion?" Teacher's answer was: "Shut up, child!"

9. The gauge transformations are illegitimate. According to conventional physics not the potentials but the intensities determine the motion of the test charge (exactly the opposite is true), and thus any change of the potentials which leaves the intensities the same is allowable, i.e. one can calibrate the potentials. It is easy to see that the calibration divA = 0 is allowable.

Thus conventional physics believes that a really existing force, the Whittaker force fw = -qvdivA/2 = qvSwhitt can be put equal to zero. Monstrosity! To see the action of fw take two metal spheres the one charged positively and the other negatively. Put around one of the spheres a circular wire along which current flows, so that it is perpendicular to the line connecting the spheres. When connecting the spheres by a wire and current begins to flow, the circular wire begins to rotate. The only force which acts on the circular wire is fw .

10. There is no propagation of interaction. As only mass can move from one point to another, "interaction" can be only a ghost. But a rational man does not believe in ghosts. on the other hand, the mathematical expressions of Bmar and Smar show that the "fields" cannot propagate in space with a certain velocity, as Bmar and Smar depend on the direction of motion of the test charge. To these people who may object that one is not sure whether the Lorentz-Marinov equation is the right one, my answer is: Until the day when some falsifying experiment should be presented (ths day will never come!) the world is impelled to accept it as true.

11. Potential, radiation and radiation reaction electric intensities. These three kinds of intensities can be obtained if putting in the expression for the Lorentz electric intensity Elor (see (3)) the observation electric and magnetic potentials Φ= q/4πε0r , A = µ0qv/4πr with r = r' - v'.r'/c , v = v' + u'r'/c,

(5)

where r , v , u are distance, velocity and acceleration at the observation moment t and r' , v' , u' at the advanced mornent t' = t - r/c (conventional physics wrongly calls t' "retarded moment"). Conventional physics, following Liénard and Wiechert, wrongly writes A with

265

v' . For this reason conventional physics obtains only the potential and radiation intensities, Epot , Erad , and artificially introduces the radiation reaction intensity Erea coming to phantasmagoric "self-accelerations". Proceeding from (5) I (and any child who can differentiate!) obtained also the radiation reaction intensity Erea = -µ0qw/6πc , where w = w' is the charge's super-acceleration. Erad = µ0qr'×{(r' - v'r'/c)×u'}/4π(r' - v'.r'/c) is due to moving mass (radiated energy), as charges moving with acceleration lose energy, while Erea acts on the radiating charge itself. To obtain all radiation effects one has simply to integrate the obtained formulas for a single charge. That's nearly all about radiation of electromagnetic waves!

12. There are no "fields". According to the "field-marshals" the "fields" exist physically. One can move them and a moving magnetic field produces electric field, etc. When I hear all these stupidities, I get diarrhea. After repeating the Rowland experiment (a magnetic needle near a charged disk deviates when the disk is set in rotation), I carried out the inverse one (the disk at rest, the needle rotates) and the co-moving one (disk and needle rotate), taking instead of a needle a Hall detector. According te the "field-marshals" the inverse experiment must give the same effect as the direct one (I observed no effect), while the co-moving experiment must give null result (I observed the same effect as the direct experiment). The inertial experiments can be done charging a conveyer belt.

13. Current conducting wires become charged positively. Conventional physics asserts that they remain neutral (Clausius postulate). Meanwhile always after measurements, the rheostat in the photograph [included in the original but not here, due to its poor quality] remained charged and touching it by hand there was a spark. The positive sign was established by the method known to ancient Greeks. Every child explains the effect taking into account that the positive electrode of the battery "sucks" electrons from the wire while the negative electrode "spits" electrons and the former effect is primary.

14. B-machines and S-machines. The electromagnetic machines working on B are called Bmachines and these ones working on S are called S-machines. By the help of the first three fingers of his right hand any child older than 15 can show when looking at the third term in (3) that the B-generators brake. Meanwhile by the help of only one finger any child younger than 15 can show when looking at the fourth term in (3) that the S-generators accelerate.

15. The perpetuum mobile SIBERIAN COLIU. Swhitt produced by the first term in (2) and for a complete circuit is null. For this reason can be observed only at interrupted circuits (see item 9). However Smar can be different from zero also for a complete circuit. Why then has nobody observed it? - Because all people have worked with cylindrical or quasi-cylindrical magnets for which Smar = 0 . Who has cut a cylindrical rnagnet in two pieces rotating the one half up-down? - NOBODY!!! The first man who has done this is called Gennadi Nicolaev and lives in Tomsk [... - Russian words follow]. For this reason I called this magnet the SIBERIAN COLIU magnet and the perpetuum mobile which I constructed with it is the SIBERIAN COLIU machine. The machine shown in the photograph [once again not included in the original] is a SIBERIAN COLIU machine. It will work as a perpetuum mobile if the driving torque produced by the current induced in the ring when it will be set in rotation with a certain velocity will be larger than the friction torque. I constructed this machine in the photograph in 1993 and the last three years I did nothing else than to try to increase its driving torque and decrease its friction torque. The driving torque was produced only by the S (i.e., Smar ) currents. Smar is very strong near the cutting plane, from the one side positive, from the other negative. The dozens of my SIBERIAN COLIU machines are presented with photographs in DEUTSCHE PHYSIK.

266

16. All conventional theories for the origin of Earth's magnetization are wrong. If rotating a cylindrical piece of any metal by a boring machine, one sees that it becomes magnetized.

Conventional physics believes first that only ferromagnetics become magnetized and second that the magnetization is proportional to the angular rotational velocity, as this was promulgated by Barnett. My friend C. Monstein demonstrated that the magnetization is proportional to the linear rotational velocity and I called this the Monstein-Barnett effect.

Proceeding from the Monstein-Barnett effect I calculated the magnetization of the Earth, the Sun and the planets, obtaining excellent coincidences with the measured values. As Venus is the only planet whose nucleus is liquid, it is not magnetized. The most cherished conventional theory for Earth's magnetization is the "unipolar dynamo theory" of Elsasser. It is ridiculous, as a unipolar machine can work only at the existence of sliding contacts and moving with respect to each other parts.

17. Magretic energy does exist. By the most elementary speculations and calculations I showed that: a) the gravitational energy of two masses is not a negative quantitiy, as accepted by conventional physics, but a positive quantity, b) the gravitational potential generated by all masses of the universe is equal to c2 , c) electricity and gravity are two completely analogical sciences from a mathematical point of view. The only difference is that the gravitational "charges" are the proper masses m0 = m/(1 - v2/c2)1/2 and that negative masses do not exist.

There are no other differences. Thus a magretic energy, i.e., a "magnetic kind" of energy in gravity must exist and gravity is to be called gravimagretism (this is the title of part IV of my encyclopaedic work CLASSICAL PHYSICS). I proposed a very simple experiment which can reveal the existence of magretic energy. This experiment, moreover, can serve for measurement of the Earth's absolute velocity.

18. The recession hypothesis for the galaxies is wrong. I call stellar "red shift" this one which is caused by the gravitational action of the star on the emitted by it light, galactic "red shift" this one which is caused by the gravitational action of the respective gaIaxy and cosmic - by all cosmic matter. Conventional physic believes that the big "red shifts" of Iight coming from remote galaxies are due to their recession velocities. This is a phantasmagoria. The most simple calculation, which can be carried out by any child, shows that they are due to the gravitational action of all cosmic matter and that they are proportional not to the distance of the emitting galaxy (or quasar) but to the square of this distance. I showed that the experimental data fit much better to a square plot. Respectively, instead of a Hubble constant, a Hubble-Marinov constant is te be introduced, for which the children obtain the strictly defined value HM2 = 2πγµ/3c2 , where γ is the gravitationa constant and µ is the average mass density in the Universe.

NOTE. On the 5 March 1996 I submitted to NATURE my paper AFTER 500 YEARS COLUMBUS-EGG-PROBLEM HAS FINALLY BEEN SOLVED, in which I show how a body can be maintained in a state of UNSTABLE equilibrium (problem which, contrary to the general opinion, Columbus has NOT solved). My "Marinov egg" is supported by magnetic forces. If it has SPHERICAL form, it has three degrees of freedom (the Euler angles) free and represents moreover a PERPETUUM MOBILE. If before the 1 May the paper will not appear in the scientific columns of NATURE, I shall publish it as a paid advertisement. In the first (or second) case 15 days after the publication I shall present my SIBERIAN COLIU perpetuun mobile at a press conference.

Stefan Marinov Morellenfeldgasse 16, A-8010 Graz

-----

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[The previous pages are reproduced from pp. 34-35 of Marinov's Deutsche Physik (International Glasnost Journal on Fundamental Physics), Vol. 5, N. 19, July-September 1996, and appeared in Nature, Vol. 380, N. 6572, 28 March 1996, p. xiv, as a payed Advertisement, with the attached NOTE as reported. Marinov extensively explains later on in his journal (pp.

40-45) how he tried to publish instead the following text, but that he was told that: "we are enable to publish the advertisement unless [this note] is deleted [...] we would naturally refund your money" (letter from Nature, 15th March 1996), so that he had to accept at last the publication of an "amended" version.] > In my advertisement (whose text is published on p. 34 of this issue) the following NOTE was attached: NOTE. In 1986 Dr. Maddox, the then-editor of NATURE, accepted for publication my big paper "Experimental violations of the principles of relativity, equivalence, and conservation of energy and angular momentum". During my visit in March 1987 he personaily began to compose this paper on his computer and I stayed in his office and corrected any sheet which he gave me. He could not compose the whole paper and I left London. However during a year the composition of the paper remained, as Schubert's symphony, unvollendet. Thus in June 1988 I flew to London and composed the paper myself in NATURE's composition office. The paper had to appear on the 18 August 1988 but because of the Benveniste's case ìts publìcatiori was postponed for the 13 October. "I do not have the stomach for a second battle in such a short tirme" wrote to me Dr. Maddox on the 29 July. This paper is still not published. If the paper will not appear in the scientifìc columns of NATURE until the 1 May 1996, I shall publish it as a paid advertisement. In the first (or second) case 15 days after the publicatìon of the paper I shall present my perpetuum mobile SIBERIAN COLIU at a press conference.

As in a week or so after my 13-February-letter no answer came from Mrs. Smith, I asked her on the phone which is the matter. She told me that there are problems with the NOTE and that she has to consult Dr. Campbell and Dr. Maddox. Until the 26 February no answer came and I phoned again. [...] [The conclusion of this story has already been mentioned: after Nature's refusal of 15th March, Marinov proposed a different shortened version, which was found acceptable: "I can confirm that your amended paragraph of today is acceptable for publication" [loc. cit., p. 45].

----[The following one is Nature's letter of 26th January 1996 (see the quoted issue of Deutsche Physik, p. 38) which refused a paper proposed by Marinov only a few days before, namely on 22nd January 1996. It was this circumstance which forced him to ask for the publication of the payed advertisement above.]

268

MARINOV'S NOTE. First I would like to note that if an editor has pricks of conscience when rejecting a paper, he never mentions in bis rejecting letter (if he decides such a letter to write!) the title of the paper and the date of submission. The same does Dr. Campbell in his above letter. Thus the title of my rejected article was EXPERIMENTAL VIOLATIONS OF THE PRINCIPLES OF RELATIVITY, EQUIVALENCE, AND CONSERVATION OF ENERGY AND ANGULAR MOMENTUM, and it was submitted on the 22 January 1996 by post.

This paper, as a matter of fact, was accepted for publication by Dr. Maddox in April 1986 and in final form in June 1988 but it never appeared in NATURE (see the story in detail in the following pages). The paper, as composed by me in June in London was published in THE THORNY WAY OF TRUTH, Part III (1988), p. 146.

But Dr. Campbell allowed to me to publish an advertisenìent in NATURE and in her fax of the 9 February Mrs. Smith wrote me that the price for two pages will be 5290 £.

----[Furthermore, on April 1996, after a new correspondence's exchange, Dr. Campbell wrote to Marinov the following final letter, which is published at p. 50 of the quoted issue of Deutsche Physik, together with a comment of our poor friend Stefan*.]

269

> Only in religion and similar AUTHORITATIVE spiritual and ideological domains are there "orthodox" and "unorthodox" views. In physics there are views confirmed or rejected by experiments. Of course, there are views for whose verification there are no experiments, or contradictory views which predict the same experiments. However a FORMULA can be either right or wrong, a formula cannot be "orthodox" or "unorthodox". In my writings I present FORMULAS. And I present EXPERIMENTS which can be calculated by these formulas and which cannot be calculated by the formulas of "orthodox" physics.

----[* On the morning of July 15th 1997, Stefan Marinov committed suicide in Graz, the Austrian town where he lived very poorly since many years as an exile. As far as his scientific activity is concerned, since the times of the previous Advertisement, he had the resources to edit three more numbers of Deutsche Physik, namely NN. 20, 21 and 22: the very last one is dated April-June 1997...

More information about this singular figure of dissident XXth Century physicist can be found in the article N. 13 ("In Stefan Marinov memoriam") published at the web page: http://www.dipmat.unipg.it/~bartocci/listast.htm .]

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Intorno alla legge di resistenza al moto dei corpi in un mezzo pulviscolare (N. Moisseiev) INTRODUZIONE. Ci proponiamo nel presente articolo di esporre la deduzione della legge di resistenza al moto dei corpi in un mezzo pulviscolare, basandoci sugli stessi schemi che furono già posti a fondamento di. talune sezioni di un nostro precedente lavoro(1).

Questioni relative alla teoria del moto in un mezzo resistente cominciano nuovamente a suscitare interesse fra gli studiosi che lavorano nel campo della cosmogonia ed in campi affini. Indichiamo ad esempio la serie dei lavori pubblicati dal prof. T. Levi-Civita (2), i quali mirano tanto a dedurre la legge razionale di resistenza al moto, quanto a stabilire le equazioni differenziali del moto stesso, ed altresì la serie di studi di G.N. Duboscin (Russ. Astronomical Journal), dedicati principalmente all'analisi generale delle forme e delle proprietà del moto di un punto in un mezzo resistente ed in campi di forze centrali.

Il problema stesso può essere trattato da due punti di vista diversi: come problema di resistenza di un fluido compressibile o no al moto in seno di esso, oppure come problema di resistenza al moto di un mezzo composto di punti discreti, di molecole, l'azione reciproca. delle quali ha importanza e va presa in considerazione solamente per definire la struttura del mezzo nel suo insieme, mentre nell'interrelazione loro col corpo che subisce resistenza al suo moto, dette particelle reagiscono su di esso in modo affatto indipendente l'una dall'altra.

La prima questione, che rappresenta in sostanza un problema di idro od aerodinamica, può presentare interesse per l'astronomia solamente in relazione al moto in mezzi di densità sufficientemente grande, come per es. il passaggio di una meteora attraverso l'atmosfera di un pianeta ecc.

Il secondo problema per altro presenta per la cosmogonia un interesse considerevolmente maggiore, avendo esso da fare con mezzi molto rarefatti. Ed è per l'appunto questo secondo aspetto del problema che prendiamo di mira nel presente lavoro. § I. - Espressioni generali per la resistenza nel caso di flusso semplice.

Rappresentiamoci un corpo sferico S , di raggio D intorno al cui centro è descritta una sfera di raggio ρ , che divide il campo - in cui si può trascurare l'attrazione di questo corpo S - dal campo, interno per rapporto a questa "sfera d'azione", in cui il moto di un punto isolato viene retto unicamente dall'attrazione del corpo S . Rappresentiamo con x0 il quoziente D/ρ .

Ammettiamo poi che lo spazio esterno alla sfera d'azione sia, con densità uguale, riempito di particelle materiali tanto piccole per dimensioni e per massa che si possa non tener conto della loro azione reciproca. Sia n il numero di particelle per unità di volume e µ la massa di una particella isolata. Supponiamo, che tutte le particelle abbiano masse eguali.

Supponiamo poi che il corpo S si muova rispetto al "centro di moto" (3) del complesso di particelle con una velocità r . Esaminiamo, nel paragrafo presente, il caso in cui le particelle non abbiano velocità proprie per rapporto al loro "centro di moto". Questo caso per l'appunto noi chiameremo caso di flusso semplice. Chiameremo asse del flusso la direzione della velocità del corpo per rapporto allo sciame di particelle.

La resistenza che le particelle offriranno al moto del corpo S consterà di due contributi diversi:

271

1. Resistenza delle particelle che passano attraverso la sfera d'azione senza urtare il corpo S ; 2. Resistenza di particelle urtanti il corpo. L'uno si considererà come assolutamente anelastico.

Applichiamoci a dedurre la formola che corrisponde alle particelle della prima specie.

Indichiamo, come si usa(4), con α l'angolo fra la velocità di una particella e il raggio vettore nel momento d'entrata nella sfera d'azione; esso sarà anche eguale all'angolo del raggio vettore del punto d'entrata coll'asse del flusso. Siano poi R e N le coordinate polari, per le quali l'asse del flusso serve di asse polare, e finalmente N(ρ) l'angolo N corrispondente al punto d'uscita dalla sfera d'azione.

Allora, la proiezione della velocità d'entrata sull'asse del flusso sarà -r, e la proiezione della velocità d'uscita dello stesso punto: r cos(N(ρ) + α) .

Perciò l'aumento di quantità di moto per il corpo S in direzione dell'asse del flusso in conseguenza dell'incontro con una particella sarà eguale a: - µ r cos2[(N(ρ) + α)/2] .

(1)

D'altra parte l'equazione della traiettoria di una particella entro la sfera d'azione può essere assunta sotto la forma: (2)

r2 ρ sin2(α) +

R R R (1 - r2ρ)sin(α)sin(N) + cos(α)cos(N) =0, ρ ρ ρ

donde ricaviamo: (3)

[(N(ρ) + α)/2] = arctg[(1 - r2ρ)tg(α)] .

Così l'espressione (1) si trascrive nel modo seguente: (1.1)

-2µr

1 .

1 + (1 − r 2 ρ ) 2 tg 2 (α )

Perciò il completo aumento di quantità di moto del corpo in direzione dell'asse del flusso nell'intervallo di tempo δt provocato dall'incontro con particelle che non vengano ad urtare il corpo stesso sarà:

(4)

M δt = - µ n 4πρ2 δt

π 2

sin(α ) cos(α )dα 1 + (1 − r 2 ρ ) 2 tg 2 (α ) α = α ( D)

∫

dove α(D) rappresenta il valore limite di α , che corrisponde al. caso in cui la particella viene a contatto col corpo S, cioè:

272

D 2 2D D 1 + 2 (1 − ) 2 , α(D) = arcsin 2 ρ r ρ ρ e M la massa del corpo S. E così, finalmente, per la reazione cercata abbiamo l'espressione (5)

dr )1 = dt µ n 2π ρ (1 − r 2 ρ ) 2 (1 − r 2 ρ ) 2 ln = [ - 1 + sin2(α(D))] . ( 2 − r 2 ρ ) r 2 ρ ( r 2 ρ − 2) 1 + r 2 ρ ( r 2 ρ − 2) sin 2 (α ( D ))

R1 = M (

Occupiamoci ora della deduzione della seconda parte della reazione, dovuta all'urto con le particelle per le quali α < α(D) .

E' facile vedere che se ωR è l'angolo del raggio vettore con la velocità, alla distanza R, e r R la velocità alla stessa distanza, la componente della quantità di moto di una particella urtante il corpo S nel punto (N,D) lungo l'asse del flusso sarà: (6)

-µ rD cos(N - ωD ) .

Approfittando dell'equazione della traiettoria e della legge delle aree otteniamo: (6.1)

cos(N - ωD ) = cos(α ) x 2 ( r 2 ρ − 2) + 2 x − r 2 ρ sin 2 (α ) − r 2 ρ (1 − r 2 ρ )[ x ( r 2 ρ − 2) + 1]sin 2 (α ) = .

[1 + r 2 ρ ( r 2 ρ − 2) sin 2 (α )] x 2 ( r 2 ρ − 2) + 2 x

Per trovare l'espressione spettante alla variazione di velocità del corpo S nel piccolo intervallo di tempo δt , in conseguenza dell'urto colle particelle del nostro sciame, possiamo procedere nel modo seguente: Immaginiamoci un certo corpo P* , la cui massa µ* sia eguale alla somma delle masse di tutte le particelle, che verranno ad urtarsi col corpo S durante l'intervallo di tempo δt , mentre la componente della quantità di moto rispetto al corpo S sia eguale alla somma delle componenti delle quantità di moto delle particelle medesime, cioè alla somma delle quantità (6). Essendo δt abbastanza piccolo, l'effetto dell'urto con questo corpo fittizio P* e l'effetto dell'urto con lo sciame delle particelle coincideranno fra loro. Così, l'aumento di velocità del corpo S si esprimerà con la formola seguente, derivante dalle legge di urto di corpi assolutamente anelastici: (7)

δr =

(µ r) * M+ µ *

dove M e µ* sono rispettivamente le masse dei corpi S e P* e (µr)* la componente delle quantità di moto del corpo P* rispetto a S . La formola (7) rimane naturalmente valida indipendentemente dalle velocità assolute dei corpi in questione, poiché in essa intervengono solo velocità relative.

Abbiamo poi:

273 α (D)

(8)

(µr)* = -µ n 2πρ

2

∫ rr

D

cos( N − ω D ) sin(α ) cos(α )dα

.

δt

α =0

e α (D)

(9)

µ* = µ n 2πρ

2

∫ r sin(α ) cos(α )dα

.

δt .

α =0

Perciò la reazione cercata sarà in questo caso semplicemente eguale a: α ( D)

(10)

dr R2 = M ( )2 = - µ n 2πρ2 r rD ∫ cos( N − ω D ) sin(α ) cos(α )dα dt α =0

dove a cos(N - ωD) va sostituita la sua espressione (6.1).

Per rD abbiamo la formola seguente: (6.2)

rD =

1 2 − x + r2ρ x . ρx

Riassumendo ciò che precede, perveniamo alla conclusione che la forza di resistenza offerta dal nostro mezzo al moto del corpo S sarà rappresentata dalla formola: (11)

R = R 1 + R2 .

Quest'espressione - particolarmente per il secondo addendo - riesce abbastanza complicata.

Non staremo perciò a trascrivere le espressioni complete per il caso generale, ma ci limiteremo all'analisi della legge trovata nelle sue caratteristiche essenziali. E per questo esamineremo in una prossima Nota i casi particolari più importanti.

(1) N. Moisseiev, Ueber einige Grundfragen der lheorie des Ursprungs der Kometen, Meteore und des kosmischen Staubes, I., II., III. Teil, "Publications de l'Institut Astrophysique", vol. V, fasc. I. (2) T. Levi-Civita, Corpuscoli cosmici e distribuzione Maxwelliana, "Atti Acc. Pontificia", Anno LXXXIII (1930), pp. 176-189; Ancora sul moto di un corpo di massa variabile, questi "Rendiconti", vol. XI, 1930, pp. 626-632; ecc.

(3) Vedi Ueber einige Grundfragen ecc., I. Teil, $ 1.

(4) V. loc. cit.

----Questo lavoro, presentato dal Socio Tullio Levi-Civita nella seduta del 3 gennaio 1932, è stato pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1932, Vol. XV, pp. 135-139.

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Exodus of Einstein's Special Theory in Seven Simple Steps (Carl A. Zapffe) Introduction.

For those who admire the orderliness of epistemology in theoretical physics, and are committed to the requirements of logic in experimental physics, the following should be of interest, and particularly because it knifes through the confusion of a century's wrangling over c ± v values for the velocity of light.

The Seven Steps.

Seven steps of factual information come under present consideration, the first two of which serve to shake loose the long-standing and generally unquestioning fixation upon Einstein's special theory of relativity (STR) so that it can be re-examined without bias: I. The mass-energy relationship E = mc2 does not depend upon the STR, whereupon the fate of the two are not inseparable.

As Lewis [1] demonstrated in 1908, and Einstein himself admitted in 1950 [2], the fact of mass-energy equivalence has been inherent within the charge-momentum relationships of Maxwell's field equations since long before Einstein was born.

II. Elementary-particle phenomena in nuclear physics, which do exhibit the (1 - v2/c2)-1/2 relationship of an asymptotic c for both decay life τ and mass increase in terms of e/m , do not necessarily confirm the Lorentz transfomation for t and x .

This traditional identity is pure surmise, following from the convenience of the (1 - v2/c2)-1/2 term already appearing in the Lorentz transformation, and the heuristic appeal of an argument that, since even the complex structure of the human being is composed of elementary particles, that which measures time τ for the one measures time t for the other.

But on the one hand, these velocity-dependent changes - and specifically if velocity be proved absolute - submit as well to the same treatment as the rate equations of chemistry and thermodynamics, which of course support neither one transformation nor another; while on the other hand heuristics is scarcely the dependable tool for bridging such a gap as that between pions and hemoglobin. Metallurgists use similar τ measurements for the decay behaviour of the positron [3,4], which is about as elementary as a particle can get; and the changes in this case have no relationship whatever with velocity, the velocity being v = 0 .

Next we encounter these two massive criticisms of the STR epistemology, one pinpointing the long debate over the chronometric paradoxes, the other using the steps of logic to return the physical model from Einstein back to Lorentz: III. An impossible contradiction stands in the prediction of the Einstein equations that two clocks, in motion relative to one another, can each be found running slow.

This classical controversy was spearheaded by the late Herbert J. Dingle, whose book Science at the Crossroads [5] should be read. Despite the widely ranging imagination of STR apologists, the only acceptable answer next follows.

IV. Only if the velocity is absolute can this contradiction be resolved; and if velocity is absolute so is space.

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This was the monumental work of Ives [6], and the classical papers of Builder [7,8], recently confirrned experimentally by studies of isotropy and anisotropy of the 3°K background radiation [9].

V.

But if both velocity and space are absolute, then so is time.

This follows simply from v = x/t ; and the time t is presumably that d 2s/dt2 of the cosmically unfolding "Big Bang", or its competing models. Therefore any velocity-dependent features, and specifically those of elementary particles, are referable on the one hand to the chronometry of this cosmic unfolding, and on the other hand to the isotropy of its radiative framework.

There only remains to resolve certain problems with the seemingly electromagnetic or Maxwellian substructuring of this space.

Return to Galilean-type Transformation.

VI. An elementary principle of geophysics is that light from the aurora borealis or australis, and indeed every other electromagnetic disturbance within the domain of the terrestrial magnetosphere, arrives upon the surface at velocity c relative to geocentric rest coordinates. Similarly, it is presumed in astrophysics that all radiation traversing a stellar magnetosphere does so at velocity c relative to the coordinates of the repective magnetosphere.

VII. Since experimental physics has similarly proved, from the time of Arago's starlit prisms in 1810 [10], to such recent tests as those of Brillet and Hall [11], that light from either terrestrial or extraterrestrial sorces similarly traverses the local magnetosphere at velocity c , .simple principles of geometry and trigonometry then require that c ± v light velocities do obtain, though the differential is only discoverable along the magnetosheath which separates the Maxwellian domain of one magnetosphere from that of another.

This is the main thrust of the Magnetospheric Ether-Drag Theory [12, 13], which merely calls attention of relativists to principles already welI established in geophysics.

Conclusion.

From this progression of seven observations, one can only arrive at the following seven conclusions: 1.

Einstein's physical model for his special theory of relativity must be abandoned in favour of that of Lorentz.

2.

Lorentz's physical model must similarly be abandoned because of its outmoded field features from standpoints of magnetospheric physics.

3.

The Einstein-Lorentz transformation must then be abandoned also because of these errors in points of physical model.

4.

With abandonment of the Lorentz transformation, velocity-dependent phenomena such as those in elementary-particle physics enter the province of mere rate equations: dϕ/dv , d2ϕ/dt2 , dτ = f(v) = τ0 (1 - v2/c2)-1/2 , ... etc.

5.

All (1 - v2/c2)-1/2 relationships in general become interpreted merely as asymptotic cosine or sec θ functions, identical with the linear equations for subsonic aerodynamics and hydrodynamics, and unrelated except fortuitously to this same factor in the Lorentz-Einstein transformation.

6.

No alteration at all attends the mass-energy equivalence E = mc2 .

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7.

A physical model is new at hand, long known to geophysics but completely novel to relativistic physics, in which space is structured in terms of the phenomenology of electrodynamics, and which not only permits experimental confirmation, but promises an entirely new navigational approach to astronautic odometry - measuring of one's position in celestial reaches of so-called "empty" space.

Bibliography [1] Lewis, G.N.: A Revision ol the Fundamental Laws of Matter and Energy, Phil. Mag. 16, 70517 (1908).

[2] Einstein, A.: Out of My Later Years, Philosoph. Lib., New York, viii + 282 (1950).

[3] Lynn, K. G. and Byrne, J. G.: Positron Lifetime Studies Made in Fatigue-Damaged AISA 4340 Samples, Metall. Trans. (A) 7, 604-6 (Apr. 1976).

[4] Hadnagy, T. D.; Byrne, J. G.; and Miller, G. R.: Effect of Porosity on the Mean Lifetime of Positrons in Scintered and Hot-Pressed Alpha-Alumina, J. Am. Ceramics Soc. 60, 461-3 (Sept.Oct. 1977).

[5] Dingle, H.: Science at the Crossroads, Martin Brian and O'Keefe, London, 256 pp. (1972).

[6] Hazelett, R. and Turner, D. (ed. by): The Einstein Myth and the Ives Papers, The Devin-Adair Co., Old Greenwich, CO. ix + 313 (1979).

[7] Builder, G.: Ether and Relativity, Australian J. of Phystcs 2, 279-97 (1958).

[8] Builder, G.: The Constancy of the Velocity of Light, Australian J. Phystcs 2, 457-80 (1958).

[9] Smoot, G. F.; Gorenstein, M. V.; and Muller, R. A.: Detection of Anisotropy in the Cosmic Blackbody Radiation, Phys. Rev. Letts. 39, No. 14, 898-901 (3 Oct. 1977).

[10] Arago, F.: (Fr.) The Velocity of Light, Abs. Procès-verbaux des Séances de 1'Académie des Sciences, Paris, p. 399 (l0 Dec. 1810).

[11] Brillet, A.; and Hall, J. L.: Improved Laser Test of the Isotropy of Space, Phys. Rev. Lett. 42, 549-52 (1979).

[12] Zapffe, C. A.: A Magnetospheric Ether-Drag Theory and the Reference Frames of Relativistic Physics, SST. 2 No. 4, 439-54; disc. 455-9 (1979); 3, No. 4, 483-5 (1980).

[13] Zapffe, C. A.: The Magnetosphere in Relativistic Physics, Ind. J. Theoret. Phys. 30, No. 1 (1982).

***** This essay first appeared in The Toth-Maatian Review, Volume 3, Number 4, January 1985, pp. 1531-1535. By: CARL A. ZAPFFE, 6410 Murray Hill Rd., Baltimore, MD 21212.

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RECENSIONI/ REVIEWS

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Albert Einstein, The Incorrigible Plagiarist (Christopher Jon Bjerknes) (XTX Inc., DownersGorve, Illinois, USA, 2002) "The secret to creativity is knowing how to hide your sources" (Albert Einstein) Proposing again the remark which we made some time ago in the presentation of Kostro's Einstein and the Ether (Episteme, N. 3, 21 April 2001, pp. 306-310), "common people", and even "common scientists", will be surprised by the facts they discover in Bjerknes' book (about 400 pages), which is quite useful, in that it establishes a realistic - and more reasonable! - picture of one of the most propagandized scientific myths of all time, namely Einstein's myth (see for instance: Alan J. Friedman & Carol C. Donley, Einstein as Myth and Muse, Cambridge University Press, 1985).

As a matter of fact, reading this text should be a must for all people professionally interested in the "history" of Physics or of Science (for these readers the book, its "polemical" thesis notwithstanding, could become an indispensable tool, packed as it is with information, quotations, meticulous references, etc.), but it is highly recommended even to teachers, scientists of all kind, philosophers, epistemologists, in general to every person interested in the evolution of human civilization and knowledge. Indeed, it would be difficult to deny that the emergence of modern science is one of the most relevant events of all times, and that Relativity in particular is the "theory" which had the greatest impact and influence on XXth Century Western thought - though, in our opinion, and clearly in Bjerknes' as well, a negative one).

The book is a successful attempt to break down some of the many commonplaces and misconceptions which fill the typically apologetic History of Science, and the author does not

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seem at all afraid to take on such a "giant". As a consequence, the result of his efforts is a genuinely "rare find" and an interesting one.

In addition, we must emphasize that Christopher Jon Bjerknes is the great great grandson of Carl Anton Bjerknes, who created the Pulsating Sphere Theory of Gravity and of Electromagnetism, and who played an important r么le in the creation of the concept of charged particle mass.

Vilhelm, Carl's son, also became famous for his work in Meteorology (Polar Front Theory; see for instance Appropriating the Weather: Vilhelm Bjerknes and Construction of a Modern Meteorology, by Robert Marc Friedman, Cornell University Press, 1993; Vilhelm Bjerknes, MEM Volume of the American Meteorological Society, 1962), but his primary focus was always on Physics and Hydrodynamics of Aether Models, and he was the scientist who gave the Columbia lectures which are quoted in Almansi's paper (Fields of force, Columbia University Press, New-York, 1906; see the section entitled Reprints in this same volume of Episteme).

Continuing a truly fine family tradition, Vilhelm's son, Jacob, is also quite famous for his work in Meteorology (Theory of Cyclones - El Ni帽o), and now we can say that Christopher Jon is carrying on following the footsteps of "aether theorists", who disliked (as we do) Einstein's theory, and the consequent disappearance of the concept of aether from mainstream Physics.

We must emphasize that this choice of "party" does not influence the usefulness of Bjerknes' essay even for those not willing to admit this criticism of Relativity. As a matter of fact, the book could even be construed to be rather more in favor of Relativity than the contrary, since the proof that Einstein "borrowed" many ideas from others famous scientists, renders them responsible for the dangerous nichilistic and irrational drift of modern scientific thought, which Episteme has always aimed to fight...

We proceed with the presentation of the book presenting first its Table of Contents, and further a few excerpts. Afterwards, we publish some additional commentary, mainly Phipps' review (another scientist well known for his rather critical attitude against Relativity; we thank Dr. Eugene F. Mallove, the Editor-in-Chief of Infinite Energy Magazine, for his consent to publish it in parallel). We end this "chapter" with an Appendix written by Bjerknes himself for the next edition of his research, honored to be able to present it to our readers in exclusive preview.

TABLE OF CONTENTS: 1. THE PRI0RITY MYTH 2. SPACE-TIME, OR IS IT "TIME-SPACE"?

3. "THEORY OF RELATIVITY" OR "PSEUDORELATIVISM"?

4. HERO WORSHIP 5. E = mc2 6. EINSTEIN'S MODUS OPERANDI 7. HISTORY 8. MILEVA EINSTEIN-MARITY 9. P0LITICS AND ANECDOTES NOTES INDEX

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----info@xtxinc.com http://www.xtxinc.com [Two articles of the author, together with information about his life and work, are published in this same volume of Episteme] ----Excerpts (Reprinted by permission. All rights reserved) It is easily proven that Albert Einstein did not originate the special theory of relativity in its entirety, or even in its majority. The historic record is readily available. Ludwig Gustav Lange, Woldemar Voigt, George Francis FitzGerald, Joseph Larmor, Hendrik Antoon Lorentz, Jules Henri PoincarĂŠ, Paul Drude, Paul Langevin, and many others, slowly developed the theory, step by step, and based it on thousands of years of recorded thought and research. Einstein may have made a few contributions to the theory, such as the relativistic equations for aberration and the Doppler-Fizeau Effect, though he may also have rendered an incorrect equation for the transverse mass of an electron, which, when corrected, becomes Lorentz' equation.

Albert Einstein's first work on the theory of relativity did not appear until 1905. There is substantial evidence that Albert Einstein did not write this 1905 paper on the "principle of relativity" alone. His wife, Mileva Einstein-Marity, may have been co-author, or the sole author, of the work.

If Albert Einstein did not originate the major concepts of the special theory of relativity, how could such a historically significant fact have escaped the attention of the world for nearly a century? The simple answer is that it did not.

----Book Description (from an auto-review appeared in Canberra Times, an Australian newspaper, Thursday, 19 September 2002) The name ''Einstein'' evokes images of a good-humoured genius, who revolutionised our concepts of space, time, energy, mass and motion. Time named Albert Einstein "person of the century". The language itself has incorporated "Einstein" into our common vocabulary as a synonym for extraordinary brilliance. Many consider Einstein to have been the finest mind in recorded human history.

That is the popular image, fostered by textbooks, the media, and hero worshiping physicists and historians. However, when one reads the scientific literature written by Einstein's contemporaries, a quite different picture emerges: one of an irrational plagiarist, who manipulated credit for their work.

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Einstein is perhaps most famous for the special theory of relativity, published in 1905 in the German physics journal, Annalen der Physik. The paper was devoid of references, a fact that Einstein's friend and Nobel prize winner for physics, Max Born, found troubling. ''The striking point is that it contains not a single reference to previous literature,'' Born stated in 1955, before the International Relativity Conference in Bern. ''It gives you the impression of quite a new venture. But that is, of course, as I have tried to explain, not true.''

Though Einstein's 1905 article contained no references, it was so strikingly similar to a paper written by Hendrik Lorentz the previous year, that Walter Kaufmann and Max Planck felt a need to publicly point out that Einstein had merely provided a metaphysical reinterpretation and generalisation of Lorentz' scientific theory, a metaphysical reinterpretation and generalisation Henri Poincare had already published.

As Charles Nordmann, astronomer to the Paris Observatory, pointed out: ''It is really to Henri Poincare, the great Frenchman whose death has left a void that will never be filled, that we must accord the merit of having first proved, with the greatest lucidity and the most prudent audacity, that time and space, as we know them, can only be relative. A few quotations from his works will not be out of place. They will show that the credit for most of the things which are currently attributed to Einstein is, in reality, due to Poincare.''

Einstein acknowledged the fact, but justified his plagiarism in a cavalier fashion in Annalen der Physik in 1907. "It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I believe I am entitled to leave out a thoroughly pedantic survey of the literature, all the more so because it is hoped that these gaps will yet be filled by other authors, as has already happened with my first work on the principle of relativity through the commendable efforts of Mr. Planck and Mr. Kaufmann."

The completed field equations of the general theory of relativity were first deduced by David Hilbert, a fact Einstein was forced to acknowledge in 1916, after he had plagiarised them from Hilbert in late 1915. Paul Gerber solved the problem of the perihelion of Mercury in 1898. Physicist Ernst Gehrcke gave a lecture on the theory of relativity in the Berlin Philharmonic on August 24, 1920, and publicly confronted Einstein, who was in attendance, with Einstein's plagiarism of Lorentz' mathematical formalisms of the special theory of relativity, Palagyi's space-time concepts, Varicak's non-Euclidean geometry and of the plagiarism of the mathematical solution of the problem of the perihelion of Mercury first arrived at by Gerber. Gehrcke addressed Einstein to his face and told the crowd that the emperor had no clothes.

This was Einstein's response published in the Berliner Tageblatt und Handels-Zeitung on August 27, 1920, translated into English in the book Albert Einstein's Theory of General Relativity edited by Gerald E. Tauber: ". . . Gerber, who has given the correct formula for the perihelion motion of Mercury before I did. The experts are not only in agreement that Gerber's derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber. Mr Gerber's work is therefore completely useless, an unsuccessful and erroneous theoretical attempt.

"I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of mercury. I have not mentioned the work by Gerber originally, because I did not know it when I wrote my work on the perihelion motion of Mercury; even if I had been aware of it, I would not have had any reason to mention it."

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The fact that Einstein was a plagiarist is common knowledge in the physics community. What isn't so well-known is that the sources Einstein parroted were also largely unoriginal. In 1919, writing in the Philosophical Magazine Harry Bateman, a British mathematician and physicist who had emigrated to the United States, unsuccessfully sought acknowledgment of his work.

"I am perhaps entitled to do this as my work on the subject of general relativity was published before that of Einstein and Kottler, and appears to have been overlooked by recent writers."

My book is a documentation of Einstein's plagiarism of the theory of relativity. It discloses his method for manipulating credit for the work of his contemporaries, reprints the prior works he parroted, and demonstrates that he could not have drawn his conclusions without prior knowledge of the works he copied but failed to reference.

Numerous republished quotations from Einstein's contemporaries prove that they were aware of his plagiarism. Side-by-side comparisons of Einstein's words juxtaposed to those of his predecessors prove the almost verbatim repetition. There is even substantial evidence presented in the book that Einstein plagiarised the work of his first wife, Mileva Maric, who had plagiarised others.

"Although generally associated with the names of Einstein and Minkowski, the really essentia physical considerations underlying the theories are due to Larmor and Lorentz." -- Alfred Arthur Robb "Einstein published a paper which set forth the relativity theory of PoincarĂŠ and Lorentz with some amplifications, and which attracted much attention." -- Sir Edmund Whittaker "The appearance of Dr. Silberstein's recent article on 'General Relativity without the Equivalence Hypothesis' encourages me to restate my own views on the subject. I am perhaps entitled to do this as my work on the subject of General Relativity was published before that of Einstein and Kottler, and appears to have been overlooked by recent writers." -- Harry Bateman "All this was maintained by Poincare and others long before the time of Einstein, and one does injustice to truth in ascribing the discovery to him." -- Charles Nordmann "Many of you have looked upon [Einstein's] paper 'Zur Elektrodynamik bewegter Koerper' in Annalen der Physik ... and you will have noticed some peculiarities. The striking point is that it contains not a single reference to previous literature. It gives you the impression of quite a new venture. But that is, of course, as I have tried to explain, not true." -- Max Born "In point of fact, therefore, PoincarĂŠ was not only the first to enunciate the principle, but he also discovered in Lorentz's work the necessary mathematical formulation of the principle. All this happened before Einstein's paper appeared." -- G. H. Keswani "Einstein's explanation is a dimensional disguise for Lorentz's. ... Thus Einstein's theory is not a denial of, nor an alternative for, that of Lorentz. It is only a duplicate and disguise for it. ... Einstein continually maintains that the theory of Lorentz is right, only he disagrees with his 'interpretation.' Is it not clear, therefore, that in this, as in other cases, Einstein's theory is merely a disguise for Lorentz's, the apparent disagreement about 'interpretation' being a matter of words only?" -- James Mackaye

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----Mr Bjerknes, an American historian of science, has authored six books on Einstein and the theory of relativity. Albert Einstein: The Incorrigible Plagiarist (ISBN 0971962987) is available at www.amazon.com.

----A reviewer, a physicist, July 18, 2002 ALBERT EINSTEIN WAS INDEED A PLAGIARIST This book is very well documented, and, therefore, very convincing. I read the Dover reprint of 'The Principle of Relativity' years ago, and realized then that Einstein just copied Lorentz, because Lorentz' article appeared a before Einstein's and says essentially the same things. But this book goes far beyond that and really shows a pattern by Einstein of plagiarism. I was surprised to discover that Einstein's wife may have written the journal articles for him. The number of citations and quotations in this book is really impressive and together form a compelling argument stated in a very logical progression of facts. My only regret is that there isn't more on the general theory of relativity, but the author hinted that more is to come, and that this book is part of a series. I look forward to the future releases. I'm pleased with it and would recommend it. It will change your view of Einstein and of the theory of relativity. If you are doing research, I can tell you that I have never seen a book which provides more information on the complete history of the theories than this book, including Whittaker's.

***** Review of Albert Einstein The Incorrigible Plagiarist (Thomas E. Phipps, Jr.) (From Infinite Energy Magazine, N. 47, 6 October, 2002) (http://www.infinite-energy.com) Hagiophobia is defined as "a morbid dread of holy things." There is no question that the author of this book, Christopher Jon Bjerknes, is an exemplary sufferer from this too-rare complaint. For in our time Albert Einstein has been sanctified â&#x20AC;Ś perhaps even above Albert Schweitzer, who certified the holiness of all living things, himself included. Einstein's life having been told and retold by numerous hagiographers, Bjerknes has made it his aim to provide the market with equally numerous anti-hagiographies - this being apparently the sixth he has written. The publishers have burdened the latest with a disclaimer, "This book is intended solely for entertainment purposes." However, we all know that nothing entertains better than a good character assassination.

For this purpose the book employs the Socratic method, the asking of loaded questions - in the style of, "Was this man ever known to stop beating his wife?" Physicists, who lead the pack of Einstein idolaters, will dismiss Bjerknes's questions with contempt. But I think others will be impressed, if nothing else, by the sheer doggedness of the scholarship that has gone into the bibliography. This fills almost half the book and comprises 567 numbered endnotes,

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some of which stretch for more than a page and include extensive references to the literature.

Among these notes will be found almost anything that has been written by or about Einstein or his ideas, to the present date. My own limited scholarly resources noted only one omission: Karl Popper, the philosopher who first (?) linked the names of Einstein and Parmenides, is absent. But Parmenides is here, as he amply deserves to be.

From the start we note a deep schism: the author would like to side with feminists who see Einstein's work as actually done by his much smarter first wife Mileva; but, since Bjerknes also wants to paint that same work as stolen from earlier investigators, he faces an abiding problem of whose character to assassinate. Here the Socratic method proves a life-saver: Rather than offering a definitive choice, he provides weaponry for assassinating both Albert and Mileva, and leaves it to the reader's political preference, an open question, which candidate to take as the priority target.

Given all this smoke, how much fire is present? Einstein (or Einstein-Marity, the first wife) stands accused primarily of "plagiarism" in respect to the basic ideas of the special relativity theory. Narrowly construed, plagiarism refers to the copying of an earlier author's published words. No such charge can be laid against Einstein. The author exhibits not a single instance of word-copying or what the litigious would term copyright infringement. But that is not what Bjerknes means. He is referring to the theft of ideas without acknowledgment. Here the case is much stronger and also much fuzzier. Einstein's 1905 paper (which - amazingly - was originally submitted to Annalen der Physik under the name Einstein-Marity, according to the first-hand account, cited here, of Abram Joffe) contained not a single reference to earlier work. This is frowned on in modern science, and should have been challenged by the editor even then. For Einstein would have been a poor scholar, indeed, if he had failed to read Poincare's prior work on relativity, which explicitly enunciated the Principle of Relativity.

One can understand omission of any reference to the much earlier work of Wilhelm Weber, who developed the first and last relativistic formulation of electrodynamics in terms of relative coordinates, velocities, and accelerations - since such would have directed attention to the persistence of absolutist elements within "special relativity" theory. (The "observer" or "frame" is such an element - a tertium quid extraneous to the intrinsic elements to be described in nature, and wholly absent from Weber's theory. Minkowski's covariant symmetrizing of the quid among all its quiddities alleviates, but does not eradicate, this echo of absolutism.)

Another dilemma of the author in respect to special relativity is whether to concentrate his attack on the theory itself or on its creator. If the theory is no good and was in fact stolen by Einstein (or by Mileva) from predecessors, then it would seem the blame for this no-goodness should fall most heavily on the latter. Error plagiarized is not error sanitized. Its provenance aside, Bjerknes clearly distrusts the special theory (as does the present reviewer); but the book makes little serious contribution to the comparatively vast (though little known and little regarded) literature of its logical criticism.

Einstein's (or Einstein-Marity's) originality consisted in adjoining the Poincare relativity principle to the Maxwell equations (which contain only one field propagation velocity parameter c and thus necessitate what we now call "Einstein's second postulate") and in showing that these stark logical ingredients suffice to imply a kinematics based on the mathematical coordinate transformations that Lorentz had already spelled out. Clearly the ideas pre-existed. But, as all inventors know, it is not permissible to patent ideas. If the combining of pre-existing ideas in new patterns is to be called "plagiarism," then it would not be an over-statement to say that all scientific progress and all invention depend on just this kind of plagiarism â&#x20AC;Ś for what did Newton do but plagiarize from the giants on whose shoulders he acknowledged standing? He neglected only to attach names to the giants. So did Einstein. In both cases the behavior was perhaps a trifle magisterial â&#x20AC;Ś and also perhaps more than a trifle forgivable. Still, unpleasant doubts persist in the Einstein case: Bjerknes shows that Einstein's scientific publications reveal a lifetime pattern of similar magisterial behavior.

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The absence of attributions in the 1905 paper was not a one-off occurrence. For example, I quote from page 231 of the book: "David Hilbert, on whom Einstein went calling for help, published the general theory of relativity before Einstein. Why after many years of failure, did Einstein suddenly realize, within a few days after David Hilbert's work was public, the equations which Hilbert published before him, and then submit his, Einstein's, identical formulations?"

As you can see, this last (stripped of its Socratic question mark) constitutes a genuine charge of plagiarism â&#x20AC;Ś but it is not backed by chapter and verse citation, equation number by corresponding equation number, word by word. Lacking such substantiation, the charge cannot stand in court. In law, equations, like ideas, cannot be copyrighted or patented. Still, here is more smoke. It is doubtful if all such can be permanently cleared away. But one would like to see scholarship comparable to that of Bjerknes applied to the task. Otherwise, a polluted atmosphere and a bad odor linger.

In conclusion, I recommend the book to Einstein scholars and to sociologists of science as a genuinely valuable bibliographical resource for further research on the man and his times and as a target for the Einstein hagiographers to shoot down if they can. Other readers, in search of more than entertainment, must proceed with caution.

Thomas E. Phipps, Jr. 908 South Busey Avenue Urbana, IL 61801, USA (XTX, Inc., Downers Grove, IL 60515, 2002, Paperback $19.95, ISBN 0-9719629-8-7)

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A Short History of the Concept of Relative Simultaneity in the Special Theory of Relativity (Christopher Jon Bjerknes) Abstract. There is a common misconception enunciated in numerous histories, that Albert Einstein was the first person to propose the relativity of simultaneity. It is often alleged that the paper, "Zur Elektrodynamik bewegter Körper", Annalen der Physik, Series 4, Volume 17, (1905), pp. 891-921, at 892-895, contained the first proposal of a clock synchronization method employing observers and light signals. Given the absence of references in Einstein's work, it has been further assumed by some that the revised thought-experiment regarding a midpoint and relative simultaneity, which appeared in Einstein's 1916 work, "Die Relativität der Gleichzeitigkeit", Über die spezielle und die allgemeine Relativitätstheorie, Chapter 9, Friedr. Vieweg & Sohn, Braunschweig, (1917), pp. 16-19, was also an original idea. The historic record proves otherwise.

Piecing together the Missing References in Einstein's Plagiarized Works In 1887, Woldemar Voigt published the following relativistic transformation of space-time coordinates [1]: x' = x - vt , y' = y / γ , z' = z / γ , t' = t - vx / c2 , where γ = 1 / ( 1 - v2 / c2 )1/2 .

Poincaré asserted that simultaneity is relative, in 1898: "XII. But let us pass to examples less artificial; to understand the definition implicitly supposed by the savants, let us watch them at work and look for the rules by which they investigate simultaneity.

I will take two simple examples, the measurement of the velocity of light and the determination of longitude.

When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this moment, happened nevertheless fifty years ago, I seek his meaning, and to that end I shall ask him first how he knows it, that is, how he has measured the velocity of light.

He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment; it might be contradicted by it if the results of different measurements were not concordant. We should think ourselves fortunate that this contradiction has not happened and that the slight discordances which may happen can be readily explained.

The postulate, at all events, resembling the principle of sufficient reason, has been accepted by everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of simultaneity, entirely different from that which we have enunciated above.

This postulate assumed, let us see how the velocity of light has been measured. You know that Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its prediction. But how is this prediction made? It is by the aid of astronomic laws, for instance Newton's law.

Could not the observed facts be just as well explained if we attributed to the velocity of light a little different value from that adopted, and supposed Newton's law only approximate? Only this would lead to replacing Newton's law by another more complicated. So for the velocity of light a value is adopted, such that the astronomic laws compatible with this value may be as simple as possible. When navigators or geographers determine a longitude, they have to solve just the problem we are discussing; they must, without being at Paris, calculate Paris time. How do they accomplish it? They carry a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the

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quantitative problem of the measurement of time. I need not take up the difficulties relative to this latter problem, since above I have emphasized them at length.

Or else they observe an astronomic phenomenon, such as an eclipse of the moon, and they suppose that this phenomenon is perceived simultaneously from all points of the earth. That is not altogether true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there would be a correction to make according to a complicated rule.

Or else finally they use the telegraph. It is clear first that the reception of the signal at Berlin, for instance, is after the sending of this same signal from Paris. This is the rule of cause and effect analyzed above. But how much after? In general, the duration of the transmission is neglected and the two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be made by a complicated calculation; in practise it is not made, because it would be well within the errors of observation; its theoretic necessity is none the less from our point of view, which is that of a rigorous definition. From this discussion, I wish to emphasize two things: (1) The rules applied are exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as that of light, because such a velocity could not be measured without measuring a time.

XIII To conclude: We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.[2]"

Circa 1899, Poincaré clarified the fact that he saw no distinction between "time" and "local time": "Allow me a couple of remarks regarding the new variable t': it is what Lorentz calls the local time. At a given point t and t' will not defer but by a constant, t' will, therefore, always represent the time, but the origin of the times being different for the different points serves as justification for his designation."

"Disons deux mots sur la nouvelle variable t': c'est ce que Lorentz appelle le temps locale. En un point donné t et t' ne différeront que par une constante, t' représentera donc toujours le temps mais l'origine des temps étant différente aux différents points: cela justifie sa dénomination.[3]"

In 1900, Poincaré stated: "In order for the compensation to occur, the phenomena must correspond, not to the true time t, but to some determined local time t' defined in the following way.

I suppose that observers located at different points synchronize their watches with the aid of light signals; which they attempt to adjust to the time of the transmission of these signals, but these observers are unaware of their movement of translation and they consequently believe that the signals travel at the same speed in both directions, they restrict themselves to crossing the observations, sending a signal from A to B, then another from B to A. The local time t' is the time determined by watches synchronized in this manner.

If in such a case V = 1 / K0

½

is the speed of light, and v the translation of the Earth, that I imagine to be parallel to the positive x axis, one will have: t' = t - vx / V 2."

"Pour que la compensation se fasse, il faut rapporter les phénomènes, non pas au temps vrai t, mais à un certain temps local 'N défini de la façon suivante.

Je suppose que des observateurs placés en différents points, règlent leurs montres à l'aide de signaux lumineux; qu'ils cherchent à corriger ces signaux du temps de la transmission, mais qu'ignorant le

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mouvement de translation dont ils sont animès et croyant par conséquent que les signaux se transmettent également vite dans les deux sens, ils se bornent à croiser les observations, en envoyant un signal de A en B, puis un autre de B en A. Le temps local tNest le temps marqué par les montres ainsi réglées.

Si alors V = 1 / K0

½

est la vitesse de la lumière, et v la translation de la Terre que je suppose parallèle à l'axe des x positifs, on aura: t' = t - vx / V 2 . [4]"

We know that Einstein had read Poincaré's paper.[5] In 1902, Poincaré asserted, and we know, from Solovine's accounts [6], that Einstein had read this work of Poincaré's: "There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by convention. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have explained this in an article entitled 'Mesure du Temps.' [7]"

Again, in 1904, Poincaré asserted that simultaneity is relative, and elaborated on the light synchronization method that Mileva Einstein-Marity and Albert Einstein copied, in 1905, without citation to Poincaré. Poincaré stated in 1904, "We come to the principle of relativity: this not only is confirmed by daily experience, not only is it a necessary consequence of the hypothesis of central forces, but it is imposed in an irresistible way upon our good sense, and yet it also is battered.

Consider two electrified bodies; though they seem to us at rest, they are both carried along by the motion of the earth; an electric charge in motion, Rowland has taught us, is equivalent to a current; these two charged bodies are, therefore, equivalent to two parallel currents of the same sense and these two currents should attract each other. In measuring this attraction, we measure the velocity of the earth; not its velocity in relation to the sun or the fixed stars, but its absolute velocity.

I well know what one will say, it is not its absolute velocity that is measured, it is its velocity in relation to the ether. How unsatisfactory that is! Is it not evident that from the principle so understood we could no longer get anything? It could no longer tell us anything just because it would no longer fear any contradiction.

If we succeed in measuring anything, we would always be free to say that this is not the absolute velocity in relation to the ether, it might always be the velocity in relation to some new unknown fluid with which we might fill space.

Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all attempts to measure the velocity of the earth in relation to the ether have led to negative results. This time experimental physics has been more faithful to the principle than mathematical physics; the theorists, to put in accord their other general views, would not have spared it; but experiment has been stubborn in confirming it.

The means have been varied in a thousand ways and finally Michelson has pushed precision to its last limits; nothing has come of it. It is precisely to explain this obstinacy that the mathematicians are forced today to employ all their ingenuity.

Their task was not easy, and if Lorentz has gotten through it, it is only by accumulating hypotheses.

The most ingenious idea has been that of local time.

Imagine two observers who wish to adjust their watches by optical signals; they exchange signals, but as they know that the transmission of light is not instantaneous, they take care to cross them.

When the station B perceives the signal from the station A, its clock should not mark the same hour as that of the station A at the moment of sending the signal, but this hour augmented by a constant representing the duration of the transmission. Suppose, for example, that the station A sends its signal

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when its clock marks the hour o, and that the station B perceives it when its clock marks the hour t.

The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to verify it, the station B sends in its turn a signal when its clock marks o; then the station A should perceive it when its clock marks t. The timepieces are then adjusted. And in fact, they mark the same hour at the same physical instant, but on one condition, which is that the two stations are fixed. In the contrary case the duration of the transmission will not be the same in the two senses, since the station A, for example, moves forward to meet the optical perturbation emanating from B, while the station B flies away before the perturbation emanating from A. The watches adjusted in that manner do not mark, therefore, the true time, they mark what one may call the local time, so that one of them goes slow on the other. It matters little since we have no means of perceiving it. All the phenomena which happen at A, for example, will be late, but all will be equally so, and the observer who ascertains them will not perceive it since his watch is slow; so as the principle of relativity would have it, he will have no means of knowing whether he is at rest or in absolute motion.[8]"

Mileva Einstein-Marity and Albert Einstein parroted PoincarÊ's clock synchronization procedures, without acknowledging that PoincarÊ had stated them first. From the Einsteins' 1905 paper: "I. KINEMATICAL PART § 1. Definition of Simultaneity [Consider a system of coordinates, in which the Newtonian mechanical equations are valid. In order to put the contradistinction from the [moving] systems of coordinates to be introduced later into words, and for the exact definition of the conceptualization, we call this system of coordinates the 'resting system'.]

If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.

If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by 'time.' We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, 'That train arrives here at 7 o'clock,' I mean something like this: 'The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.'

It might appear possible to overcome all the difficulties attending the definition of 'time' by substituting 'the position of the small hand of my watch' for 'time.' And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch.

We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space.

But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A. Let a ray of light start at the 'A time' from A towards B, let it at the 'B time' be reflected at B in the direction of A, and arrive again at A at the 'A time'.

In accordance with definition the two clocks synchronize if

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tB - tA = t'A - tB. We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid: 1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B. 2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous resting clocks located at different places, and have evidently obtained a definition of 'simultaneous,' or 'synchronous,' and of 'time.' The 'time' of an event is that which is given simultaneously with the event by a resting clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

[We set forth, according to present experience, that the magnitude ( 2 A B ) / ( t'A - tA ) = c is a universal constant (the velocity of light in empty space).]

It is essential to have time defined by means of resting clocks in the resting system, and the time now defined being appropriate to the resting system we call it 'the time of the resting system.'[9]"

Albert Einstein believed he had a right to plagiarize, if he could put a new spin on an old idea.

He asserted this "privilege" in 1907: "It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I believe I am entitled to leave out a thoroughly pedantic survey of the literature, all the more so because it is hoped that these gaps will yet be filled by other authors, as has already happened with my first work on the principle of relativity through the commendable efforts of Mr. Planck and Mr. Kaufmann.[10]"

D. F. Comstock wrote, in 1910, in his popular exposition on the theory of relativity: "The whole principle of relativity may be based on an answer to the question: When are two events which happen at some distance from each other to be considered simultaneous? The answer, 'When they happen at the same time,' only shifts the problem. The question is, how can we make two events happen at the same time when there is a considerable distance between them.

Most people will, I think, agree that one of the very best practical and simple ways would be to send a signal to each point from a point halfway between them. The velocity with which signals travel through space is of course the characteristic 'space velocity,' the velocity of light.

Two clocks, one at A and the other at B, can therefore be set running in unison by means of a light signal sent to each from a place midway between them.

Now suppose both clock A and clock B are on a kind of sidewalk or platform moving uniformly past us with velocity v. In Fig. 1 (2) is the moving platform and (1) is the fixed one, on which we consider ourselves placed. Since the observer on platform (2) is moving uniformly he can have no reason to consider himself moving at all, and he will use just the method we have indicated to set his two clocks A and B in unison. He will, that is,

send a light flash from C, the point midway between A and B, and when this flash reaches the two clocks he will start them with the same reading.

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To us on the fixed platform, however, it will of course be evident that the clock B is really a little behind clock A, for, since the whole system is moving in the direction of the arrow, light will take longer to go from C to B than from C to A. Thus the clock on the moving platform which leads the other will be behind in time.

Now it is very important to see that the two clocks are in unison for the observer moving with them (in the only sense in which the word 'unison' has any meaning for him), for if we adopt the first postulate of relativity, there is no way in which he can know that he is moving. In other words, he has just as much fundamental right to consider himself stationary as we have to consider ourselves stationary, and therefore just as much right to apply the midway signal method to set his clocks in unison as we have in the setting of our 'stationary clocks.' 'Stationary' is, therefore, a relative term and anything which we can say about the moving system dependent on its motion, can with absolutely equal right be said by the moving observer about our system.

We are, therefore, forced to the conclusion that, unless we discard one of the two relativity postulates, the simultaneity of two distant events means a different thing to two different observers if they are moving with respect to each other.

The fact that the moving observer disagrees with us as to the reading of his two clocks as well as to the reading of two similar clocks on our 'stationary' platform, gives us a complete basis for all other differences due to point of view.

A very simple calculation will show that the difference in time between the two moving clocks is [The time it takes light to go from C to B is ½ / (V - v) and the time to go from C to A is ½ / (V + v).

The difference in these two times is the amount by which the clocks disagree and this difference becomes, on simplification, the expression given above. - Notation found in the original.]

1/V β / (1 - β 2 ) where l = distance between clocks A and B; v = velocity of moving system; V = velocity of light; β = v / V. The way in which this difference of opinion with regard to time between the moving observer and ourselves leads to a difference of opinion with regard to length also may very easily be indicated as follows:

Suppose the moving observer desires to let us know the distance between his clocks and says he will have an assistant stationed at each clock and each of these, at a given instant, is to make a black line on our platform. He will, therefore, he says, be able to leave marked on our platform an exact measure of the length between his clocks and we can then compare it at leisure withy any standard we choose to apply.

We, however, object to this measure left with us, on the ground that the two assistants did not make their marks simultaneously and hence the marks left on our platform do not, we say, represent truly the distance between his clocks. The difference is readily shown in Fig. 2, where M represents the black mark made on our platform at a certain time by the assistant at A, and N that made by the assistant at B at a later time. The latter assistant waited, we say, until his clock read the same as clock A, waited, that is, until B was at B'; and then made the mark N. The moving observer declares, therefore, that the distance MN is equal to the distance AB, while we say that MN is greater than AB. Again it must be emphasized that, because of the first fundamental postulate, there is no universal standard to be applied in settling such a difference of opinion. Neither the standpoint of the 'moving'

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observer nor our standpoint is wrong. The two merely represent two different sides of reality. Any one could ask: What is the 'true' length of a metal rod? Two observers working at different temperatures come to different conclusions as to the 'true length.' Both are right. It depends on what is meant by 'true.' Again, asking a question which might have been asked centuries ago, is a man walking toward the stern of an east bound ship really moving west? We must answer 'that depends' and we must have knowledge of the questioner's view-point before we can answer yes or no.

A similar distinction emerges from the principle of relativity. What is the distance between the two clocks? Answer: that depends. Are we to consider ourselves with the clock system when we answer, or passing the clocks with a hundredth the velocity of light or passing the clocks with a tenth the velocity of light? The answer in each case must be different, but in each case may be true.

It must be remembered that the results of the principle of relativity are as true and no truer than its postulates. If future experience bears out these postulates then the length of the body, even of a geometrical line, in fact the very meaning of 'length,' depends on the point of view, that is, on the relative motion of the observer and the object measured. The reason this conclusion seems at first contrary to common sense is doubtless because we, as a race, have never had occasion to observe directly velocities high enough to make such effects sensible. The velocities which occur in some of the newly investigated domains of physics are just as new and outside our former experience as the fifth dimension.[11]"

Citing Comstock's above quoted work, Robert Daniel Carmichael wrote, in 1912: "§ 9. Simultaneity of Events Happening at Different Places. - Let us now assume two systems of reference S and S' moving with a uniform relative velocity v. Let an observer on S' undertake to adjust two clocks at different places so that they shall simultaneously indicate the same time. We will suppose that he does this in the following very natural manner: [Compare Comstock, Science, N. S., 31 (1900) [sic]: 767-772. - Notation found in the original.]

Two stations A and B are chosen in the line of relative motion of S and S' and at a distance d apart. The point C midway between these two stations is found by measurement.

The observer is himself stationed at C and has assistants at A and B. A single light signal is flashed from C to A and to B, and as soon as the light ray reaches each station the clock there is set at an hour agreed upon beforehand. The observer on S' now concludes that his two clocks, the one at A and the other at B, are simultaneously marking the same hour; for, in his opinion (since he supposes his system to be at rest), the light has taken exactly the same time to travel from C to A as to travel from C to B. Now let us suppose that an observer on the system S has watched the work of regulating these clocks on S'. The distances CA and CB appear to him to be ½ d (1 - β 2 )1/2 instead of ½ d. Moreover, since the velocity of light is independent of the velocity of the source, it appears to him that the light ray proceeding from C to A has approached A at the velocity c + v, where c is the velocity of light, while the light ray going from C to B has approached B at the velocity c - v.

Thus to him it appears that the light has taken longer to go from C to B than from C to A by the amount ½ d (1 - β 2 )1/2 / ( c - v ) - ½ d (1 - β 2 )1/2 / ( c + v ) = vd (1 - β 2 )1/2 / ( c2 - v2 ) .

But since β = v / c the last expression is readily found to be equal to

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( v / c2 ) [ d / (1 - β 2 )1/2 ] .

Therefore, to an observer on S the clocks on S' appear to mark different times; and the difference is that given by the last expression above.

Thus we have the following conclusion: THEOREM VII. Let two systems of reference S and S' have a uniform relative velocity v. Let an observer on S' place two clocks at a distance d apart in the line of relative motion of S and S' and adjust them so that they appear to him to mark simultaneously the same time. Then to an observer on S the clock on S' which is forward in point of motion appears to be behind in point of time by the amount ( v / c2 ) [ d / (1 - β 2 )1/2 ] , where c is the velocity of light and β = v / c (MVLR).

It should be emphasized that the clocks on S' are in agreement in the only sense in which they can be in agreement for an observer on that system who supposes (as he naturally will) that his own system is at rest-notwithstanding the fact that to an observer on the other system there appears to be an irreconcilable disagreement depending for its amount directly on the distance apart of the two clocks.

According to the result of the last theorem the notion of simultaneity of events happening at different places is indefinite in meaning until some convention is adopted as to how simultaneity is to be determined. In other words, there is no such thing as the absolute simultaneity of events happening at different places.[12]"

Albert Einstein, who sought a "new point of view" from plagiarizing Poincaré's 1900 clock synchronization method, plagiarized Comstock (1910) and Carmichael (1912), in Einstein's book of 1916: "THE RELATIVITY OF SIMULTANEITY UP to now our considerations have been referred to a particular body of reference, which we have styled a 'railway embankment.' We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. I. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train.

Then every event which takes place along the line also takes place at a particular point of the train.

Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length AB of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance AB on the traveling train. Just when the flashes [As judged from the embankment. - Notation found in the original.] of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes

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of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.

We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance w per second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance w relative to the railway line in a time which is equal to one second as judged from the embankment.

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.[13]"

This chapter "by Einstein" has often been criticized as being "absolutist" and "Lorentzian".

One understands why it was written in the fashion that it was, when one reads the source material, which Einstein plagiarized to produce it.

References and Notes 1. W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in 1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39, Number 3, (June, 2001), pp. 211-230; URL: http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf . Lorentz acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the "Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig, (1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica, Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars, (1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity, Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1, 1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122.

2. H. Poincaré, "La Mesure du Temps", Revue de Métaphysique et de Morale, Volume 6, (January, 1898) pp. 1-13; The Value of Science, The Science Press, New York, (1907), pp. 26-36.

3. H. Poincaré, Electrité et Optique, Gauthier-Villars, Paris, (1901), p. 530.

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4. H. Poincaré, "La Théorie de Lorentz et le Principe de la Réaction", Archives Néerlandaises des Sciences Exactes et Naturelles, Series 2, Volume 5, (1900), pp. 252-278, at 272-273.

5. A. Einstein, "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie", Annalen der Physik, Volume 20, (1906), pp. 627-633, at 627.

6. J. Stachel, Ed., The Collected Papers of Albert Einstein, Volume 2, Princeton University Press, (1989), pp. xxiv-xxv.

7. H. Poincaré, Science and Hypothesis, Dover, New York, (1952), p. 90.

8. H. Poincaré's St. Louis lecture from September of 1904, La Revue des Idées, 80, (November 15, 1905); "L'État Actuel et l'Avenir de la Physique Mathématique", Bulletin des Sciences Mathématique, Series 2, Volume 28, (1904), p. 302-324; English translation, "The Principles of Mathematical Physics", The Monist, Volume 15, Number 1, (January, 1905), pp. 1-24.

9. The Principle of Relativity, Dover, New York, (1952), pp. 38-40. In order to maintain conformity with the original German text, necessary corrections have been made, as indicated by bracketed text.

"Resting" has been substituted for "stationary", in conformity with the original German text.

10. A. Einstein, "Ueber die vom Relativitaetsprinzip gefordterte Traegheit der Energie", Annalen der Physik, Series 4, Volume 23, (1907), pp. 371-384, at 373.

11. D. F. Comstock, "The Principle of Relativity", Science, New Series, Volume 31, Number 803, (20 May 1910), pp. 767-772, at 768-770.

12. R. D. Carmichael, "On the Theory of Relativity", The Physical Review, Volume 35, Number 3, (September 1912), pp. 153-176, at 170-171; republished in "The Theory of Relativity", Mathematical Monographs No. 12, John Wiley & Sons, New York, (1914/1920), pp. 40-41.

13. A. Einstein, "The Relativity of Simultaneity", Relativity: The Special and the General Theory, Chapter 9, Methuen, London, (1920), pp. 30-33.

----[A presentation of the author is given at the end of the first of his previous two papers published in this same issue of Episteme] cbjerknes@attbi.com

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[Spettacolare immagine della grande galassia a spirale NGC 1232 della costellazione Eridano.

La galassia è grande circa il doppio della nostra Via Lattea e dista 100 milioni di anni luce.

La regione centrale contiene stelle vecchie rossastre mentre i bracci a spirale sono popolati di giovani stelle blu e di regioni in cui nascono nuove stelle.

Sulla sinistra c'è anche una piccola galassia compagna. L'immagine è basata su tre fotografie in ultravioletto, blu e rosso ed è stata realizzata nel 1998 con il VLT (Very Large Telescope) dell'ESO (Osservatorio Europeo del Sud). Dell'ESO fanno parte dieci paesi fra cui l'Italia.]

La natura del tempo (Propagazioni super-luminali - Paradosso dei gemelli - Teletrasporto) (a cura di Franco Selleri) (Edizioni Dedalo, Bari, 2002) "I fisici di Copenhagen e di Göttingen non si limitarono ad enunciare le loro tesi anticausali ed antirealistiche, ma crearono una sequela impressionante di veri e propri <<teoremi di impossibilità>>" (Franco Selleri)

Attenendosi a una formula ormai consueta, Episteme ritiene di fare cosa utile ai suoi lettori di lingua italiana con il presentare un'opera che esce nelle librerie più o meno nello stesso periodo di questo numero "speciale" della rivista, e che al pari di esso è testimone di quel "discomfort towards the actual establishment's philosophy of Nature and of Science", di cui si diceva nelle righe di introduzione al capitolo dedicato alla "fisica alternativa" on line.

Le "analogie" naturalmente non finiscono qui, e vanno dagli argomenti trattati al fatto che tra gli autori ve ne sono di già ben noti ed apprezzati a chi frequenta la nostra pubblicazione, senza tacere la circostanza (già lamentata nella "Lettera dell'editore..." con cui si apre il presente volume) che talora le argomentazioni critiche contro la "relatività", e "derivazioni"

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(siffatti sono da ritenersi invero, sia pure in maniera indiretta, taluni sviluppi della fisica teorica del XX secolo), non appaiono interamente "cristalline" - ciò che, come si è affermato nella citata "Lettera", nulla toglie peraltro al generale interesse, e soprattutto alle finalità, del complesso dell'opera. Per esempio, alcune considerazioni sul paradosso dei gemelli, sull'effetto Sagnac, etc., che "confondono" trattamento delle accelerazioni in relatività speciale (in assenza cioè di gravitazione, vale a dire di curvatura dello spazio-tempo) e relatività generale (il collegamento viene effettuato - secondo una procedura del resto assai comune in simili casi - attraverso il "principio di equivalenza", che è in realtà assai più "delicato" delle sue enunciazioni-utilizzazioni "ingenue"), oppure discutono in maniera implicita, sebbene in un contesto relativistico, "oggetti fisici" mediante le "categorie ordinarie" di spazio e di tempo, il che non può naturalmente non ingenerare equivociapparenti "contraddizioni interne" (tra i responsabili della poco brillante situazione descritta bisogna annoverare per la verità gli stessi fisici "ortodossi", Einstein in primis, del quale non sarebbe un totale autentico "paradosso" sostenere che non avesse "compreso" appieno le "esigenze" della sua propria teoria...).

Ma lasciamo che sia direttamente il libro in oggetto a presentarsi, riportando alla fine, secondo il nostro solito modo, l'intero suo sommario.

----La comprensibilità del tempo nei processi naturali è stata messa fortemente in dubbio dalla fisica del Novecento, soprattutto a causa delle relazioni di indeterminazione di Heisenberg e del relativismo filosofico che ha accompagnato l'affermarsi delle teorie di Einstein. Gli sviluppi recenti presentati in questo libro, permettono il recupero di una descrizione soddisfacente del tempo e del cambiamento.

In base a quanto sosteneva Popper, la realtà del tempo e del cambiamento è il punto cruciale della scienza. Gli autori dei saggi qui raccolti concordano con lui e ognuno di essi discute un diverso problema riguardante la natura del tempo in modo semplice e chiaro. Numerosi sono gli argomenti trattati: la relazione di indeterminazione energia-tempo e lo scontro EinsteinBohr; il tempo medio di vita delle particelle instabili; il teletrasporto in tempo zero da Star Trek alla meccanica quantistica; la trattazione relativistica del tempo e la questione della simultaneità; il misterioso effetto Sagnac e le sue implicazioni sul tempo; il paradosso dei gemelli secondo la relatività del tempo e secondo una teoria alternativa basata sulla simultaneità assoluta; i segnali "super-luminali". Gli autori offrono inoltre risposte a tanti interrogativi come ad esempio: un orologio su un aereo in volo segna il tempo più lentamente? Il campo gravitazionale terrestre influenza il tempo segnato dagli orologi atomici sui satelliti in orbita? Il tempo futuro è predeterminato come sostiene l'interpretazione ortodossa della teoria della relatività? Se lo è, come è possibile la nostra evidente libertà di scelta? È possibile sfruttare i segnali super-luminali per inviare messaggi verso il tempo passato? L'opera si rivolge ad un pubblico ampio con un interesse scientifico, ma anche a studenti e studiosi.

----Introduzione, Franco Selleri La relazione di indeterminazione energia-tempo, Augusto Garuccio Introduzione - Che cos'è l'azione? - Quanto è piccolo il quanto d'azione - Le relazioni di indeterminazione e il dibattito sulla meccanica quantistica - Uno scontro tra giganti - Come interpretare la relazione energia-tempo - Regole di indeterminazione, causalità, descrizione

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spazio-temporale degli eventi quantistici Il teletrasporto?, Milena D'Angelo Reversibilità e irreversibilità del tempo in Meccanica Statistica, Giuseppe Gonnella Il principio dell'aumento dell'entropia - Il punto di vista molecolare e la meccanica statistica Il teorema H - Le obiezioni di Loschmidt e Zermelo - L'entropia di Boltzmann - Il tempo e l'universo As time goes by... - Le antiparticelle e la freccia del tempo, Vincenzo Berardi Viaggiare nel tempo - Le antiparticelle - La scoperta del positrone - L'interpretazione di Feynman - Indietro nel tempo? - Epilogo Ritardo degli orologi in moto, Michele Barone Effetti al secondo ordine di v/c - Convenzione o Proprietà della Natura? - Violazioni dell'invarianza delle trasformazioni di Lorentz Il paradosso dei gemelli, Romano Manaresi Il viaggio - Il paradosso - Il senso comune - TRR, Il principio di relatività - Realtà e apparenza - La (non) soluzione di TRR - Inversione di marcia - TRG, Il principio di equivalenza - Il potenziale gravitazionale - La soluzione di TRG - Velocità o accelerazione? Spiegazione causale e spiegazione strutturale - Effetto gemelli senza accelerazioni - La previsione di TRR - Lo spazio-tempo di Minkowski - Nessun conflitto - Le Trasformazioni Inerziali - L'effetto gemelli <<assoluto>> - Impossibilità di individuare lo spazio assoluto Conclusioni Il futuro è predeterminato?, Nicola Russo La teoria della relatività e il tempo - Einstein-Parmenide e il libero arbitrio - Le teorie equivalenti alla relatività - Le trasformazioni inerziali - La realtà ritrovata Gli orologi della teoria relativistica, Ludwik Kostro La parola "orologio" nel linguaggio ordinario e in quello scientifico - La dilatazione del tempo nei sistemi di riferimento in moto e nei campi gravitazionali - Esempi di processi periodici che anticipano anziché ritardare - Processi naturali la cui esistenza dipende interamente dal campo gravitazionale - Processi fisici la cui esistenza non dipende dal campo gravitazionale - Processi fisici parzialmente influenzati dal campo gravitazionale - Gli orologi e la teoria della gravitazione di Newton - Relatività generale e orologi a sorgente di energia gravitazionale - Quali orologi considerava Einstein nella sua teoria? - Conclusioni Il tempo sui satelliti del GPS e l'effetto Sagnac, Francesca Intini La misura del tempo - Il Sistema di Posizionamcnto Globale - Il tempo del GPS - Come funziona - Fattori di correzione - Le correzioni relativistiche - La correzione di Sagnac L'effetto Sagnac - Conclusioni Simultaneità relativistica, Massimo Brighi Cosa accade, adesso, su Marte? - Simultaneità classica - Sistemi di riferimento ed eventi - Lo spazio-tempo di Minkowski - Simultaneità relativistica (la soluzione di Einstein) Simultaneità, sincronizzazione e velocità di sola andata - La velocità della luce - Trasporto di orologi - Simultaneità non standard - Proprietà della relazione di simultaneità - Simultaneità assoluta - Il teorema di Malament - Simultaneità in sistemi di riferimento accelerati e relatività generale - Conclusioni

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I FLOP nella trattazione relativistica del tempo, Rocco Vittorio Macrì Il concetto di Falsificatore Logico Potenziale (FLOP) - La metafisica operativoverificazionista e i FLOP del Gedankenexperiment - La <<nave di Galileo>> e i FLOP nei fondamenti relativistici - Considerazioni conclusive sui razzi vettori della TRS Esperimenti <<super-luminali>>: una panoramica, Erasmo Recami Introduzione - Relatività Speciale ed Estesa - La situazione sperimentale E' possibile inviare messaggi verso il passato?, Franco Selleri Segnali superluminali e paradosso causale - La regola reinterpretativa di Recami - Il tempo non può essere capovolto - Trasformazioni fra sistemi inerziali - Le trasformazioni equivalenti - La relatività della simultaneità resta esclusa - Solo la simultaneità assoluta è possibile

----[Franco Selleri insegna fisica teorica all¹Università di Bari. È autore di alcuni libri pubblicati in una decina di lingue e di numerosi articoli scientifici che trattano di fisica delle particelle e di fondamenti della teoria dei quanti e della relatività.] ordini@edizionidedalo.it http://www.edizionidedalo.it/