The Archaeologist of God

Francis BALDEWYNS Foreword Observé Galiléeminkowsk

The Archaeologist of God On the 100th anniversary of the experimental confirmation of Albert Einstein's General Relativity (29th May 1919) and the World Year of Physics

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Editions du Prof

Francis Baldewyns

The Archaeologist Of God First published in 2005 on the occasion of the 50th anniversary of Albert Einstein’s death (March 14, 1879-April 18, 1955) and the World Year of Physics, this book has been completed and digitally edited in 2015, on the occasion of the 60th anniversary

Editions du Prof

Foreword

The archaeologist of God was published in March 2005 at Éditions du Prof, and registered under the reference: D / 2005/9789/01 at the Royal Library.

"La Libre" well-known Belgian newspaper qualified my book "eclectic"

Photo taken during the summer of 1933 during the last and long stay of Einstein and his wife Elsa in Belgium.

They pose here in front of the “Villa Savoyarde” at Coq-Sur-Mer on the Belgian Coast.

The villa still exists at No. 5 Shakespeare Avenue.

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Why this title?

Science is excavation done in God

Victor Hugo Some science takes away from God, but a lot brings it back

Louis Pasteur God does not play dice

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Foreword While I was still at the "primary school" of Engis, an industrial village located in Belgium, halfway between Liège and Huy, our teacher asked us to listen to the radio and read the newspapers, as far as possible.

The aim of this lesson was to find out the picture of an important character…

A neighbour gave me a newspaper «La Dernière Heure» of April 19, 1955. On the front page, we could see the photo of Doris Day, visiting Paris, before spending a week at the Cannes Film Festival. The Hungarian war was going to start, and we learned a Mr Nagy had been expelled from the Presidency of the Hungarian Council.

Finally, Prince Albert of Liege, the future Albert the Second, King of Belgium, also had his picture since he became the godfather of Henry, the newborn son of the Grand Duchess Josephine of Luxembourg.

Despite the request of my teacher, I thought that the European visit of Doris Day was the main event, as I was listening to his songs all day long, including "Whatever Will Be" she sang in Hitchcock's movie: «The Man Who Knew Too Much».

No, it was not her, but this hairy man named Einstein. The article explained that, after fleeing Nazi Germany, he had discovered a formula that had allowed the creation of an atomic bomb in the United States. Then he became a great pacifist.

I did not understand at this time that he could be a pacifist after providing the world with a formula explaining how this one could self-destruct.

Our teacher explained to us that the human being does not always have control of what he discovers: the diabolical applications, for example, like the atomic bomb, are not effectively wanted by the scientists whose theories come from.

No man of science was so famous during his lifetime and after his death, the newspaper specified.

In 1955, already, I felt very attracted to science. Everything I heard and read about Einstein was no stranger to that. However, I was still unable to understand what he found out.

My father, concerned with my education, bought Paris Match (Picture below), Le Soir and La Libre Belgique on April 19, 1955. I present them to you after the one of «La Dernière Heure» my former neighbour’s newspaper I have kept for half a century.

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Einstein's profession of faith The 1958 Exhibition was close. It helped me discern the fullness of happiness in acquiring knowledge that repels unknown and mystery.

Although I come from a modest family, I never heard my parents complain; they had confidence in life that still touches me today when I remember those happy moments I shared with them.

Pampered, yes, but not force-fed. I was four or five years old when my father, who was with me in a toy store, was surprised by the frugality of my choices.

"A lead soldier, only that!" he said. This lead soldier enjoyed and filled me. It made me happy for a few years. Still, I had some quirks. In 1957, two years after Einstein's death, I remember having this silly idea for a 12-year-old boy: getting a statuette. The problem is that it was not for sale anywhere.

My parents did not consider it as an eccentricity, and they searched for it, to no avail. It was apparently not, indeed, a sudden and thoughtless desire, if you look over my statuette collection, you’ll understand that the third dimension always attracted me. At the beginning of the new millennium, forty-five years later, I filled my frustration of the fifties and bought two statuettes of the scholar, including the left one in the Jewish area of Prague.

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Einstein's profession of faith "The time machine" of Herbert George Wells was, at that time, the science fiction novel that fasci nated me the most, and this film gave me a vision of what could be a trip in the past, but also the impossible return to the future.

Education-minded Einstein is here with (From right to left) Heinrich Becker, Minister of Education in Prussia from 1925 to 1930, H.G. Wells (the English science fiction writer) and Paul Löbe, President of the Reichstag from 1924 to 1932

A clip from «The Time Machine» (G.Pal, 1960)

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Einstein's profession of faith

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«Tot est r’latef» said Marcel Philippot, with the accent of Liege, what it means in French «Tout est relatif». He was my science teacher at the « Athénée de Huy » and sometimes wanted to look like Einstein. «Everything is relative» indeed.

He spoke to us a lot about the scientist whose life had made clear his concern to experience the mystery.

Einstein wondered what would happen if he could ride a ray of light, and he explained what he called "the Special Relativity" what really fascinated me.

We know, thanks to him, that space and time are not independent of each other, and that, in order to be able to determine an "event" (2) we must provide, in addition to the three spatial dimensions, the time dimension.

Actually, the future and the past are separated by this finite lapse of time which depends on the distance between the observer and the observed body, but also on their relative velocity.

Marcel Philippot during a lesson on Electromagnetism

2 Voir

glossary.

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Einstein's profession of faith This is probably because already at that time, I discerned the fullness of happiness in the acquisition of knowledge that makes recede in the unknown and mystery, that the study of the existent seemed to me an inexhaustible deposit. To such an extent that this notion of spacetime, extrapolated to the human, was really part of my own life, not that I wanted to do things quickly, but I did not see why I should embarrass myself with the superfluous and should waste this precious fourth dimension by burdening myself with a thousand other constraints adults named "properties" or "assets."

I was never psychoanalyzed, but I do not exclude to be. And it is possible that my passion for knowledge comes from a certain flight from the boredom and anguish that threatened my teenager life. I distanced myself from materialistic values.

When I was a child, death was for me only the inflexion point that separates life on earth and eternity, that means a distant situation I would "live" like a prolonged sleep. The material needs were unknown to me, although limited, and my most important aim was to use fully the present time without worrying about the future.

The present, I saw it as the net of a fisherman I had to throw into the promising waters. I was happy and felt rich to have the opportunity to conquer these inexhaustible deposits that are: works of art, poetic imagination, history of humanity, scientific knowledge. This pleasure satisfied my mind and made me lose my awareness of the boredom that threatened me.

It is, therefore, not surprising that less than ten years after Einstein’s death, I was tempted by the job of the researcher, because it seemed to guarantee this renewed flow of knowledge to which I aspired so much.

Few men were as famous in their lifetime as Albert Einstein, and he is still so fifty years after his death for accomplishing one of the greatest revolutions in the history of science and freelancing the adventure of the mind. Never before, progress in science and history of the world had been so closely linked: thanks to Einstein, physics became an essential dimension of the history of societies. He was not only a great physicist and mathematician, but also a philosopher, a pacifist and a humanist, a poet and a musician, a being full of kindness and humour, a science artist, genius creator, but also still governed by a number of deeply rooted values and beliefs.

But God, in my title, what is he doing there?

And how, above all, will science bring us closer to the Creator, when it is supposed to be all-powerful and to have been the basis of the desertification of churches in the West? Did it not manage to explain what the religious called "mysteries?"

This is the main objective of this book: to show how Albert Einstein and other contemporaries have profoundly changed the perception of the cosmos.

Certainly, the God of the Bible is mistreated by the discoveries of these men, and the iconography of the Roman and Florentine frescoes becomes a fiction comic really far from the God to whom the title of this book alludes.

Are the sciences not what Victor Hugo expressed in his time?"Sciences are excavations in God" and did not Louis Pasteur say?"A little science takes away from God, but many bring it back."

The purpose throughout this book is clear: to demystify Einstein and other great scholars who counted for him and for whom he was a fundamental ally.

Professor of Mathematics and Science, I sincerely hope to challenge younger generations by suggesting a more judicious positioning in our Universe full of mysteries, in the humble, respectful and passionate manner of archaeologists.

This questioning was also responsible for my exceptional turnaround when I decided to leave my White collar existence, crushed by the utilitarian necessities of the modern enterprise, to reconnect with intelligibility. I moved away from the ruined activities of mind and decided to become a teacher of hopes.

At forty-eight years old, I presented and succeeded in "Aggregation in chemical sciences" at the University of Liège.

As I wrote in my essay, The End of the Machine Men: "Although my existence was not a long calm river, I could, at my pleasure, regulate the flow of its stream and draw the way of its meanders. I have no regrets. While keeping the river metaphor, after crossing some strong torrential rivers that made me drift, and after experiencing several storms, the last of which might have been fatal, my boat entered a port so radiant that I dropped anchor there. And since then, my soul is peaceful.

My new home port was the Sart Tilman Institute of Chemistry (photo attached). Since then, I have filled the intellectual vacuum that frustrated me so much.

This book is part of my approach. Through the journey of Albert Einstein, his profession of faith and his discoveries, we will try to get closer to our Creator. Anxious not to alter the message to the man we commemorate in this book, whenever I have the opportunity, I will quote as precisely as possible the sentences he has pronounced or written. Among these sentences, I will first choose the one that best 15

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Einstein's profession of faith expresses the psychology of the character, but also my own behaviour face to the necessities of science teaching: "In the interest of clarity, it seemed to me inevitable to repeat myself often, without caring less about to give my exposition an elegant form; therefore, I followed the opinion of the brilliant theoretician , L. Boltzmann:"to leave the concern for elegance to the tailors and shoemakers."

Every time I approach an important person in history, and I am inevitably led to study his environment, his means, tools, aspirations, goals and philosophy. In the special case of Victor Hugo, in 2002, during the commemoration of the bicentenary of his birth, it was unthinkable that I did not refer to his wives, in the general sense of the term: his wife, his daughters and his mistresses. For Einstein, could I have avoided formulas and mathematical developments? No, I do not think so: a biography of Victor Hugo, without women, is like a biography of Einstein without mathematics; it's like a kiss without a moustache or a soup without salt.(personal opinion).

In order not to burdensome chapters, I chose to give the mathematical explanations in the appendix which is reserved for them. On the other hand, the main scientific words that can pose some difficulties are highlighted throughout the text and defined in the glossary at the end of the book. I have also set aside a biographical appendix for the Nobelist scientists who counted for Einstein and for whom they were important.

While wishing you a fruitful reading, may you also, dear readers, take part in the pleasure that was mine to accompany the archaeologist of God from 1879 to 1955.

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Einstein's profession of faith First chapter Einstein's profession of faith "It is my own profession of faith as well" A great gift from heaven is to belong to the category of those who can devote the best of their energy to the observation and exploration of objective reality. And I'm really happy to have had this opportunity that allows the man to depend less on the circumstances of fate or his neighbour. This independence must not make us forget our duties to all humanity, past, present or future.

Our situation on Earth may seem strange: each one of us has a brief stay there, without having wanted it or asked for it, without knowing the why or the how. From our everyday life, we only learn that we are there for others, for those we love and for those whose destiny is related to ours. I am often troubled by the idea that my own life is based upon the work of my fellow men, and I am aware of having a great debt to them.

I do not believe that our will is free. The words of Schopenhauer "Man can do what he wants, but he cannot want what he wants" accompany me in all the circumstances of life and reconcile me with the behaviour of others, even when they hurt me. This awareness that our will is not free helps me not to take seriously those who claim to decide and act, and not to lose my good humour.

I have never looked for fortune and luxury, and even, I despise them rather. My passion for social justice has often opposed me to other men, as has my refusal of any obligation or dependence that I did not consider absolutely necessary. I have the greatest regard for the individual and an invincible disgust for violence and fanaticism. All of this turned me into a passionate pacifist and anti-militarist.

I regret all nationalism, even mere patriotism.

I have always considered unfair and dangerous all the privileges based upon social status and property, as well as all excessive worship of the personality. I adhere to democratic ideals without, however, ignoring the weaknesses of democracy as a method of government. For me, the first goals that a state must pursue are social justice and the economic protection of the individual.

You do not have to be a scientist or a high-flying physicist to be a disciple of this man who had the humility to say: Although in my everyday life, I am a loner, the awareness of belonging to the

silent community of those who struggle for truth, beauty and justice, prevents me from feeling lonely.

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Einstein's profession of faith Let us comment on the essential phrases of the scientist's profession of faith, but also the quotations of all those who have helped to clarify the origin of the cosmos, of man and of life in general.

As a scientist, I like this phrase because it specifies what the sciences are for me: an infinity of observations and experiences that are the only "ways in which nature stands out."Let us comment on the essential phrases of the scientist's profession of faith, but also the quotations of all those who have helped to clarify the origin of the cosmos, of man and of life in general.

The happiness to explor e the object ive reality Stuart Mill, who lived in the nineteenth century, wrote: "In a world, where so many subjects deserve our interest and are a source of pleasure, and where so many other ones need to be corrected and improved, anyone with the necessary minimum of moral and intellectual capacities, is capable of leading a life that can be described as enviable"(3).

A century later, Albert Einstein wrote in his "Profession of Faith": "It is a gift from heaven to belong to the category of those who can devote the best of their energy to observation and exploration of objective reality. And I'm really happy to have had this opportunity that allows the man to depend less on the vagaries of destiny on his neighbour. "(4) The wonder i n front of the secr ets of the Cosmos The technique is illusory in relation to infinity. Pure science, which gradually demystifies the mysteries of the cosmos, is self-sufficient. Uncontaminated science is freer than all religions put together, for it has no limit in its freedom to discover and be amazed at the phenomena of the cosmos.

Pure science allows us to support the infinite desire and no longer imprisons us in the narrow and insatiable utilitarianism, but opens the way for more and more objects of contemplation.

At the end of his "Profession of Faith," Einstein shares his happiness with us: "It is enough for me to be able to marvel at these secrets and humbly to attempt to capture by the mind a pale picture of the sublime structure of everything, which is " In the twentieth century, when science seems always powerful - I should rather say the technique emanating from it - philosophy seems to me more than ever essential for the awakening of mankind.

The scientific body, on the other hand, is not what is shown, but the result of theoretical construction, a methodological hypothesis. "Scientific representation," said Heidegger, "can never encircle the being of nature, because the objectivity of nature is only, from the beginning, a way in which nature stands out."

3 Mill, JS, Utilitarianism-Test on Bentham, Quadrige PUF, Paris 1998, p.45-46 4 Sugimoto, K., Albert Einstein, Illustrated Bibliography, Belin, traduct. French, 1990, p.113 5 From the Greek monos, "one" - This is the philosophical theory according to which the universe and the spirit are one: the spirit belongs to the universe, which determines it. Nothing goes beyond the universe.

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Einstein's profession of faith Einstein has the same God as Spinoza The fourth sentence of Einstein's "Profession of Faith," to which we often refer, calls on the mystery: "The most beautiful and profound experience man can make is that of mystery. The one who does not experience it seems to me to be, if not a dead person, at least a blind man.

It is on the mystery religions are founded, and every serious activity of art or science.

Realizing that behind all that we can discover, there is something that escapes our understanding, and whose beauty and sublimity can only reach us indirectly, is the feeling of sacred, and in that sense, I can say I am religious. " This sentence contains all the secret of the happiness of knowledge, especially when it makes us aware of the infinite. The more we study, the more we discover, but the more we see open abysses of the unknown.

"Einstein claimed to believe in the God of Spinoza, who reveals himself in the orderly harmony of what exists, and not to a God who cares about the deeds and destiny of humans."

(6) Whether God does not play dice, as Einstein said, or He plays, the main point in this New York Times article is that he wanted to express a feeling of cosmic solidarity. God represents for him a transcendence. And all the great physicists of the twentieth century, Bohr and Schrödinger, among others, have also expressed this sense of belonging to something beyond them.

Steven Weinberg asked himself: "But what difference does it make if we say God instead of Order or Harmony except it allows us to avoid the accusations of atheism? Of course, everyone is free to talk about "God" in this sense, but it seems to me that it is a less false concept than an unimportant one." (7) « Bu t E in s te in a ls o h as h is re sp on sibility in the bom b» When the Nazis came to power (Jan. 30, 1933), Einstein was in America, but he returned to Europe from early March. A few hours before his departure, he attended a reception at the Waldorf-Astoria and spoke in public about the new German regime, announcing that he would not return to a country that respected neither the liberty of citizens nor freedom of speech and research. Einstein landed in Antwerp and went to Brussels, to the German embassy, to renounce formally German nationality. Already, at sea, he had sent his resignation to the Berlin Academy of Sciences, as Planck had asked him after his statements on the German political situation. He went for a while to Coq-sur-Mer, a Belgian seaside resort.

Alas, "The Bomb Question" took place. Einstein, yet a bitter pacifist, brought a decisive impetus to its construction. The letter he wrote to President Roosevelt on 2 August 1939 bears witness to this: "In the last four months, thanks to the work of Joliot in France, and those of Fermi and Szilard in America, it has become possible to envisage a nuclear reaction without a large amount of uranium, which would generate a lot of energy and very many elements of radium type (...) This new fact could lead to the realization of bombs (...) A single bomb of this type, transported by a ship and exploding in a port, could destroy all the installations and a part of the surrounding territory (...) In front of this situation, you may wish to have permanent contact between the government and the group of physicists working in America on the chain reaction."(8) Thus, after his demonstration that energy is equal to mass multiplied by the square of the speed of light, and without really having wished to be, Einstein was named as the coresponsible for the instructions of Hiroshima and Nagasaki, whose announcement affected him deeply, and made him regret having written to Roosevelt.

Einstein became an outspoken opponent of any pursuit of nuclear experimentation, and he continued to struggle to prevent the use of atomic weapons. In 1946, he became president of the Emergency Committee of Atomic Scientists and in 1948 in his "Message to Intellectuals" he made the following appeal: "Man has not succeeded in creating forms of political and economic organization, which would guarantee peaceful coexistence between 6 "Interview" in the New York Times of April 25, 1979.

7 Weinberg, S., The Dream of an Ultimate Theory, Odile Jacob, Paris, 1997, p. 218 8 Sugimoto, K., op. cit., p. 173

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Einstein's profession of faith the researchers of all nations. It failed to build a system of international relations that would eliminate war and banish forever the terrible instruments of death capable of destroying whole populations. We, the researchers, whose tragic destiny has been to contribute to the creation of ever more effective methods of annihilation, must assign ourselves the essential duty to do everything in our power to prevent the use of these weapons with mortal purposes for which they were invented. What other more important missions could we have? What social goal could we be more expensive? " In 1952, he was proposed the presidency of the State of Israel to succeed Weizmann, who had just died, and who ensured it since the creation of the state in 1948. Einstein refused.

Actually, we must distinguish between science and techno-science, whose uses are often unpredictable. Einstein said he had not measured how far the extravagances could go. Science thus appears both as the base of humanity and a source of human distress when one wants to make it "useful."

Every day brings us new issues of concern. It is useless to recall them all, but most affect the happiness of men, which can be created and maintained only on the condition of being protected from the perils of nature (epidemics, earthquakes ...), and products from instrumental rationalism. The bomb is one of them.

These problems are fundamental, and they deserve our full attention because, as we see, they can even be caused by anyone who wants peace. So, let's commit ourselves without any career-minded thinking in the way of solutions. There is no cosy path; the actions of Green Peace and “Médecins sans Frontières” are admirable, but they will only be effective if more men and women prefer the power of love to the love of power.

Let's prepare future generations to enter the world of adults by refusing to be enslaved by the ravings of instrumental rationalism. Let us spiritualize men again by the "Know" and only consider products intended for the well-being of humanity. Let's not consider it as a set of consumers called to boost the economy but as the "Raison d'être" of everything that is manufactured in order to help it to overcome all the evils that threaten it.

Einstein's conclusion: "Man can do what he wants, but he cannot want what he wants."

Other scientists, Nobel's laureates in physics and chemistry, and other philosophers, all contemporaries, do not fear either to associate matter and spirit as being two inseparable pictures of the real (to make the part of chance and the necessity in evolution,) or even to announce that the dream of a single law of the universe aroused by monotheistic religions is taking shape.

Whether we are inclined to explain the world by opportunity or by the action of a spirit preexisting the origin of the universe, we accept the idea that the biosphere, and mankind, in particular, are composed of "a single substance diversely modified," as La Mettrie said, (9) but so variously modified that at a particular level of complexity, it finds itself capable of acting other than a specific machine actuated from outside. This matter has in it the capacity to modify or arrange the impulses that it receives.

Although Einstein's profession of faith has guided us positively in our reflection throughout this chapter, we can only conclude this chapter by opposing the absolute determinism that the scholar expressed in another sentence of his profession of faith: "I do not think our will is free. The words of Schopenhauer: "Man can do what he wants, but he cannot want what he wants" accompany me in all the circumstances of life and reconcile me with the behaviour of others, even when they hurt me. This awareness that our will is not free helps me not to take seriously those who claim to decide and act, and not to lose my good mood."

9 Physician and materialistic French philosopher of the Enlightenment, author of the Man-machine, who develops a mechanistic theory of the human body which has had a strong impact.9

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Absolute determinism, which Einstein defends as an ineluctable reality, does not, in his eyes, absolve a man from his actions. And everyone will appreciate how far he, and some other German scholars, could have refrained from offering their services to President Roosevelt to turn to the Nazis. The opposition between two ex-friends, Bohr and Heisenberg (see chapter six), will lead us to reflect on the essential choices we face in our lives.

Let us hope that this theory of absolute determinism does not lead us to accept the mechanical fatality that wants to impose a certain human technology. This one and its products will only have a sense if they contribute, according to definite categorical imperatives, to the humanization of the next civilization. We believe in the selfdetermination of humanity, which can do what it wants, but it can also want what it wants if it creates the necessary legal and social conditions.

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Illustrated Biography of Albert Einstein

Chapter Two Illustrated Biography of Albert Einstein Coming from a family of merchants, Albert was born in Ulm on March 14, 1879.

A year of events for physicists: Max Planck received a doctorate at the University of Munich, Max Von Laue was born on October 9, Otto Hahn On the 8th of March, the English physicist Maxwell dies at Cambridge.

Werner von Sieges builds the first electric locomotive, which is admired at the Berlin Industrial Exhibition. .

Ulm Town Hall, and view of the Danube.

His natal house disappeared in 1944 during an Anglo-American bombing.

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Illustrated Biography of Albert Einstein While Albert entered primary school in a Catholic school in Munich, at the age of 6, was born October 7, 1885, in Copenhagen, a certain Niels Bohr.

At the age of 10, in 1889, Albert entered the Luitpold Gymnasium in Munich; the year Gustave Eiffel built the tower that bears his name for the World Fair in Paris. It is also the year of the birth of a certain Adolf Hitler and Charlie Chaplin.

At the age of 16, in 1895, Albert failed the entrance examination of the Polytechnicum in Zurich.

Admitted to the second test, he follows only the courses that interest him, and he preferably works in the physics lab.

At the age of 17, in 1896, he received training as a professor of mathematics and physics. This is the year he meets Mileva Maric, his future wife. This is the year when Rรถntgen discovers x-rays.

At the age of 21, in 1900, Albert graduated as a mathematics teacher.

At the age of 23, in 1902, he found a job in Bern at the Federal Patent Office.

It was also the year of the birth of an illegitimate girl who will not survive.

The house Einstein occupied in Bern from 1903 to 1905 when he discovered his famous formula E = m.c 2

Laboratory of Zurich Polytechnic School where worked the student Einstein Translation of the commemorative plaque affixed to the house: "In this house, Albert Einstein created in the years 1903-1905 his fundamental law on the theory of Relativity."

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Illustrated Biography of Albert Einstein

In 1902, in a Bern newspaper, he offers private lessons in mathematics and physics.

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PrivateLeçons Lessons in Mathematics and privées de mathématiques et de phyPhysics conscientiously given for sique données consciencieusement studentset and pupils, élèves pour étudiants Albert Einstein, du official Albert Einstein,détenteur holder of the diplôme officiel de polytechnicien diploma of polytechnician Impasse du Droit,32, premier étage One hour free trial Une heure d’essai gratuite At the age of 24, in 1903, he married Mileva Maric and published his Theory of the Foundations of thermodynamics.

At the age of 25, in 1904, was born his first son, Hans-Albert.

This is the year when he expounded his ideas on "Special Relativity" to his colleagues.

At the age of 26, in 1905, Albert published various articles in the "Annalen der Physik", two of which lay the foundations of the general theory of Special Relativity.

This is the year when 280,000 unemployed German workers go on strike demanding a social protection law.

At the age of 27, in 1906, he obtained a doctorate at the University of Zurich.

And Max Planck accepts, first, the principle of "Special Relativity."

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Illustrated Biography of Albert Einstein At the age of 31, in 1910, the birth of Albert's second son, Edouard At the age of 32, in 1911, Einstein was appointed full professor at the German University of Prague. It was in Prague that he was confronted with the Jewish question. Einstein met Max Brod and Franz Kafka there.

Above left, the house where Einstein lived on the outskirts of Prague Above right, the Old Synagogue Below left, the entrance to the Prague Cemetery and to the right, the Jewish graves.

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Illustrated Biography of Albert Einstein It was in 1911, too, when he took part in the first Solvay Council in Brussels with Sommerfeld and Wien, Marie Curie, Lorentz, Planck (Sommerfeld, Wien and Planck, see chapter 6.5 for Marie Curie and Lorentz, see bibliography)

At the age of 34, in 1913, Einstein and his friend Marcel Grossmann published an outline of the theory of general relativity and gravitation. It is also the year of the second Solvay Council. A few months earlier, Niels Bohr proposed his model of the atomic structure.

It was also in 1913 that Einstein was appointed an ordinary member of the Mathematics and Physics Section of the Prussian Academy of Sciences. He had been guaranteed both a high salary and the freedom of research. He would have the status of professor at the University of Berlin but would be exempt from all teaching.

At the age of 37, in 1916, he published in the "Annalen der Physik", "The principles of the theory of the general relativity" and becomes president of the German Society of Physics.

He intends to describe the universe as a global entity with its own existence. We no longer study the fate of bodies in the universe, but the universe itself.

Einstein thinks that a stationary Universe is impossible if it depends at most on the forces of gravitation, because sooner or later, in this case, it can only collapse on itself. He modifies his equations by a cosmological constant λ which opposes the gravitational contraction. According to him, the Universe has the form of an enormous bubble of radius R where λ is the energy of the vacuum which opposes the attraction of the masses, whose mathematical term is proportional to the average density ρM of the existing matter in the universe and the gravitational constant.

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Illustrated Biography of Albert Einstein

At the age of 40, in 1919, he divorces with Mileva Maric and, in June of the same year, marries his cousin Elsa LĂśwenthal.

Einstein's 1919 Christmas gift to a friend: cutting out silhouettes in the paper. It's about him, his wife, lsa and his two daughters-in-law.

The historical context after the First World War is as such that physicists do not escape the hatred of the English and French patriots. In 1919, English intervened with the Royal Astronomical Society so that it does not grant its gold medal to Einstein and, in 1922 in Paris, the physicist Paul Langevin meets a strong opposition when he invites Einstein to the College of France.

As recalled by Jean-Marc Levy-Leblond, about this famous visit to Paris, Bernadette Bensaude-Vincent in her book Langevin noted: "These scholarly discussions are perhaps all the more reassuring that they are less understandable. When we feel blind and helpless, it is easy to know that there are people who see clearly, "Seers", broken to the highest difficulties, able to lead the crowd and guide humanity. In short, an enlightened elite. It is even sweeter to discover that these "seers", these new magi, are also men. Einstein surprises, Einstein seduces, Einstein reassures, because he does not have the silhouette of a cleric, because he has nothing of an effigy imprint of academic stiffness. He has a smile, humour of fantasy. He is human, young, and even childish (...) A figure of hope announcing salvation. It is almost the messiah whom Paris welcomed.

On the German side, it's the opposite. In 1920, the German "ChargĂŠ d'affaires" in London wrote to his minister: "Professor Einstein, whose name enjoys an international reputation, is a major cultural asset for Germany" As Jean-Marc Levy-Leblond also writes: "Einstein plays his role of ambassador with lucidity and without illusion; he had written as early as 1919: Still a different application of the principle of relativity: I am currently going to Germany for a German scholar and in England for a Swiss Jew. Suppose that fate makes me a "bĂŞte noire", I would instead become a Swiss Jew in Germany and a German scholar in England "As to summarize these two visions, the far-right columnist Leon Daudet also treats Einstein, during his visit to Paris, as"ambassador of German-Swisscircumcised thought." (10) In the same article, Levy-Leblond recalls that Emmanuel Berl, in his novel Sylvia, wrote: "The war had left certain despair in everyone's heart; the post-war period was, nevertheless, a time of hope, of secret faith (...) The tonics, after all, were not lacking: the revolutionaries had Lenin; the industrialists had Ford, the Einstein savants, the psychologists Freud."

10 Levy-Leblond, JM., A Despicable Hero, in Sciences et Avenir from July-August 1997, pp. 22-25.

27

Illustrated Biography of Albert Einstein He travels to the United States with Chaim Weizmann to raise funds to build the Hebrew University of Jerusalem and fund the Jewish National Fund. He receives a triumphal welcome.

He is a lecturer at Princeton University.

He is in New York in 1921. Journalists are swarming around him. He is astonished and says: "I must have something of a charlatan or hypnotist in me to attract crowds like the circus."

At the age of 43, he was awarded the Nobel Prize in Physics (though retroactive for 1921) for his work on photoelectricity. He cannot go to Stockholm because he is heading for Japan.

The protocol provides that in the absence of the laureate, it is the ambassador of his country who receives it.

"The award ceremony in Stockholm took place without him, as he was on his way to Japan.

In the absence of the laureate, it is the ambassador of his country who receives for him the medal and the check. The German ambassador, after consulting the Berlin Academy of Sciences, argued against his Swiss colleague that Einstein was a German citizen and went to receive the prize from the hands of the King of Sweden. (...) Einstein had stipulated that he would only accept the guarantee of being able to retain his Swiss nationality, but there was no record of this clause in the archives. The case ended with a written declaration of Einstein according to which, as a member of the Prussian Academy of Sciences, he enjoyed German nationality."(11)

11 Sugimoto, Kenji., Albert Einstein, Illustrated Bibliography, Belin, traduct. French, 1990, p.88

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Illustrated Biography of Albert Einstein

That year, Denmark's Niels Bohr received the Nobel Prize in Physics for the current year (1922).

At the age of 44, in 1923, he went to Palestine where he warned Zionist settlers against their arrogance and historical blindness towards the Arab populations. Alas, without success.

At the age of 48, in 1927, he participated in the Soviet Research Week in Berlin and the Solvay Council in Brussels.

On this occasion, there was controversy over the foundations of quantum physics. The majority of physicists follow Max Born and Niels Bohr.

Enclosed, with Tagore, philosopher and Indian mystic.

Below, with Tagore and Elsa.

29

Illustrated Biography of Albert Einstein At the age of 50, Albert became an honorary citizen of Berlin, the year in which Louis de Broglie received the Nobel Prize in Physics (see also chapter 6.5).

At the age of 51, in 1930, the sixth Solvay council took place, the last one to which Einstein would participate.

Lorentz, deceased, it is Paul Langevin who presides.

Einstein will become a professor at Princeton that year. At the age of 52, in 1931, he must renounce his stable universe and join his expanding universe.

At the premiere of "City Lights", in January 1931. Charlie Chaplin said to him: "I am acclaimed because everyone understands me and you are acclaimed because no one understands you."

Translation: It is also the time when the threats of the Nazis begin to weigh on him.

Here, this book "100 scientific authorities against Einstein" was published in 1931.

"The aim of this publication is to oppose the"Einsteinian" terrorisms the arguments of a powerful and illustrious group of adversaries."

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Illustrated Biography of Albert Einstein

Brussels, Belgium, September 8th Great anxiety reigned at the villa "La Savoyarde", Professor Albert Einstein's Blankenberge residence, since the receipt of a ballot reporting that a secret Nazi organization was setting a price of about $455 for the head of the famous physicist.

Mrs Einstein was particularly alarmed, as her husband continues as usual morning marches and small walks in the dunes.

The police watch in the vicinity of the villa, and the bodyguards precede and follow the teacher during his walks.

Below this picture is written: "The valet of the German embassy at Brussels received the task of curing the hallucinations of an asylum seeker who was lying around there and claimed to be a Prussian."

At the age of 53, in 1932, he left for the United States. This is the year that Werner Heisenberg receives the Nobel Prize in Physics.

At the age of 54, in 1933, his German nationality was withdrawn, and his property was sequestrated.

Einstein leaves America for Europe at the end of March and settles for a few months in Belgium, in LeCoq-sur-Mer. At the end of November, he is in Princeton.

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Illustrated Biography of Albert Einstein

Above, on the left, in 1933 with the King of the Belgians, Albert The First; and below at Coq-sur-Mer, with Elsa in 1933.

Practising the bicycle, and comparing it to science, he used to say: "If it does not move, it falls."

This is the time when Einstein felt all the media pressure on him, and he could not really endure.

He writes to Solovine, his childhood friend, in the centre of the picture below, and with whom he founded the "Olympia Academy" in Bern.

"Enough nonsense. I hope we'll be able to see each other again when the excitement around my person is soothed. In the meantime, hello to your A.E. If you meet Jewish scientists coming from Germany, try to put them in touch with me. I am seeking to establish a Hebrew University abroad (England) at least to provide first aid to refugees and to offer them a kind of spiritual asylum."

32

Illustrated Biography of Albert Einstein Albert Einstein's Belgian breakaway 80 years ago, Einstein was in Europe for the last time, before a final exile in the United States. The scientist, threatened by the Nazis, will remain a few months at Coq, where he will try to help German Jewish refugees and will water down his visceral pacifism.

On August 2, 1933, four men sipped a digestive in the gardens of the “Hôtellerie du Coeur Volant”, in the middle of “the Coq” seaside resort. They have just stalled their stomachs with iced melon, sole "meunière" and "Crèpes Suzette”.

Face encircled by a huge white beard and a strict black hat, James Ensor stretches his long bony hands.

In the morning, the "prince of painters" hosted Anatole de Monzie, French Minister of Education, and his chief of staff, Marcel Abraham, came to Ostend to give him the Legion of Honor. Ensor invites them to fork to the Rooster. He recently composed a dishevelled ode to greet a global celebrity who has resided in the seaside since April. Ensor lets go: "You, the man of lights, you reflect suns, invent planets, invent moons, invite comets and illustrate constellations."

At the other end of the text, a worried man welcomes the eulogy. Albert Einstein, however, likes to be impassive. The Moon is his domain, they think, he conducts his physics walks away from the realities of the world. However, not this time. The scientist has the brain and the senses worked by his homeland of origin, this Germany that goes crazy, and that he decided never to return.

33 34

Illustrated Biography of Albert Einstein On January 30, 1933, Adolf Hitler won the Chancellery. Einstein teaches temporarily in Pasadena. For several years, he warns: the rise of the Nazis promises only dark hours. In California, he met Chaplin, laughed in his diary of "a fat lady" whose "occupation is to make friends with celebrities" and played quartets of Mozart, his idol in music, with the hyper-prolific Haydn. Wherever he lands, he appears with his violin case. Like to better get rid of this implacable label of scientist-star.

Farewell to Germany The worldly sweets of California will fade for good into the ashes of the Reichstag fire. Faced with the first persecutions of the Jews, Einstein postpones his return to Germany. He opens the floodgates in an interview with the New York Telegram. "I will only live in a country where the political freedom, the tolerance and the equality of all citizens prevail before the law."

He cannot know that at the same time, or almost, brown shirts are sacking his apartment in Berlin. In a flash, stores owned by Jews are subject to boycotts. The campaign against the non-German spirit swells. It will reach its dark zenith in the pyres of the great autodafé of May 1933, where the writings of Einstein will be consumed, alongside those of Freud and Marx.

Two months before, the scientist embarks, with his second wife, Elsa, aboard the steamship Belgenland.

Antwerp direction, with a stopover in Southampton. He will send his letter of resignation aboard the ship to the Prussian Academy of Sciences. Alain Findling, the producer of classical music concerts currently immersed in a vast investigation into the life of Einstein, notes that the scientist continues, in full crossing, to rise against the German regime and signs, in Southampton, "a call to civilized peoples of the universe"to avoid" a regression to barbarism."

"On arrival in Antwerp, a welcoming committee is organized, led by a professor of medicine, Arthur de Groodt, says Alain Findling. A crowd of journalists waiting for him. A press conference is improvised. watch very cautiously, just declaring that he will not return to Germany."

Part of the media will be perplexed, even mocking. Thus, the Gazette exclaims: "What a circumspection!

What reserve!" Before returning Einstein "to his small scientific calculations." After a few days at Chantecroy Castle, in Mortsel, owned by Arthur de Groodt, Einstein will leave for a more humble home, the Villa “Savoyarde” du Coq, rented for the occasion by the wife of the doctor.

By Quentin Noirfalisse (In French)

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Illustrated Biography of Albert Einstein

Professor Albert Einstein dictates to his secretary, long time in her job, Fräulein Helen Dukas, at Coq-sur-Mer, Belgium, where he took refuge from Nazis.

Helene was born October 17, 1896, in Breisgau, the daughter of Leopold and Hannchen Liebmann Dukas. She was one of six children in a Jewish family and is best known for being the assistant of Albert Einstein.

After the death of both of her parents, she took a job as a kindergarten teacher.

Later on, after holding a few teaching jobs, she found work as a secretary for a publishing house in Berlin. It was the wife of Albert Einstein who first interviewed her for a job as his assistant.

Helene is credited with collecting and organizing Albert Einstein's papers, and also publishing and co-authoring a book about him. She died February 10, 1982, in Princeton.

It's easier to disaggregate a prejudice than an atom Albert Einstein

35

Illustrated Biography of Albert Einstein

He will now work until his death at the Princeton Institute for Advanced Study.

Einstein bought this house in August 1935, 112 Mercer Street in Princeton

Here is the article of an American newspaper of December 22, 1936, announcing the death of Elsa Einstein, at the age of 58 years.

We can read there: "During their marriage years, Mrs Einstein was a partner in the creation of the abstruse mathematical calculations which won the German worldwide renown.�

36

Illustrated Biography of Albert Einstein At the age of 59, in 1938, Albert published an article: "Why do they hate Jews?". This is the year that Enrico Fermi receives the Nobel Prize in Physics.

At the age of 60, in 1939, he wrote to President Roosevelt about the possibility of making an atomic bomb.

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Illustrated Biography of Albert Einstein

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Illustrated Biography of Albert Einstein

At the age of 61, in 1940, he took an oat h to become an American cit izen.

HÊlène Dukas, Albert Einstein and his daughter-in-law Margot taking the oath of American citizen Einstein were investigated before and after his oath. .

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Illustrated Biography of Albert Einstein

Above, the FBI report of April 15, 1950, with annotations from Edgar Hoover, the FBI leader: "He told the Polish ambassador that the United States was no longer a free country and that his activities were carefully scrutinized. He was a sponsor of a committee defending the rights of 12 communist leaders."

On February 12, 1950, on the NBC Network, Einstein recommended banning all violence among nations to prevent the "general annihilation" of humanity. .

40

Illustrated Biography of Albert Einstein "Contacts and associates" Einstein's social and professional contacts since 1938 have included a number of known members and supporters of the Communist Party. One of his former assistants at Princeton University who was subsequently refused by the Atomic Energy Commission was recommended by Einstein. The Bureau's investigation showed that his secretary, HÊlène Dukas, who resided in Einstein's house, had established numerous contacts with individuals known to be communists, many of whom were suspected of being Soviet agents. The scope of the Dukas inquiry was necessarily limited to discrete techniques.

Information not yet fully exploited indicates that he may have had contact with Emil Klaus Fuchs, who was recently arrested in England as a Soviet spy age Various Einstein was one of many distinguished Germans who lent their influence and prestige to the German Communists before Hitler's rise.

In 1940, the army refused to explain to Einstein what was "the limited field of study for which his services were necessary" after the Navy had given his consent. Einstein publicly declared in 1947 that the only true real party in France with a solid organization and a precise program was the Communist Party.

In May 1948, he and "10 former Nazi headhunters" held a secret meeting to observe a new ray of light from a secret weapon that could be directed from planes to destroy the cities, according to the Arlington Daily, Arlington, Virginia, May 21, 1948.

The Army Intelligence Service subsequently informed the Bureau that this could be unfounded and that no machine could be designed to be effective at a range greater than a few feet. " Another FBI report dated March 9, 1955, one month before Einstein's death, the original of which is on the next page.

Helen Dukas, secretary of Dr Albert Einstein, Princeton, NJ, was interviewed about possible involvement in espionage activities on behalf of Russia (1928-1933) in Berlin, Germany. She denied any knowledge of the identities of known spies who might have been in contact with Dr Einstein's office during the relevant period. She is not aware of the "Intellectual Workers Club" in Berlin during this period. She claimed that "she was his only secretary since 1928 and that the only other assistants he had had were his wife and his eldest daughter-in-law, both of whom had died. She stated that Dr Einstein kept his only office in Berlin at his place of residence and that there were no other employees in the house. She added that currently, Dr Einstein was in poor health."

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Illustrated Biography of Albert Einstein

42

Illustrated Biography of Albert Einstein At the age of 62, in 1941, he participated in a violin recital in Princeton for refugee children.

He never missed an opportunity to release his violin, but that did not make him an outstanding musician.

The Bomb It is easy to be a pacifist, the bad languages will say when we have discovered the most terrible formula which allows men to extract from matter the energy capable of devastating the world. The fission of the atom poses a question to the conscience of the scientists (In the same way, today, as the genetic manipulation to which our man is not bound.)

And yet, it is said, "in the only reality that exists for science, there is neither question nor conscience! "It was not really the case of Einstein, who says, too late it is true:"There are things that it would be better not to do."

And Einstein did not forget his duties since he could not be both Jewish and German. Not wanting to put himself at the service of barbarism, he had to leave his native country and, at that moment, he measured how much the intellectuals depend on the society which demands from them that they accept what it imposes.

In July 1945, scientists and soldiers were preparing the Trinity test; the atomic bomb was waiting for its explosion.

The triggering took place on July 16 at 5:29 am. The heat emitted was so intense that the sand from the site was transformed into greenish glass beads, and a shockwave swept over the scientists who expressed a mixture of exultations and fright.

On July 28, the Japanese rejected the last ultimatum of the allies. On August 6, three weeks after the Trinity test, the B29 "Enola Gay" bomber carried the "Little Boy" bomb into its hold and at 8:15 am, dropped the 4,300 Kg bomb on Hiroshima.

On August 9, a second bomb fell on Nagasaki (photo attached).

On August 14, Japan capitulated, and it was the end of the Second World War. At the age of 66, Einstein is deeply affected by the atomic bombing. He regrets having intervened with Roosevelt and warns humanity against the danger of nuclear destruction.

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Illustrated Biography of Albert Einstein

Robert Oppenheimer, the "father of the American atomic bomb" converses here with Einstein.

Obsessed with the memory of Los Alamos, where men with a certain innocence prepared the first atomic test by calling it "experience," as if it represented an extension of their "usual activities," Oppenheimer liked to quote the terms an old Sanskrit text: "I am death that delights everything, that shakes the worlds."

44

Illustrated Biography of Albert Einstein At the age of 73, in 1952, after the death of Chaim Weizman, President of the State of Israel since its inception in 1948, Einstein refused to succeed him, despite the insistence of Ben Gurion (photo attached).

At the age of 73, in 1952, in a rare interview, he accepted.

At the age of 74, in 1953, he published the latest version of the theory of general relativity.

The city of Bern invites him to celebrate, two years in advance, the fiftieth anniversary of relativity. Einstein is already very sick, he knows he is at the end of the roller. He declined the invitation, but added in his letter: "I hope that someone will seize this opportunity to honour properly the merits of Lorentz and PoincarĂŠ in this respect." (12) At the age of 76, on April 18, 1955, Einstein died at Princeton Hospital.

12 Auffray., JP., Einstein and PoincarĂŠ. On the traces of relativity, Paris, Editions Le Pommier,

45

Illustrated biography Albert Einstein The main theoreticalofdiscoveries Here are the latest pictures of Einstein in Princeton and in the company of Jewish children. His solidarity with the Jewish people, based on his "hard destiny," was the deepest of his personal feelings. (13)

13 Sugimoto, K., Albert Einstein, Illustrated Bibliography, Belin, traduct. French, 1990, p.166

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Illustrated biography of Albert discoveries Einstein The main theoretical

The essential key to understand more and better about Albert Einstein

47

The main theoretical discoveries

Chapter Three The main theoretical discoveries "In my life, I have never ceased to glimpse, even for a moment, the order of things that are hidden in nature. Any scientific approach requires believing in the harmony of the world. Our greed to understand is eternal."

3.1. The Planck constant On December 14, 1900, Planck published his radiation law, which gave rise to quantum theory. This revolutionary theory has become the basis of modern physics. He postulated for the first time that energy exchanges are intermittent.

Introduced by Planck, the quanta correspond to a physical entity, the photons, elementary components of the radiation by which Einstein subsequently interprets the photoelectric effect.

E  hf ď€ E is the energy of a photon. It is equal to the mathematical product of "f"(the frequency of the wave) and a constant "h" called Planck constant and equal to 6.626.10-34 Joule.second. Actually, this constant expresses the minimum energy threshold that can be measured on a particle.

3.2. Photoelectricity Let's take a closer look at the screen Einstein consults.

A swarm of photons is moving towards a metal target. The shocks of these "grains of light" will release electrons from the atoms. And an electric current appears within the metal.

Light is made of particles, "grains" and when they are numerous, they give the impression of being a wave. Each grain carries with it a bundle of well-defined energy called "quantum" (plural: quanta).

In 1926, the American physicist Gilbert Lewis will baptise "Photons" these grains of light. They are 1 billion times more abundant than any other particle. Their speed is 300,000 km/s. For the discovery of photoelectricity, Einstein will receive the Nobel Prize in 1921.

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The main theoretical discoveries

Let us refer to the theory of photoelectricity that Einstein enunciated in 1905 and which awarded him the Nobel Prize. He demonstrated that when the energy of a luminous quantum "hf" reaches a precise value, equal to the work of extracting an electron from a specific metallic surface, then, and only then, this electron leaves this surface. For the phenomenon to occur, the frequency "f" must be equal to that of the electronic vibration of the illuminated metal. If this is not the case, the increase in light intensity will have no effect.

Low intense

High intense

Low intense

High intense

f f0 Source : Voyages dans le Cosmos (Hubert Reeves) La rĂŠalitĂŠ quantique page 52 49

The main theoretical discoveries The kinetic energy of the photoelectrons is equal to

Ecin  hf WA 1

mv  hf  W 2

2 max

A

with hf 

hc



h = the Planck constant (6.62.10-34), f is the electronic vibration frequency of the metal under consideration and WA is the extraction work The kinetic energy of the ejected electron can be found by determining the difference of potential required to halt its motion; we then have:

where V is the stopping potential and e the charge of the electron (the unit is the electron-volt) The frequency is limited to the quantified values specific to the target metal.

It is, therefore, the frequency that must be targeted and not the intensity of the radiation. (See also explanation 1 of the mathematical appendix) 3.3. Special Relativity and the speed of light The first theory of Einstein, which dates from 1905, is called "special" as opposed to that of 1915, entitled "general relativity" Special because it applies only to places animated by a uniform rectilinear motion and not to accelerated motion, which concerns "general relativity. " As a thought experiment, Einstein wondered what he would see if he rode on a ray of light.

He knew it was biologically impossible because according to the Special Relativity, the length of the animated bodies of this speed would be reduced to zero and the time would be stopped.

But still, in his experience of thinking, Einstein asked himself if he could see himself in a mirror. As the image in the mirror is transported itself by a ray of light that travels at the same speed (300,000 km/s) will he ever be able to catch up with Albert's retinas?

Here is the answer to the dream of young Albert. The ray of light that sends its own image to its retinas goes at 300,000 km/s, but this speed is absolutely independent of the speed of the vehicle that Albert rides, even if the vehicle is the light itself.

Why? Because the light challenges the principle of adding speeds. On June 30, 1905, Einstein gives his theory to the Annals of chemistry.

As Einstein writes (14) "Suppose, a train is moving at a constant speed v and a man is moving in one of the wagons in the direction of its length, that is to say in the direction of travel train, with speed w. How fast or how fast does the man advance in his progress relative to the embankment? The only possible answer seems to result from the following reflection: 14 Einstein, Albert., The theory of Special and General Relativity, translated into French by Maurice Solovine for Gauthier-Villars in 1923; Preface by Marc Lachièze-Rey, Dunod, Paris 2004, pages 18 and following .

50

The main theoretical discoveries If the man remained motionless for a second, he would advance relative to the slope, a length v equal to the speed of the wagon. However, in reality, it travels during this second relative to the wagon and therefore relative to the slope, the length of w which is equal to the speed of its march. It thus travels in total during this second, relative to the slope, the length: W = v+w Let's continue with Einstein's own sentences: "Suppose that finding myself in front of the window of a wagon of a uniform train, I drop, without impressing it, a stone on the embankment. I then see (abstraction made on the influence exerted by the resistance to the air) the stone falling in a straight line. A pedestrian who observes the mischief of the trail finds that the stone in his fall describes a parable. I ask now: "the places" that the stone travels, are they "really" situated on a "straight-line" or on a parabola?"

The answer is self-explanatory (...) The stone describes, with respect to a coordinate system rigidly linked to the wagon, a straight line, but with respect to a coordinate system rigidly linked to the ground, a parable. This example clearly shows that there is no trajectory per se, but only a trajectory relative to a specific reference body.

The phenomenon of the propagation of light must naturally, like any other phenomenon, be related to a rigid reference-body (coordinate system). We choose our embankment as such and assume that the air above it has been removed. Suppose we send along the slope a ray of light that propagates with respect to it with speed c. Let us suppose that our wagon moves on the railway with the speed v and in the same direction as the ray of light, but, of course, with a speed much smaller than the latter.

We now ask, "What is the speed of propagation of the light beam relative to the wagon? It is easy to see (...) that the speed for the light sought in relation to the wagon is: W=c–v The speed of propagation of the light beam relative to the wagon is, therefore, smaller than c.

But this result is in contradiction with the principle of relativity (...) According to this principle, the law of propagation of light in a vacuum should, like any other general law of nature, be the same, or then one chooses the wagon, or one chooses the rail law like the body of reference. But this seems, according to our reflection, impossible. For if any luminous ray propagates, relative to the slope, with velocity c, the law of propagation of light should thereby be different from the wagon, which is in contradiction with the principle of relativity. " The relativistic effects imagined by Lorentz, contraction of length and dilation of time find a logical place in Einstein's theory. It is the barrier of the speed of light, 300,000 km per second which produces these deformations for the observer.

After the following chapter "The relativity of the simultaneity," we will first take cognizance of "Lorentz transformations," then we will consider the demonstration of the constancy of the speed of light, and then we will understand that there is no incompatibility between the Principle of Relativity and the Law of Propagation of Light.

3.4. .The relativity of the simultaneity

M’

51

The main theoretical discoveries Excerpt from Einstein's book (Footnote 14 reference) "Suppose a very long train moving on a railway with a constant speed v in the BA direction. Train travellers will benefit from using the train as a rigid reference object (coordinate system) to which they will report all events. Any event that took place along the track also took place at a certain point on the train. The definition of simultaneity can also be formulated in exactly the same way with respect to the train as compared to the track. The following question thus naturally arises: Two events (for example the two lightnings A and B), which are simultaneous with the track, are they also simultaneous with the train? We will show earlier that the answer must be negative.

When we say that flashes A and B are simultaneous with the railway, we mean that the rays from points A and B meet in the middle M of the distance A-B located on the track. But places, A and B on the track correspond to places A and B on the train. Let M 'be the middle of the line A-B of the running train. This point M 'coincides well with the point M at the moment when lightning occurs (seen from the slope) but it moves on the drawing to the left with the speed v.

If an observer on the train seated in M' was not trained with this speed, he would remain permanently in M and the light rays coming from A and B would reach him simultaneously, that is, to say that these two rays would meet at the point where it is. In reality he runs (seen from the embankment) to the ray of light coming from A, while he flees before the one that comes from B. He will, therefore, see the ray of light that comes from A earlier than the one that comes from B. Observers using the train as a reference object must, therefore, conclude that Lightning A occurred prior to Lightning B. This leads to the following important result: Events that are simultaneous with the railway are not simultaneous with the train and vice versa (relativity of the simultaneity). Each reference object (coordinate system) has its own time; an indication of time makes sense only if the reference object to which it relates is indicated.

3 .5 . Lorentz Transf ormations The Lorentz transformation allows, when we know the coordinates (x, t) of an event in a reference system Σ, to obtain the coordinates (x ', t') of this event in another system Σ 'in uniform rectilinear motion with respect to Σ. This transformation can be obtained using the only fundamental postulate of Special Relativity: the light always propagates in a vacuum with a certain speed independent of the state of motion of the light source. We present the approach here adopted by Einstein [1] to obtain these coefficients.

(1) A light signal moving along the x-axis in Σ propagates at a constant speed according to the equation x = ct, or: 2) Since the same signal propagates also with velocity c in another system Σ 'in uniform translation with respect to Σ, the propagation relative to Σ' will be given by: (3) The points in time that satisfy equation (1) must also satisfy equation (2).

"Lorentz transformations" had already highlighted this dilation of time, and this contraction of the lengths linked to the movement.

In the perspective of Einstein, the mass also seems to increase with speed and ends up opposing insurmountable resistance to any further acceleration. The faster you move, the closer you get to the speed of light, the harder it is to increase speed.

52

The main theoretical discoveries

Yv vt

Ov Z

X Xv

Zv

These two artesian coordinate systems represent two frames of reference whose 'solid line axis system moves at the speed v (Velocity or Vitesse in French) in the positive direction of the x-axis.

Any point referenced in the solid-line axis system represents a mobile whose coordinates are measurable in the two reference frames.

Hence the transformations of Lorentz

’

Taking into account the transformation of the coordinates of time

2

At very high speeds, the vision of space is deformed. The perception of time is also disturbed.

For those who live the event, the durations are always the same but the spectators have another vision. For them, the number of frames per second is higher, and the events are slow. As was the case with the Einstein train, a motionless observer sees the length of the mobile shorten according to its speed. Effect of perspective, therefore of perception. The pilot does not notice anything.

Whether the mobile is at a standstill or reaches its maximum speed, it does not change dimensions.

It's the images that change, not the size of the bodies.

Diagram of a ball seen at rest and after its exit from the gun on the axis of its trajectory

The electric field of an electrically charged particle is no longer symmetrical if this particle moves at a very high speed..

53

The main theoretical discoveries Let's talk about the situations experienced by an astronaut, who observes a light pulse going from the floor to the ceiling and then, by reflection on a mirror, from the ceiling to the floor.

If tp is the time needed for a light ray to accomplish the distance AB + BC = 2d When time is measured by the pilot, himself tp, then

and the point of light impact, after reflection on the mirror, is A (the same as the starting point) Consider now the same event seen by a fixed observer who sees the Space Shuttle. After reflection of the light beam on the mirror, the point of impact is C, different from the starting point.

This observation is expressed quantitatively by the Pythagorean theorem:

If "t0" indicates the duration (unknown) of the event for an observer at rest seeing the shuttle pass, the distance travelled by the light pulse on the outward direction is, for this observer:

And the distance traveled by the light during the same time is:

54

The main theoretical discoveries

B

Fixed source seen by the pilot

A

Landmark mirror

C

observer

B Landmark mirror

D

A Mobile source seen by an external observer In this case, the round trip of the light ray takes longer

By incorporating the2last two equations into equation (2) and noting that BD = h, we get : t 2 and

whence

Given that

we get :

55

C

The main theoretical discoveries 



3.6. The behaviour of rulers and clocks in motion.

Let's start from the axis systems of the two reference frames defined during the Lorenz transformation, p.49. Let’s suppose the referential O is stationary and the referential Ov moving at speed v in the direction of the x-axis. We deduce that the displacement of any point in the direction of the xaxis travels, for a time t, a distance equal to:

If is the length measured by a fixed observer, when the interplanetary machine is stopped (v = 0) and if l v is the length measured by the same fixed observer while the machine is moving at high-speed v (not negligible compared to c), the relationship between the two observed lengths is as follows:

whence

Which means that at high-speed l v becomes lower than in a proportion that will depend on the pilot’s speed.

The same conclusions are also valid if the pilot (mobile) perceives the fixed observer. This one will appear shorter.

If the pilot fell along the "Atomium" in Brussels, he would see it as crushed, shortened in the direction of the fall.

56

The main theoretical discoveries Application of the behaviour of rulers and clocks in motion. Explanation with the muons The “Muons” are elementary particles that are in the cosmic radiation and that fall permanently on the Earth. These particles entering the atmosphere should disappear, but yet they are detected in large numbers, and the device at the "EXPO EINSTEIN L’AUTRE REGARD – TOUR ET TAXIS – BRUXELLES 2005" emits a beep every time a muon passes through, a proof that their time of live are much longer, because they move at almost the speed of light, which lengthens their lifetime as Einstein predicted.

The muon ages less than the motionless observer; therefore, their lifetime units are longer than the unit of time experienced by the observer.

For this one, a clock in movement seems slow compared to a motionless clock. Of course, this effect occurs at any time meter.

A Minkowski diagram, in two dimensions, allows a representation of this phenomenon and can help a qualitative and intuitive understanding.

This clock slowing phenomenon extends, in general relativity, to clocks close to a massive body, which will slow down compared to those which are farther away.

In 1911, Einstein gave this amazing consequence of the principle of relativity: "If, for example, we place a living organism in a box (...) we could have this organism, after a sufficiently long flight, return to its point of departure very little changed, whereas organisms of the same nature that remained motionless at the initial places would have given way to new generations for a long time.

For the moving organism, the long journey would have been only an instant course, if the speed of the movement was close to that of the light!

This observation is also opposed to Newton for which, whatever the place where we are and whatever the speed which animates us, the clock gives the same hour.

"Two twins are 25 when one of them is on a space trip. The twin who is in the spaceship measures time on a precision watch. When he returns to Earth, he claims to be 31 years old while the twin who has not left is certain to be 43 years old.

The brother remained on Earth would have aged 12, while the traveller would have taken only six years!

What was the speed of the space network? The answer: 283,000 kilometres per second.

(See also explanation 2 in mathematical appendix).

ct

B

57

The main theoretical discoveries Hermann Minkowski (1864/1909) is a German mathematician. He was a professor of Albert Einstein in Zurich when he was a student at the Ecole Polytechnique Fédérale from 1896 to 1900.

This graph shows Minkowski's spacetime whose explanations numbered 5,6,7 and 8 are given in the mathematical appendix.

In short, clocks synchronized at the same place are carried away, one by the terrestrial twin and the other by the "spatial" twin.

The moving clock will indicate that the space twin's landing will be shorter than the immobile clock of the "land" twin.

Which means that the space twin is younger on his return than the twin left on Earth.

How is it possible? The terrestrial twin travels a universe line parallel to the time axis "t", while the space twin describes an oblique (dashed) portion of the universe.

Then he turns back to join the Earth according to a portion of a universe line symmetrical to the first.

In Minkowski's reference frame, where time is represented as the fourth dimension in addition to spatial coordinates, the three steps of "take-off", "turn-around" and "landing" are not straight.

The length of the dotted line is equal to the product of c by the time (ct) that has elapsed in the spacecraft. The length of the continuous line corresponds to the universe line of the terrestrial twin.

Quote of Minkowski : Source : Hendrik Antoon Lorentz, Albert Einstein, Hermann Minkowski, Hermann Weyl, Arnold Sommerfeld (1952). “The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity”, p.75, Courier Corporation

58

The main theoretical discoveries What did it happen with these twins?

It means that the observer's time, measured in his own system of axes, is greater than the own time consumed by the spatial twin. The observer has therefore aged more. And that is also why the astronaut moving at a speed close to the speed of light and returning to Earth is convinced that he has aged less than the earthlings he finds.

Actually, if we calculate the spatiotemporal distance travelled by ship using the classical tools of Euclidean geometry, we would find the path ABC longer than the path AC; in the case of Minkowski spacetime, the path length ABC (see diagram) is shorter than that of the AC path. Therefore, the duration of the trip is shorter for the space traveller than for the one remaining on Earth.

Certainly, but if one placed oneself in the place of the space traveller, his line of universes would be parallel to the axis of time, and it is the line of the twin remaining on Earth which would have the same pace as the dashed line. Would not we find while the traveller who stayed on Earth railed?

No, because this diagram is meaningless because the earth does not feel acceleration when it leaves or rejoins the spaceship. It is, therefore, the traveller who feels the acceleration that rejuvenates. Einstein had shown it: acceleration and gravity are identical, and it is they who determine spacetime.

The constancy of the speed of light is now demonstrable from the Lorentz transformations: see explanation 4 in the mathematical appendix.

As shown in this souvenir watch, the time lived at the speed v is equal to the time lived at zero speed multiplied by the square root of 1 - v2 / c2, where c is the speed of light.

59

The main theoretical discoveries Diagram of Minkowski It is moved by Herman Minkowski in 1908.

It is a representation in which the reference frame (R, in blue) is considered at rest and the second (R 'in red) in uniform rectilinear motion at a speed "2 V" with respect to (R).

As a result, the Minkowski diagram is constructed by giving (R) orthogonal axes. The first bisector represents the universe line of a light1ray in green).

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

17 18 19 20 In the Minkowski diagram shown above, we have represented an event (E) with its coordinates, constructed by carrying out parallels to the axes in the two marks (x, c.t) and (x ', c.t').

Excerpt from "The Paradoxes of Physics" - "Travels in the Cosmos" collection presented

by Hubert Reeves.

The diagram seen by the observer at the stop and whose coordinates are the coordinates "C t" and "s" which sees a second observer moving away to the right at a constant speed.

To represent the coordinates of this one, it is necessary to incline the axes "c t" and "s" towards the interior. The angle ď Ş that forms the two axes c t 'and ct will be the same as the one formed by the two spatial axes s' and s.

The higher is the relative speed between the two observers, the more pronounced the angle will be. At the limit, the two axes converge to form the diagonal of the light.

We find that the more the axes s and s' get closer to the bisector, the more the units of c t' and elongate, which corresponds to a slowing down of time. It is as if the observer moving at high speed had a clock that slows down. (This would be the case of the space twin)

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The main theoretical discoveries

3 .7 . T h e the o ry o f re la tiv ity a pp lied to th e m a s s .

Einstein writes(15): ÂŤ According to the theory of relativity, the kinetic energy of a material point of mass m is no longer given by the expression but is replaced by this one

The second expression tends to infinity when speed v tends towards the speed of light c. The speed must, therefore, always remain smaller than c, no matter how large the energies used to accelerate it.

By developing the expression for kinetic energy in series, we obtain:

When V2 / C2 is small compared to 1, the third of these terms is always small compared to the second, the only one considered in classical mechanics. The first term, mc2, does not contain velocity, so it should not be taken into account when it comes to knowing how the energy of a material point depends on the speed.

"An animated body of velocity v, which absorbs a quantity of energy E0 (E0 is the energy absorbed with respect to a coordinate system moving with the body) in the form of radiation, without its speed being modified, experiencing an increase in energy equal to

The sought energy of the body is then given, taking into account the expression indicated above for the kinetic energy, by

c2 The body, therefore, has the same energy as a mass body We can, therefore, say that if a body absorbs an energy E0, its inert mass increases by

The inert mass of a body is not constant, but variable in proportion to the variation of its energy. The principle of conservation of the mass of a system is identified with that of the conservation of energy and is only valid if the system does not absorb or emit energy.

If we write the expression for energy in the following form

0

We see that the term mc2, which has already struck us, is nothing else than the energy that the body already possessed before the absorption of the energy E0. .15

Einstein, Albert., The theory of Special and General Relativity translated into French by Maurice Solovine for Gauthier-Villars in 1923; Preface by Marc Lachièze-Rey, Dunod, Paris 2004, pages 50 and following

61

The main theoretical discoveries The graph of mass increase versus speed is as follows

Another approach to the relationship between mass and energy Classical mechanics have established a relation between the average force F exerted on an object of mass m0 during a time interval t, and the momentum obtained by this object.

This formula can be applied to the golf ball which receives a momentum force for a short time, but which gives the ball a certain speed proportional to its mass.

Using the formula of mass variation with velocity, as we learned from the special relativity: 2 c

we obtain In Newtonian mechanics, kinetic energy variation is equal to work done by the force F over a distance x, that is E = F x Starting from the state of rest (v = 0), the difference in kinetic energy is, therefore, equal to

L

The resolution gives:

62

The main theoretical discoveries It is the most famous equation in the world, born in 1905 between two days of work at the Bern Patent Office. This year we are commemorating its centennial.

This equation means that mass and energies are interchangeable quantities. Excepted the constant of proportionality: c2 (the square of the speed of light). In other words, a kilo of matter, whatever its nature, could produce billions of kilowatt-hours (the annual output of a very large nuclear power plant) if it were fully transformed into pure energy.

One gram of material contains an exorbitant amount of energy. Using the units of the KMS system m is expressed in Kg and c2 = 9.1016 (meter/second) See the example of energy conversion in the matter in explanation 3 of the mathematical appendix.

3 .8 .T h e G en e ra l R e lativ ity a n d the N ew to nia n fo rtre s s To know where we are going, we must also know where we come from. How to appreciate Einstein without mentioning the discoveries of one of the greatest scientists of all time: Isaac Newton.

Isaac Newton (1643-1727) in one of his great works, "Philosophiae Naturalis Principia Mathematica" (Principles of Natural Philosophy), 1687, dominates the history of scientific thought.

Recall the three basic laws of Newton

Newton's principle of in ertia or first law states that, in a Galilean frame of reference, everybody that is subjected to a resultant zero force is immobile or in uniform rectilinear motion.

Newton's second law says that the acceleration "a" of an object is proportional to the force F which applies to it and inversely proportional to its mass m. a=F/m The inertial mass tends to resist acceleration, so to reduce it. In short, we always find the inertial mass in a context of acceleration, and without gravitation.

Newton's third law reads as follows: "The forces always occur in pairs. If the object A exerts a force F on object B, then the object B exerts an equal and opposite force -F on 'object A'.

According to his law of universal gravitation, two masses m1 and m2 attract with a force proportional to the product m1. m2 and is inversely proportional to the square of their distance.

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The main theoretical discoveries

Fcentripète

 6,672.1011

m1.m2 r2

6,67.10-11 is the Gravitational constant G If the Earth revolves around the Sun, it is because the two stars attract each other. This is true also for the Earth and Moon.

A planet is in a stable orbit when gravity does not make it fall on the Sun and when the centrifugal force, which is created on the orbit, does not bring it out of the Sun. The centrifugal force depends on the mass m of the planet, its orbital velocity v, and the distance r from the planet to the Sun.

mv2 Fcentrifugal  r

When an object makes a circular motion, the resulting force (F) of its motion is perpendicular to the radius of the circle

Resulting force perpendicular to the radius

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The main theoretical discoveries

Henry Cavendish (1731-1812) defined the universal gravitational constant with a rotating balance in 1798.

A wand is suspended horizontally. At the ends of the rod are hung masses known accurately. If a much larger known mass is approached, the rotating balance makes a small rotation. G is calculated from the torsion angle.

If we know G (6.67-10-11) and g (9.81 m / s2), we can then calculate the mass of the Earth: a body of mass m on the surface of the Earth is attracted by the centre of gravity of the Earth with a gravitational force F equal to: :

mg is called the weight of a body of mass m The average radius of the Earth is 6,371,012 meters. The calculation is then simple

M 

9,81.(6371012)2 6,672.10

11

 5,968.1024 Kg

No matter where a body is in the universe, and whatever its speed, it will have identical measurements. And from the point of view of time, everything happens as if a single clock gave the same time to the whole universe.

65

The main theorical discoveries The tides The generating force of the tides is a consequence of the gravitational forces in the system Sun, Earth, Moon.

The Earth and the Moon revolve around a common centre of gravity that lies inside the Earth globe.

The action of the Sun is neglected for simplicity. As the Earth rotates around its axis, the generating force of the tides is constantly variable. Thus the force exerted by the Moon causes a slight swelling of the earth's surface and consequently a flow of water: the tides.

The expression of the acceleration ag of the tides is: 1

With m1 the mass of the moon and r1 the mean distance between Earth and Moon (16)

For Newton, the only timeline is common to all experimenters. Everyone shares the same time, and it does not mix with space. Newtonian weather is unique, and the jet lag of our different time zones is only a convenience for the various nations to make the best use of the day-and-night beaches. For Einstein, everything is different: its structure is revealed by the path of light: it is curved. And four dimensions, not three, are absolutely necessary: the three spatial dimensions + the time. Whatever be the physical movement, it combines a spatial shift along a space direction and a time shift along all the time scale.

Paradoxically, the same rule for measuring one-dimensional bodies is different according to the place where they stand in relation to the speed of the observed object.

Unlike Newton, Einstein proclaims that time and space are interdependent. Hence the creation of the new concept: "spacetime". Cannot touch one without touching the other. (17) 16 Breuer Hans, Atlas of Physics, La Pochotheque, The Pocketbook, Paris, 1997, p.45 17 Science and Life Junior-Special Issue (No. 59-January 2005)

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The main theorical discoveries Here we see the curving spacetime and the watches displaying different hours. It is not a question about the differences of hours "according to the terrestrial meridian, but of an astronomical hour function of the deformation of the spacetime. Just as the measuring tape displays units varying with the curvature of spacetime.

From the time of Newton, physicists debated the nature of light: waves or particles. Newton had a preference for particles while Huygen defended the waves.

Why is Einstein attacking the Newtonian fortress that seems to have appealed to everyone for three centuries?

First of all, because Newton considers space as rigid, for which each place is directly addressable by the three well-known dimensions: width, height and depth.

Here are some sentences that Einstein might have pronounced or even would have pronounced. (18) "A normal adult never stops to think about space and time. This question, the children alone are asking.

I stayed in a child. I have always asked myself the simplest questions and still ask myself now: Could God have created the universe in another way, or perhaps he had no choice? And how would I have made the universe if I had the opportunity?

I learned to isolate myself from the unpredictability of human relationships. The first theory of relativity was child's play in front of gravitation.�

Still, Albert Einstein has always had the ambition to read God's thoughts, and his "thought experiments" have not done him any good.

The occupant of the elevator freely falls and accompanies the cage. The latter seems to be at rest with respect to him who no longer feels any force on his body. He is in "weightlessness." Einstein finds that the free fall cancels the weight.

Everything inside the elevator also falls to the Earth, so at the same speed. When you fall into a cabin that falls at the same speed as you, you have no particular reason to be attracted. You will not touch the floor either since you are falling at the same speed as this cabin. And you will not have more reasons to be thrown to the walls for the same reason. Therefore, you float.

The cancellation of the weight corresponds to the cancellation of the gravitation since the weight is the force with which our mass is attracted towards the Earth.

The occupant of a spacecraft that moves at a uniform speed around the Earth also lives in weightlessness, after undergoing a huge acceleration, initially. If he accelerates, again, suddenly, the astronaut will be thrown to the floor of his cabin.

Yet in the elevator as in the ship, the terrestrial attraction continues to play. Actually, what is felt like the weight is not the attraction exerted by the Earth on the person of Einstein, but the reaction of the soil of the elevator shaft subjected to this force. This is also true for the International Space Station.

1st conclusion: it is the acceleration of the elevator and the one of the spaceship that cancelled the effects of gravitation. At the moment the elevator is touching the ground; the occupant is in the same situation as at the start, just before the fall of the cage: he feels his own weight, his feet resting against the floor, the trunk and the head attracted to the bottom. This is also the case if the spacecraft suddenly accelerates while sailing at a uniform speed.

2nd conclusion: gravitation and acceleration have the same effects. This also means that all the effects of gravitation can be offset by those of acceleration. Acceleration and gravity are felt identical.

Einstein then states his principle of equivalence: a reference of inertia, placed in a field of gravitation, is equivalent to a uniformly accelerated reference frame in the gravitational free space. No experience thus allows the observer to distinguish if he is in one or the other of these frames of reference.

If Einstein's principle of equivalence is valid, gravitation must be a phenomenon due to the curvature of spacetime. In other words, the effects that gravitation produces are equivalent to the effects of being in curved spacetime.

18 A film by Françoise Wolff., Coproduction The Seven ARTE - Thema Unit online productions, 1997

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The main theorical discoveries After the death of Einstein in 1955, the astronauts also tested this principle, when their capsule, braked by the friction of the atmospheric air, is falling towards Earth with an acceleration equivalent to 5/6 g. In this case, they only feel the remaining 1/6 of the g's. They could then believe that they are in a free fall towards the Moon whose field of gravitation is equal to 1/6 terrestrial.

Einstein then states his principle of equivalence: a reference frame of inertia, placed into a field of gravitation, is equivalent to a uniformly accelerated reference frame in the gravitational free space. No experience thus allows the observer to distinguish whether he is in one or the other of these reference frames.

If Einstein's principle of equivalence is valid, gravitation must be a phenomenon due to the curvature of spacetime. In other words, the effects that gravitation produces are equivalent to the effects of being in curved spacetime.

After the death of Einstein in 1955, the astronauts also tested this principle, when their capsule, braked by the friction of the atmospheric air, is falling towards Earth with an acceleration equivalent to 5/6 g. In this case, they only feel the remaining 1/6 of the g's. They could then believe that they are in a free fall towards the Moon whose field of gravitation is equal to 1/6 terrestrial.

What Einstein ignored about the principle of equivalence.

Einstein ignored, in this principle, the gravitational tidal forces.

Why? Whereas, according to Newton, the gravitational forces acted according to the distance separating the masses concerned. According to Newton, a human being had to be subjected to forces of various intensities. The feet being closer to the Earth, they should be more attractive than the ones acting on the head.

But, for the person who is in a free fall, "It does not feel its weight anymore," says Einstein (photo above right). Yet the stretching between head and feet and lateral compression are still there.

According to Thorne (19): "Einstein justified this oversight by imagining that the person in a free fall (and its frame of reference) was very small. If, for example, you are no bigger than an ant, all parts of your body are close to each other, and so the direction and intensity of the gravitational attraction will be virtually identical with the centre and extremities of your body (...)

On the other hand, if you are a giant 5000 km tall, then the direction and intensity of gravitational attraction of the Earth will be very different between the centre and the outer parts of your body.

As a result, you will feel tremendous stretching and compression during your fall. This reasoning convinced Einstein that in a sufficiently small frame of reference in a free fall (...) one should not be able to detect any influence of the gravitational tidal forces. So, small frames in a free fall in our universe with gravity are equivalent to reference frames of inertia in a universe without gravity. However, this is not the case for large standards."

19 Thorne Kip S .., Black holes and distortions of time, 'The sulfurous heritage of Einstein), Flammarion, Paris, 1997, p.106

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The main theorical discoveries Another illustrative diagram of the principle of equivalence

69

The main theorical discoveries .3.8.

Basic Ref lect ions on the Pr inciple of Equivalence

But how is this equivalence useful? Just to deport the questions. From now on, Einstein will study the problems that will not fail to arise in an accelerated reference frame, and it will transpose the result in a reference subjected to a field of gravitation.

This transposition must be local between a point of the accelerated reference frame and a point of the gravitational field.

When a person weighs himself in an elevator, the apparent weight of the scale is different when the elevator goes up and brakes; rises and accelerates; descends and brakes; descends and accelerates.

The scale indicates how strongly the person presses on it. Let’s call this force F, apparent weight; it is vertical down.

If the person presses with a force F on the scale, by reaction (Newton's third law, the actionreaction principle), the balance presses on the person with a force N. This force is also vertical but upwards. It is called the normal force of F and is symbolized by N. The positive direction of movement of the elevator will be bottom up. When the elevator goes up by accelerating, a = + a and when it goes down by decelerating, a = -a. As for the weight, it will always be oriented downwards and P (positive reading on the scale) will be written as -P (negatively vectorial compared to reading) If the elevator is stationary or moving at a uniform speed, a = 0 and N = P The apparent weight on the scale is equal to the actual weight.

If the elevator is accelerating upward, a = + a, .N = -P + m.a The apparent weight is then greater than the weight of the person, because F = -P + m.a.

If the elevator has a downward acceleration, (it is the case of a lift that goes up slowing down or a lift that goes down by accelerating), then, a = -a, N = -P -m.a The apparent weight of the person is less than his actual weight because F = - P - m.a.

In the case of a uniform ly accelerat ed reference frame If a person is in an elevator inside a spacecraft, located in the space where the gravity is zero, and if this vessel is subject to acceleration, the person is drawn to the elevator floor because of the acceleration. The inertial mass of this person tends to resist acceleration. It is therefore drawn in the opposite direction of the acceleration (N) Cont ext of a gravit ational field If a person is in a stationary elevator on the third floor of a building, the person naturally feels attracted to the ground because of the gravitational force. And she knows that if the floor of the elevator was not present to support it (thanks to the normal force N), the gravitational mass of the person would be in a free fall towards the Earth.

Both cases show quite different situations. However, the inertial mass of the person and his gravitational mass are both subject to forces in the same direction. And if the acceleration of the space elevator was 9.8 m / s2, the inertial mass and the gravitational mass would experience identical forces.

Indeed, the acceleration would exactly equal the intensity of the gravitational field. a = + 9.8 m / s2

N = -P + 9.8 m = zero

Finally, the inertial mass and the gravitational mass are two distinct concepts, but of equal value.

In this case, the mass person in the elevator could not tell it is on Earth orbut accelerating in a Finally, the inertial and gravitational mass arewhether two distinct concepts, of equal value. .non-gravity space. It is probably in a similar context that Einstein established the principle of equivalence. This states that a uniformly accelerated frame of reference is locally equivalent to a gravitational field.

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The main theorical discoveries 3. 9. The spacetime Einstein then said that if Newton's law was suitable for most terrestrial applications, it was false, however, if it did not take relativity into account, since Newton does not specify in which reference system the distance separating the two masses must be measured.

"Fortunately, as Einstein realized, Minkowski had brought a powerful tool to simplify this complexity: From now on, space as such and time to time are destined to disappear like shadows, and only a certain union of the two will retain a certain reality "There is only one four-dimensional absolute spacetime in our universe, and a deformation of all times and of all spaces must manifest itself as a distortion of Minkowski's unique absolute spacetime." (20) But how does the Earth produce the same attraction on all objects, whatever their material and size?

As François De Closets (21) writes: "Newton found his theory watching apples fall, Einstein will find his own by falling with the apples.

In the absence of mass, space and the time remain planes, the light moves in a straight line. Space is like squared by a scaffolding of rigid bars intersecting at right angles.

Thanks to them, any event can be spatially measured. For Newton, the same object will have the same measurements at some place in the space where it is located. But Einstein does not accept that space and time are independent of each other. On the contrary, he believes that one cannot touch one without touching the other.

When it passes by a body of a large mass, its trajectory is deflected by the curvature of spacetime.

The more massive the objects, the more spacetime around them is curved, curved.

Einstein concludes: "Spacetime acts on the matter and tells it how to move. Conversely, matter acts on spacetime and tells it how to bend.

This modification of spacetime by matter moves at the speed of light.

Space does not exist absolutely. Each body modifies it and thus creates its own geometry.

Space is the sum of all these geometries.

20 Thorne Kip S .., Black holes and distortions of time, 'The sulfurous heritage of Einstein), Flammarion, Paris, 1997, pages 108,109 21 De Closets, François., Do not tell God what he must do, Seuil, Paris, 2004 20 Thorne Kip S.., Trous noirs et

distorsions du temps, ‘L’héritage sulfureux d’Einstein), Flammarion, Paris, 1997, pages 108,109

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The main theorical discoveries According to Einstein, gravity is not a force, but a geometric property of spacetime.

The preceding experiment shows a mass deforming Newtonian space: mass and energy curl space and time.

Spacetime can be represented as a two-dimensional elastic surface.

From 1917, Einstein perceives through his mathematical equations that the universe must expand or contract. But Albert is convinced that the universe is an immutable static bubble.

Backing away from his own discovery, he introduces into an equation a "cosmological constant."

But it appears that a cosmological constant can very well be included in a formula that proves the extension of the universe. It is this constant that today explains what Einstein discovered. He said that gravitation, which brings the masses together, found an opposite force capable of dispersing them and that the whole remained static.

In 1922, the Russian mathematician Friedmann, along with other scientists, showed that such a universe is unstable and must show contraction or expansion. Expansion of the universe means that the distance between galaxies is constantly increasing. Not so much according to their speed, but because space, between them, expands.

3.10. A paradox from Paul Ehrenfest, Austrian physicist, a friend of Einstein From left to right: Zeeman, Einstein, Ehrenfest, around 1920.

Ehrenfest tells Einstein: "Albert, how come the ratio of the perimeter to the diameter of a spinning disc cannot be worth Pi (Ď€), which is still a basis of geometry!"

His reasoning is simple: if we refer to Newton's laws (see chapter 3.8, page 57) the resulting movement of a moving circular movement is perpendicular to the radius between the mobile and the centre of the circle.

Therefore, if we follow the Special Relativity, Ehrenfest is right in stating his paradox, since the contraction of the length along the direction of movement (presented in chapter 3.6.) will reduce the length of the perimeter of the circle while the radius remains unchanged!

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The main theorical discoveries 3.11. Einstein's answer to Ehrenfest's paradox Einstein interprets this "thought experiment" by a principle that will be the basis of general relativity, the famous principle of equivalence.

"If you're spinning on this record, like on a carousel," he answers Ehrenfest, "you'll feel attracted to the outside by centrifugal force as if you're in a gravitational field. Therefore, there is a link between gravitation and the geometry of space."

3.12. The contribution of Friedmann and Hubble Friedmann published two articles in which he analyzed non-static solutions of Einstein's equations. Einstein still does not imagine that the path opened by Friedmann will be followed by many mathematicians. Georges LemaĂŽtre reaches the same conclusion in 1927. LemaĂŽtre even gives the first consequence of this expansion: the escape of the extra-galactic nebulae In 1949, he wrote, in Albert Einstein: a Philosopher-scientist: "The history of science provides many examples of discoveries having been made for reasons, which are no longer considered satisfactory. This could be the case of the cosmological constant."

What is this anti-gravitational energy, that prevents the masses from coming together and, on the contrary, pushing them away from each other?

In 1929, Edwin Hubble (the second from the left in this photo) showed that our universe was not static, but that it did not stop, on the contrary, to expand. The cosmological constellation then fell into disuse, and Einstein wondered if he had made a huge mistake by preaching it. In 1931, Einstein published an article examining the possibility of a spatially infinite universe.

Seventy years later, this cosmological constant was taken up again in the equations of modern astrophysicists.

Today's astrophysicists are gradually discovering that the future of the universe depends only on the density of matter it contains. If this density exceeds a certain threshold, the gravitation will prevail over the expansion, by contracting the universe.

This is the "Big Crunch." If the density is below this threshold, it is the phenomenon of expansion which prevails.

It may be that a third hypothesis occurs where the density of matter is such that expansion and gravitation compensate each other, then one would have to deal with an expansion corresponding to a flat universe.

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The main theorical discoveries What were then the proofs that brought some credit to what Einstein had discovered?

Modern astrophysicists have discovered the supernovae. Those stars that have undergone the effects of antigravitational expansion eventually explode and become as bright as an entire galaxy. By measuring this luminosity, astrophysicists can distance us. When a star moves away from the earth, the wavelength it transmits to us increases compared to the original one.

In other words, the longer the wavelength goes red (redshift) the further it goes.

This recalled Einstein's cosmological constant, which had been neglected for a long time.

The astrophysicists found that by inserting it in their formulas, the expansion of the universe was not slowing down but, on the contrary, was accelerating.

It was found that the material accounted for only 30% of the universe while energy accounted for 70%. In other words, the form of the universe depends on what is there. Matter and energy continually engender one another according to its equation.

The layers stacked along the temporal direction describe the evolution of space over time.

The universe line of the Earth is the sequence of events that it occupies during its life.

The stars follow the curvatures generated in spacetime by the other planets. The trajectory of an object = shorter path along the curvatures produced by the mass and energy.

Space and universe line

What is an event ?

In physics, and particularly in relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (A specific place and time).

For example, a vessel sinking in the Red sea is an event; it occurs at a unique place and a unique time

We will also say that two punctual events occupy the same point of spacetime if they are simultaneous to any observer able to see them.

In order to be able to determine an event, one must know, in addition to the 3 spatial dimensions, the temporal dimension. All that we have knowledge belongs to the past, and the future is composed of events over which we can still have an influence. Since not all signals can be transmitted at a speed greater than that of light, the light beam we observe represents the limit of events that are temporally accessible to us.

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The main theorical discoveries Relative to this speed, all other spatially observable events occur at considerably slower speeds and appear frozen. That's what Einstein was already seeing when in his thought experiment when he wanted to ride a ray of light.

Geometrically, spacetime can be represented by two luminous cones contiguous by their point, which is situated on their common axis. This point represents the "here and now" of the motionless observer.

The axis common to both cones is the axis of time. The upper cone represents the future (positive cone); the lower cone represents the past (negative cone). Perpendicular to the axis of time, the spatial axes indicate the other places where there can be other motionless observers, who are located in what is called "elsewhere" and who also each have their own light cones.

The surface of the cones represents the set of universe lines of the photons; we name them "Null rays" or "null curves". Each zero radius corresponds to a point in the celestial layer of the observer concerned. The vertex cone p is an absolute geometrical structure that does not depend on the observer but on the spatiotemporal point where it is located.

Outside of the future and the past, the events of the present are spatially related. In other words, the future and the past are separated by the finite lapse of time which depends on the distance of the observer to this event.

The oblique arrow indicates the world image of a mobile observer looking at the future with a speed intermediate between 0 and c

The arrow coinciding with the vertical axis of time is the image of the world of the static observer

future This dotted line: signal light when v = c (zero radius

X2

elsewhere

elsewhere

X1

Here and now

past

For example, all the phenomena that occurred on the surface of the Sun reach us only 8 minutes later. The image of the world of a mobile observer, who evolves at a constant speed, is different from the one of the static observer. We can imagine that the moving observer, placed spatially and "temporally" at a given point on the superior cone, could influence everything that will happen in the following minutes. And especially another observer, located elsewhere.

A recent example is the one of a devastating tsunami observer from December 2004, who had the opportunity to warn several people over the phone, giving them time to shelter. It's not a bright event like an explosion solar, but the here and now of an observer could save other people whose here and now an hour later would inevitably have caused their deaths.

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The main theorical discoveries P

L

Q

My universe line: I am motionless while contemplating the sky

Event O at the top of the two cones

Consider that a beam of photons is emitted from the point O by an explosion on the sun by particles whose universe lines pass through O. Let L be one of these lines of the universe. Positive passing through P, which is a point of my own universe line.

My universe line is unidimensional whereas the null cone of the future is three-dimensional. The cone and my line are in the four-dimensional space that cannot be reproduced geometrically.

If an atom is located on the zero radius of the future of O, and that it cuts at the point Q thus absorbing the photon of the explosion, then it returns immediately a beam of photons. Generating, in their turn, a positive cone, these photons will pursue each one, their respective universe line, and those who will take my direction will be seen by me at the point P. P

Spacetime vectors

O

Q

A spacetime displacement is defined by a pair of points. The vector OP is of the temporal type; the vector OQ is of the spatial type.

Thus developed the geometry and the metric of spacetime for which you will find an explanation in the reference below (22) and in the mathematical appendix of this work.

Near powerful gravitational fields, the curvature of space is more accentuated than at-large distances. The curvature of the whole results from all the masses.

22 Ludvigsen, Malcolm., General Relativity, A Geometric Approach, Dunod, Paris, 2000

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The main theorical discoveries 3.13. Einstein calls on Marcel Grossmann, his mathematician friend From left to right, from top to bottom: Hermann Minkowski (1864-1909); Hendrik.A.Lorentz (1853-1928) Henri PoincarĂŠ (1854-1912) Einstein (centre) and his comrades: Marcel Grossmann, Gustav Geissler, and Eugen Grossmann.

Marcel Grossmann around 1900

Above, from left to right: Minkowski, Lorentz, PoincarĂŠ Below, the group photo, from left to right: Grossman, Einstein and two others?

Below right Grossman

Einstein was not a great mathematician, and the mathematical basis of his research had been set out by Hendrik Lorentz and Henri PoincarĂŠ (both biographical appendices). He had also been helped by Hermann Minkowski, his former professor at the Polytechnic of Zurich, who at first considered him a lazy student because he was aware that Einstein was not using his abilities well.

He will call Marcel Grossmann for help and will not make any mystery. It is true that the latter is a fellow student he knew in 1896 at the age of 17 years. He also found him, later, thanks to the relations of his father, a job at the Patent Office of Bern.

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The main theorical discoveries "Grossmann, you have to help me, otherwise I'll go crazy!".

The mathematician organizes his return to Zurich. From the summer of 1912, they can work together.

It is also Grossmann, who will be the dedicator of Einstein's doctoral dissertation.

And it was with him again that he wrote the first work on the general theory of relativity.

Here enclosed is an Einstein manuscript where, besides the calculations, appears the name of Grossmann and comments on his competence.

The formulas relating to the dynamics of the Friedmann universe, accessible to high- school students and academics, are explained in the following subchapter and in the mathematical appendix of this book (See explanation 9) "Algebra of Gaussian surfaces, the geometry of curved Riemann spaces, Ricci tensors, mathematical instruments are now in the hands of Einstein.

But as important is the tool, so much is the worker, and this one is only a poor user. He must redo his studies in higher mathematics, which he has refused, and go forcibly through the aridest disciplines: non-Euclidean geometry, tensor algebra. "I have never worked so hard in my life," he wrote to a friend, "but he adds: I have great respect for mathematics. (...) With his mentor, Grossmann, he struggles in inextricable difficulties (...) Where Newton is satisfied with an equation, Einstein must use ten (...) Einstein may be supported by Grossmann; it is difficult till you drop.» (23) The "Einstein equation" for general relativity using nonlinear partial derivatives and particular concepts (the energy-momentum tensor and the Ricci tensor) will by pass some difficulties.

Let’s simplify (24)

Let us remember at first approximation that the left-hand side of the equation is relative to the curvature of spacetime; it is the curvature tensor of Einstein. The right-hand member is the pulse energy due to matter, pressure and tension. It is called impulse energy tensor (T)

23 De Closets, François., Do not tell God what he must do, Seuil, Paris, 2004, pages 207 and 208.

24 Schutz Bernard, Gravity from the ground up, an introduction to gravity and general relativity, Cambridge University Press, 2003, p.242

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The main theorical discoveries 3.14. Putting into the equation the dynamics of the universe (Friedmann's equations) In cosmology, the matter is necessarily conceived of as a homogeneous fluid whose every point will have the average density of the universe. During the years 1922 to 1924, the mathematician Alexandre Friedmann analyzed non-static solutions of Einstein's equations, solutions that describe a universe in expansion. Einstein will remain silent for eight years, and in 1931, he will publish an article examining the possibility of an expanding universe.

He too adds a cosmological constant, but not to demonstrate that the universe is static, but to consider various possibilities of expansion which he will last retain as a representative of the current situation.



With R, the distance between two galaxies; G, Newton's gravitational constant (6,672.10 11), curvature, tot the density of the material; , the cosmological constant; and k, the sign of curvature Friedmann's equations that explain the evolution of the universe concern: • The primordial universe dominated by radiation rather than a matter • The current universe where the matter is more abundant The current situation of the universe is such that the radius R increases, and the energy density decreases. We can consider that, compared to the original explosion, located in O; the universe can be represented by a "comobile" sphere of radius R, centred on O, which always contains the same number of particles. If its total mass remains constant.

Neither Einstein nor any of his contemporaries imagined an expanding universe, but at that time the philosophical preconceptions defended the notion of a universe that remained similar to itself. Einstein modified his field equation by including a cosmological constant whose objective was to introduce a repulsive force allowing to consider a static cosmological space, which modifies the Friedmann equation.

Various theoretical possibilities of variation of the size of the universe and its speed of expansion as a function of time.

The various hypotheses of expansion of the universe are demonstrated from Friedmann's formulas.

To date, according to research, the density of matter is about a tenth of the critical density, so we would have an open universe, represented in hyperbolic space, although the density seems underestimated. In certain regions of the cosmos appear masses of still unknown nature, which would lead us to think that the universe is quite close to a flat universe.

In summary: Assumption of the closed universe ( = 0, k = 1): if the density of matter is greater than a certain critical density (Five hydrogen atoms per cubic meter), the gravitation takes over the expansion. The universe contracts and collapses on itself. There is a "Big Crunch", the opposite of the Big Bang.

The hypothesis of the flat universe ( = 0, k = 0): if the density of the universe is about equal to the Critical density, the expansion slows indefinitely and tends to zero. In these two cases, we obtain respectively:

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The main theorical discoveries

Let’s consider two more cases: The hypothesis of open universe ( = 0, k = -1): If the density of the universe is less than the critical density, the expansion of the universe continues indefinitely without accelerating.

The hypothesis of the accelerated expansion universe (0): the energy density of the vacuum is two times greater than the density of matter, its effects surpass those of gravitation and galaxies deviate. The expansion of the universe is accelerating indefinitely.

This is the new hypothesis confirmed in the 21st century.

Hypothesis of the accelerated expansion universe 0

Hypothesis of the open universe (=0, k= 1)

time

expansion

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The main theorical discoveries 3.15. Essay of real representation of the universe. Notions of non-Euclidean geometry Einstein recognizes that it is impossible for him to conclude the finitude of the Universe.

He speaks of a closed continuum according to its spatial dimensions. A sphere, for example, is a closed continuum because it has a finite area, and yet it is possible to traverse its surface without ever finding a bound or boundary. The surface of the Earth is finite but without origin, end, or centre.

While Newton only knew the ancient Euclidean geometry, from the end of the eighteenth century, mathematicians explored new geometries that will be very useful to Einstein. Newton only knew Euclid's mathematics, the one we use every day. In summary: space is flat; the sum of the angles of the triangles is equal to 180 degrees. Euclidean geometry favours the notion of "right" as the shortest path from one point to another.

Bernard Riemann, among others, discovered other geometric universes.

Nevertheless, more generally, we introduce the notion of geodesics (straight on a plane, arcs on spheres).

The following figures present triangular geodesics. The curvature of these is directly related to density. They correspond to the Friedmann-Lemaître universe for various values of k when the cosmological constant is zero ( = 0).

K=0, flat space

K< 0, hyperbolic space K = 1, flat sphéric space

There was a time when man thought the earth was flat. Now he accepts the fact that it is round, and he knows that on the surface of the Earth, the shortest path between two points is not a straight line, but a curved line. Between New York and London, for example, the shortest way is a large circle that passes through Nova Scotia, Newfoundland and Iceland.

Like a giant triangle is drawn on the earth's surface from Two points of the equator to the North Pole do not satisfy Euclid's theorem stating that the sum of the interior angles of a triangle is equal to 180 ° C. On positive surface geometry, the sum of the angles inside a triangle is greater than 180°. While on a saddle surface, this sum is less than 180 degrees.

While on a flat surface, two parallel lines do not intersect, they intersect on a curved surface.

It is the curvature of the earth that forces two straight lines initially parallel to cut at the North Pole.

The following figures (25) present the spacetime near the Earth, where we see the time line and the direction of the Moon. It can be seen that the geodesics of two particles get closer in the case where the curvature is spherical (figure b) and deviate when it becomes hyperbolic (see following page). Einstein realized in 1912 that the tidal force and the curvature of spacetime were one.

25 Thorne Kip S .., Black Holes and Distortions of Time, 'The Sulfurous Heritage of Einstein), Flammarion, Paris, 1997, page 114

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The main theorical discoveries

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The main theorical discoveries The work of Thibault Damour, professor at the Institute of Higher Scientific Studies and member of the Academy of Sciences, focuses on the physics of gravitation and especially on the relationship between theories and experiences. He has received numerous awards, including the "Einstein Medal" I attended a few of his lectures in Paris and learned a lot. In an exceptional work, "Einstein Today," he writes: "Let us comment on the physical meaning of Einstein's equations.

The essential new idea is that the chrono-geometric structure of spacetime, that is to say, the structure which underlies all the measures that can be made locally of durations, dT, and distance, dL, is no longer a rigid structure, given a priori once and for all (as was the structure of the spacetime Pöincaré-Minkowski), but has become a field, it is that is, a dynamic, or elastic, structure that is created and/or deformed by the presence of an energy-pulse distribution." (26)

On the left, a rigid spacetime of the theory of relativity; on the right, the geometry of the "elastic" spacetime of the theory of general relativity.

See the mathematical appendix (Explanation 9) for additional information useful for understanding this hyperbolic representation.

How can the universe be both finite and unlimited? From the book of Einstein. (27) "The development of non-Euclidean geometry led to the notion that we can doubt the infinity of our space, without coming into conflict with experience (Riemann, Helmholtz).

These subjects have already been treated in detail and with an incomparable limpidity by Helmholtz and Poincare, while I can only sketch them briefly here.

We first imagine a kind of two-dimensional existence. Suppose then that there are flat beings with flat instruments and, in particular, flat rigid rulers that are freely mobile in a plane.

Outside of this plane, there is nothing for these beings and everything that happens in their plan, what they observe in themselves and in their flat objects constitute a closed causal system. The constructions, in particular, of the Euclidean plane geometry, can be realized by means of rods, for example, the construction of a network. The world of these beings is, contrary to ours, two-dimensional, but, like ours, infinitely extended. There is an infinite number of identical squares formed of sticks, that is to say, its volume (surface) is infinite. If these beings claim that their world is "plane," it makes sense, that the Euclidean plane geometry constructs can be executed by their rods, each rod always representing the same length regardless of its position.

26 Leduc Michèle., Director of the current knowledge collection, Einstein today 27 Einstein, Albert., The theory of Special and General Relativity, translated into French by Maurice Solovine for Gauthier-Villars in 1923; Preface by Marc Lachièze-Rey, Dunod, Paris 2004, page 120 and following

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The main theorical discoveries Imagine now another kind of existence in two dimensions, not on a plane, but on a spherical surface. Flat beings with their rulers of measurement and their objects are exactly adapted to this flat surface and cannot leave it; all their world of observation, on the contrary, extends exclusively to the surface of the sphere. Can these beings consider the geometry of their world as a two-dimensional geometry and, in addition, their rods as the realization of the "straight line"? They cannot, because in trying to realize a line, they will obtain a curve that we, beings with three dimensions, denote by the largest circle, that is to say, a closed curve of indefinite length, which can be measured by means of a ruler. This world also has a finite surface which can be compared to a square formed of sticks. The great charm of this reflection lies in the following knowledge: The world of these beings is finite and yet boundless.

But the beings on the spherical surface do not need to make a cosmic journey to find that they do not live in a Euclidean world. They can be convinced of this on every part of their world that is not too much small. They draw from one point, in all directions, "straight lines" (circular arcs in three-dimensional geometry) of the same length. The line joining the free ends of these lines will be called "circle." The ratio of the circumference of a circle to its diameter, both being measured with the same ruler, is, according to the Euclidean plane geometry, equal to a constant , independent of the diameter of the circle. Our beings would find on their spherical surface this ratio equal to:

That is to say a value less than  and differing all the more from  that the radius of the circle is greater compared to the radius R of the "spherical world."

This relationship allows beings in the sphere to determine the radius R of their world, even if they only have a relatively small portion of their spherical world for their measurements. But if that part is too small, they cannot more say that they are on a spherical world and not on a Euclidean world; a small part of a spherical surface is little distinguishable from an equivalent part of a plane.

If, therefore, the beings of the sphere live on a planet whose solar system only an infinitely small part of the spherical world, they do not have the possibility to decide if they live in a finite or infinite world, because the part of the world which is accessible to their experience is in both cases practically plane or "Euclidean."

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The main theorical discoveries Let's move towards this type of space. a) Finite space limited to one dimension: A wire of length L of end A and end B

B L

A

L

b) Finite and unlimited one-dimensional space like this circumference without origin and without end of length L.

c) Two-dimensional space finite and limited like this rectangle of length L and width l

l

L d) Finite and illimited two-dimensional space as the surface of a sphere (like the Earth) of finite superficies without origin, without end and without a central point. We can move on this finished surface without ever encountering a limit. e) Three-dimensional space finite and limited like this parallelepiped from which one side has been removed to show the inside of volume V limited externally by its faces of length L, of width l and height h.

h

l L f) A finite and unlimited three-dimensional curved space (so no centre) It is geometrically impossible to represent. This is the universe of Einstein.

In the Hors sÊrie de Sciences et Avenir n ° 105 of March 1996, JeanPierre Luminet, research director at the CNRS, astrophysicist at the Paris-Meudon Observatory, wondered: "Is the universe spatially closed or open? ".

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?

The main theorical discoveries Often neglected by researchers, the study of topological "variants" of three-dimensional space is likely to provide original answers to the question of spatial extension.

In "crumpled" universe models, the sky is the scene of a gigantic optical illusion. When we see a sky filled with galaxies, this aspect does not make it possible to decide if the galaxies of the distant regions are or not ghost images, that is to say, repeated images of galaxies closer.

The universe might seem to us "unfolded" while it would actually be much smaller and "folded."

In the same article, we read: "The partisans of a finite world have long stumbled on a fundamental difficulty that Archytas of Taranto, Pythagorean of the fifth century before Christ, has stated: a paradox to demonstrate the absurdity of the idea of a material edge of the world.

"If I am at the end of the sky, can I stretch out my hand or stretch a stick? It is absurd to think that I cannot; and if I can, what is beyond is either a body or space. So we can go beyond that again, and so on. And if there is always a new space to which the stick can be stretched, it clearly implies an extension without limits.

If what is beyond the world is still part of the world, the world cannot be logically limited.

It was not until the development of non-Euclidean geometries in the nineteenth century to put an end to the controversy. These geometries make it possible to design finite spaces without having an edge (just like the two-dimensional surface of a sphere). This conception is not so natural: when a speaker describes the expansion of the universe, he is often asked the question: "In what does the universe swell? The answer is that the universe does not inflate in anything at all since there is no space outside itself.

Above: the escape of galaxies: illustration of S.Numazawa 3.16. Revealing on the light After the paradox emitted by Ehrenfest in chapter 3.9. And Einstein's answer in chapter 3.10 on a consequence of the Special Relativity (at the speed of light, a rotating mobile would traverse a circumference whose length is less than Pi times the radius), we observe that a ray of light bends inside a spacecraft in the process of acceleration. This experiment reveals to us that if the acceleration of a spaceship curves the light, then the gravitation can also bend it.

Einstein concludes: "We must admit that the geometry inside the ship has been modified by its acceleration.

Geometry has become curved."

Why is light affected by gravity if photons are massless?

In the spacetime map, objects with mass are following time-type lines that are of maximum length in common.

Without gravitation, these lines are straight lines, and spacetime is "plane". In the presence of gravity, spacetime is no longer planar and the lines characterizing each object are no longer straight lines, but curves, which give the impression of an attraction by gravitation.

The mass of objects does not intervene in the problem; the fall of bodies does not depend on the mass, as Galileo had observed.

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The main theorical discoveries For the light, it is a little different because it does not follow like the masses of lines of maximum length. The light follows the "null" lines, those that are in the spacetime map between the space lines and the timelines.

But the effect of gravity is similar, spacetime is no longer a plane, and null lines are no longer straight lines, but curves, which give the impression of attraction by gravitation.

Finally, when we speak of a photon "falling" in a black hole, this is due to the curvature of spacetime around the hole and not to the effect of gravitational attraction in the classical sense.

In short, the photon escapes all the phenomena that testify to the presence of a mass in the classical sense, in spite of the experimental attempts made to detect it. So, until proven otherwise, the photon has no mass, without contradicting its energetic nature.

This illustration shows how two photons, one at a high frequency (nu_h) and another at a low frequency (nu_l), travel in curved spacetime from their origin in a distant Fast Radio Burst (FRB) source until reaching the Earth.

A lower-limit estimate of the gravitational pull that the photons experience along their way is given by the mass in the center of the Milky Way Galaxy.

CREDIT Purple Mountain Observatory, Chinese Academy of Sciences â&#x20AC;&#x153;General relativityâ&#x20AC;? abandons the notion of force and replaces it with the concept of curvature of spacetime.

The celestial bodies adopt trajectories as straight as possible, but they must submit to the configuration of spacetime. Far from any distribution of matter, the curvature of the spacetime is null, and all the trajectories are straight lines.

Near a massive body like the Sun, spacetime is deformed and bodies move on curved lines.

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The main theorical discoveries Brans-Dicke's theory states that:

where M is the mass of the sun: 1.99.1030 Kg; R, its radius: 696000 Km; G, the universal gravitational constant: 6.673.10-11; r, the minimum distance from the light ray to the centre of the Sun; ď § an additional parameter. It must be added that, according to the theory, this deviation is equal to twice that obtained in Newton's theory.

Radio image of a gravitational lens: the Einstein cross. These are four sources emitting radio radiation surrounding a fifth radio source located in the centre. With the exception of the central source, which comes from the nucleus of a galaxy estimated at 400 million light-years, the four other sources constitute the multiplied images of one and the same object, a quasar located in the background of the central galaxy at a distance 20 times greater.

The formation of multiple images of the same object results from the curvature effects that the electromagnetic radiation undergoes when it passes near a massive object, such as this galaxy in the centre of the image. This galaxy thus plays the role of a complex gravitational lens, which gives several images of the same object and amplifies the intensity of the source. Astrophysicists are examining this image taken by the Hubble telescope.

They named it the Einstein Cross. Indeed, these five stars are actually a mirage. The galaxy visible in the centre is yet real and a very distant star whose image is multiplied in four copies (they are the branches of the cross) Actually, the galaxy bends the light of the star passing nearby, as predicted Einstein. This galaxy functions like a gravitational lens, which can reverse, deform, multiply, enlarge or shrink the image of a star transported by light. .

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"The Gods need man and men need Gods"

Chapter Four Experimental Evidence LĂŠon Brillouin writes an article in the journal La Science et la Vie No. 63 of July 1922 entitled "The Einstein Theories and Their Experimental Verification." The photo is part of the article.

The interest of these sentences is to grasp the opinion of a specialist at the time when Einstein was very famous because he had just received, with retroactive effect for 1921, the Nobel Prize in Physics.

4.1. Checking the mass variation with speed To observe it, writes Brillouin, one must apply to animated particles of a very high speed: these are the electrons emitted by the radioactive bodies and constituting the radiation (their speed can reach 0.85 times the speed of light;) in highvacuum tubes, similar to X-ray bulbs, electrical discharges involve very fast electrons: with 80,000 volts, the speed is half that of light. Many experiments have been carried out.

In general, they concluded that the relativistic formula was correct, but the measurement errors were too high to lead to conviction: recent research, led by Professor Ch.-Eug.Guye of Geneva allowed an interesting and complete check. The experiments, very difficult, were continued from 1907 to 1916.

4.2. The mass defect of atomic nuclei In 1913, Paul Langevin (Photo taken from the group of physicists attending the Solvay conference of 1927) explains the "mass defect" of atomic nuclei; that is why the mass of an atomic nucleus is inferior to the sum of the masses at rest of the nucleons (see glossary) which constitute it.

According to Langevin, the nucleus, forming from its components, releases energy to stabilize its structure and this release of energy produces a loss of mass.

In 1932, two British physicists, John Cockroft and Ernest Walton, experimentally prove the transformation of mass into energy by bombarding a lithium plate with highly accelerated protons: they observe the disintegration of lithium nuclei into two helium nuclei. By studying the trajectory of these emitted helium nuclei, they measure their kinetic energy and thus empirically verify the partial conversion of the resting mass of lithium nuclei into kinetic energy.

In 1938, the German chemists Otto Hahn and Fritz Strassmann, while bombarding uranium with neutrons, find the presence of radioactive barium in the reaction products, that is to say, of an element whose nucleus counts less of protons than uranium. The Austrian physicists Lise Meitner and Otto Frisch interpret this result by the fission of uranium: the uranium, bombarded by neutrons, breaks up into two lighter nuclei and several neutrons. The energy released corresponds to a small part of the rest mass of the uranium nucleus, but it is already considerable.

Although these discoveries were fundamental, let us note, however, that Einstein did not participate in any development leading to the creation of the atomic bomb. He is not a nuclear physicist 81 and did not participate in any research leading to the construction of the atomic bomb during the war.

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Experimental Evidence 4.3. Evidence of relativity and gravitation. "General relativity" The first form of relativity, despite its great successes, was incomplete. Some theoretical problems remained impossible to treat by his methods; but above all, the very serious pitfall was the existence of gravitation; relativity asserted that no action at a distance can be instantaneous, but must propagate with a speed less than or equal to that of light; on the contrary, since Newton, all gravitation was built on the hypothesis of attractive forces existing between all the material bodies, and which one supposed to act without any delay; there was incompatibility between the two points of view.

Moreover, the inertia of energy led to the admission that the luminous energy itself had a certain mass; a luminous ray passing near the sun had to be deflected, just like a very fast comet.

But how can the precise laws of these actions be established in an exact manner?

Einstein rigorously maintains the identity of the heavy mass and the inert mass in accordance with the result of Eötvös' extraordinarily precise measurements; gravitation plays the exact same role as an acceleration; all the energy is heavy, and a ray of light will be deflected near an enormous mass such as that of the sun.

This point of view is clearly that of a physicist, with a remarkable intuition of the general notions which emerge from the measurements. The development of the theory requires a rather difficult mathematical apparatus: Einstein, when he approached this problem, did not possess the mathematical technique thoroughly enough; he learned it progressively, driven by necessity and by the intimate logic of the facts, and succeeded in edifying the theory which we admire at present.

Independently of its new consequences, it constitutes a marvellous effort to generalize all our physical laws and makes it possible to give extraordinarily condensed statements.

What consequences could be drawn from the new theory? For most of the usual cases, one found practically the same results as by the old methods: the gaps could become sensitive only in the immediate vicinity of a body of very considerable mass, for example, the Sun. Einstein could predict the following three effects: 1 ° A planet gravitating a short distance from the Sun will no longer traverse an ellipse; his trajectory will not be closed; we can imagine it as an ellipse animated by a slow rotation around the Sun; 2. A luminous ray will be deviated by a quantity twice that to which the application of Newton's law would correspond; 3. The spectral lines of the Sun, instead of being fixed, will be displaced towards the red.

We will examine successively these three points, to believe in more detail the appearances observed and their verifications.

We will consider the first two effects.

Displacement of the perihelion of Mercury The closest planet to the Sun is Mercury, so she is well suited to try to verify the first forecast of Einstein. The movement of Mercury is troubled by the attraction it receives from other planets; if we observe the trajectory of this planet, we can consider it as an ellipse whose main axis PSA is animated by a rotation around the sun.

Aphelia is called point A and perihelion is the point P, and this phenomenon is called the "displacement of perihelion."

The displacement observed is 574 seconds arc per century; the calculation of the perturbations which the actions of the other planets bring to the movement of Mercury makes it possible to explain a rotation of 532 seconds; there remained a residue of 42 seconds per century of unknown origin (...) But the theory of Einstein provides an additional rotation of 43 seconds per century.

The agreement is therefore complete on this point. (28)

28 Science and life, No. 63 of July 1922, Einstein's theories and their experimental verification, by Léon Brillouin

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Experimental Evidence pexpérimentales

The left part of the figure shows the real trajectory of the planet Mercury, which does not close on itself; I can think of it as an ellipse whose perihelion P would slowly turn around the sun S. The observed rotation is 42'' per century, and Einstein predicts 43''; The striking agreement is based on astronomical measurements made during the last centuries, and remained unexplained until today

This figure represents the results of the best measurements made by the expedition of the deviation of light near the sun

"The reasoning of Einstein was simple: according to Newton the gravitational force depends on the distance between the two objects that gravitate (for example the Sun and Mercury

11 Fcentripète  6,672.10

m1.m2 r2

but according to relativity, this distance is not the same in different cases.

Einstein's daring was startling. Having rejected Newton's absolute space and time practically without any experimental justification, he was now tempted to reject his law of gravitation and his immense success with even less experimental verification.

However, it was not the experiments that motivated him, but his profound intuition about the way in which the laws of physics were to behave " (29) Heavy light, deviation of light rays near the Sun After the Solvay Council of 1927, in the article from the journal "Science and Life", No. 120, of June of the same year, Marcel Boll, Professor at the University of Paris writes, in a great article entitled "Progress of German Physics of the last ten years": "The only moment, when such a phenomenon can practically be observed, is during a solar eclipse; some stars near the Sun are visible; we will photograph their positions very exactly and compare the photograph thus obtained to a photograph of the same region of the sky, taken when the sun is not there.

Verification experiments were organized in 1919 by the English astronomer Eddington. The eclipse of May 29, 1919, was particularly favourable, the Sun was in the middle of a large number of bright stars (the Hyades cluster); two expeditions left; one with Dr Crommelin and Mr Davidson moved to Sobral, a town in northern Brazil (Ceara); Messrs. Eddington and Cottingham, on the other hand, went to Little Prince Island, in the Gulf of Guinea (Africa).

29 Thorne Kip S .., Black holes and distortions of time, 'The sulfurous heritage of Einstein), Flammarion, Paris, 1997, p.96

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The photographs of the ellipse were hampered by a little overcast weather; one of them, however, succeeds with very great sharpness and gives as the result 1'61, with a probable error of 0.'' (30) (...)

We see that the experimental numbers agree very well with the theoretical value of 1'75, especially if we take into account the great difficulty of measurements.

In the chapter, Relativity, of the same article, Boll writes: "In 1915, the Special Relativity of Lorentz and Einstein was solidly founded: it transformed physics into a kind of four-dimensional geometry, in which time came along with the three dimensions of space.

It was in 1915 that Einstein (then in Zurich) published his first memoir on general relativity: the physical point of departure was the classification, in a logical and coherent system, of phenomena of inertia and gravitation, which were juxtaposed and independent in Newton's mechanics.

Three orders of experimental verifications came to justify, after the event, generalized relativity; they were: the incurvation of the light close to the Sun, the movement of the planet Mercury, the comparison of the colour of the lights emitted by the sun and on the Earth.

The resentment of these works was enormous, even outside the circle of physicists; One can add: inconceivable when one knows that their true understanding requires deep mathematical knowledge. But the men of this epoch, overcome by the tragic events of lived history, sought simultaneously: the marvellous who was to free them and the solid base on which they could build; they imagined finding one and the other in the marvellous results of the exact science. (...) Science has learned from Einstein, above all, not to be afraid of the suspicion that can be thrown on seemingly the most certain notions, on the most obvious truths, when the experience requires it."

In the chapter The quanta of the same article, Marcel Boll continues: "The theory of quanta was proposed in 1900 by Max Planck (Berlin), but it is only in the last ten years that it appeared that This was a fundamental reform of physics, like that of the theory of relativity. These are thanks to the Dane, Niels Bohr, who applied, with prodigious success, Planck's ideas to the structure of atoms. (...) That the matter has a corpuscular constitution, the demonstration was made in the preceding decades; it was also already known that each chemical atom had a complicated structure, composed of smaller plots, and the elements of the building had recognized the atoms of electricity (the proton, positive, and the electron, negative).

With the theory of quanta, it was a question of finding, in the natural laws, the origin of these distinct particles. Planck attributed to energy an atomic structure; Bohr founded a more general theory according to which, not only energy but also other mechanical quantities can only be integer multiples of an elementary quantity, a common part, a quantum." It is said, to shorten, that this magnitude must be quantified, according to the expression universally consecrated.

Quantification is required especially for the rotary pulse of an electron that describes an orbit.

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Experimental Evidence pexpérimentales Still in the chapter "The quantum of light," the old wave theory solidly grounded on a great number of facts, was in complete contradiction with the theory of the quantum, which may be regarded as a sort of corpuscular theory. This opposition was particularly highlighted by Einstein, who introduced the notion of quanta of light, kinds of atoms of light, and showed the possibility of explaining certain phenomena in which radiation has a mechanical action. So are the photochemical reactions, like the decomposition, by the light of the silver salts of the photographic plate. This is also the photoelectric effect, that is to say, the emission of electrons when a metal is struck by the radiation, a photoelectric effect which serves as a basis, as we know, for television attempts. The fundamental law of these phenomena, discovered by Einstein, has been verified by many researchers.

To conclude this chapter on heavy light, note that in order to verify the prediction of general relativity on the deviation of electromagnetic waves close to a massive object, astrophysicists measured, from 1969 to 1984, the deviation of radio waves emitted by several quasars (see glossary). In order to compare Einstein's theory with that of Brans-Dicke (see page 78), a graph shows measures of the coefficient (1 + ) / 2 which is equal to 1 in Einstein's theory.

These measures thus confirm the general relativity and render the BransDicke theory unnecessary. (30)

4.4. A gravitational shift of frequencies following the attraction of light After the death of Einstein, the theory of general relativity is experiencing renewed interest. Robert Pound and Glen Rebka experimentally highlight the gravitational shift of frequencies.

What is it about?

In 1958, the German physicist Mössbauer discovered that high-energy photons (gamma photons) have a well-defined frequency and when they strike identical nuclei to those who emitted them, they emit photons of the same frequency. It is said that the receptor nuclei and the photons are in resonance.

On the other hand, in the case where the incident photons change frequency, which occurs in a gravitational field, the receiving nuclei no longer resonate with the photons and then emit only a few photons. The experiment was carried out in the Jefferson Tower at Harvard University. They find that by falling into the Earth's gravitational field, photons have changed frequency.

Among many other experiments in 1970, Shapiro and his colleagues send a radar signal to Venus, which serves as a passive reflector. The moment chosen for the experiment is what is

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Experimental Evidence called the conjunction, that is to say, the moment when the Earth, the Sun and Venus are aligned.

The experimental graph above shows the delay of the signal (in seconds) as a function of the conjunction. We note that the day named zero has the maximum delay while, the previous year and the following year, it vanishes. The maximum detected delay is 200 microseconds, or 0.2 milliseconds on a path that lasts, on average, 20 minutes.

4.5. Checking the photoelectric effect by Millikan On the abscissa, different incident radiation frequencies are measured, and on the ordinate, the necessary limit voltage to be applied so that the electron removed at the first electrode does not reach the second electrode. This voltage is proportional to the kinetic energy of the electron (1/2 mv2) and to the Planck energy minus the work of extraction: E = hfW, as indicated by the annotations of Millikan (where f is replaced by the Greek letter ď Ž, and W

by P).

It can be seen that the kinetic energy of the electron released (on the ordinate) is linearly proportional to the radiation frequency (on the abscissa). And, as Einstein predicted, there is a limit frequency below which the electron is not ejected.

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Experimental Evidence pexpĂŠrimentales 4.6. The discovery of cosmological radiation in 1965 and the Big Bang.

Today, we can observe from a great distance and go back to the past. Thus, objects distant from 10 billion years of light appear to us as they were at that time.

"The simplest schoolboy now knows truths for which Archimedes had sacrificed his life," Renan wrote in the second half of the nineteenth century. Today, high school students know modern physics and the main cosmological constants that were still unknown to scientists of that time.

They know the various assumptions of the birth of the universe and know that its development has gone through various phases of which the oldest, "the era of Planck" concerns the 10-43s after the Big Bang. There were temperatures of 1032 K.

Since 1992, the photo made by the COBE (COsmic Background Explorer) satellite of cosmology has made it possible to map the image of diffuse cosmic radiation. These were valuable insights into the early stages of formation of galaxies and clusters of galaxies.

This satellite discovered small spatial variations in the intensity of the radiation that it captured. It was radiation in millimetric and centimetric waves, which was the same in all directions of space (isotropic). It appeared about a billion years after the Big Bang when temperatures fell to 3,000 ° K. At that moment, the protons could capture electrons. The universe, opaque, became transparent. He then resembled a ball of fire. This radiation today corresponds to a "black body" of 3K temperature.

This photo is exceptional since it is a trace of the primordial Universe, which has experienced a very dense and very hot phase. This fact of observation constitutes today solid support to the big-bang theory which describes the first moments of the Universe.

4.7. Checking the Twin Paradox (31) In 1976, researchers at the University of Maryland checked the twin paradox. The first graph, page 88, represents the time measured in the aircraft, and the time measured on Earth appears for the duration of the experiment of about 60 hours. The curve is divided into three portions (before, during and after the flight).

The clock placed in the high-altitude aircraft operates a little faster (effect due to the variation of the gravitational field of the Earth with the altitude), but the clock of the plane is lagging behind to that remained on Earth, because it has travelled a shorter spacetime distance (effect depending on the speed).

The second graph shows the evolution of time differences due to the algebraic sum of gravitation and velocity. .

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Experimental Evidence pexpĂŠrimentales 4.8. Experimental verification of time dilation In 1941, B. Rossi and D. Hall observed this effect directly by studying particles in the cosmic rays, the muons.

Artificially produced muons in the lab disintegrate after an average lifetime of about two microseconds. However, the cosmic-ray muons detected on the surface of the Earth have been created in the upper layers of the earth's atmosphere, more than 10 kilometres from the detectors, and the light takes about 30 microseconds to travel that distance.

How can we detect cosmic muons if their average lifetime (2 microseconds) is less than the travel time (30 microseconds)?

Einstein gives the following answer: the muon velocity being close to that of light, they live much longer from our point of view t0 (from their point of view, their lifetime is always two microseconds.)

In other words, if we apply the formula of the Special Relativity

tv = t 0 and if we imagine that the velocity v increases considerably, the second factor with the root tends towards 0 we note that the time tv lived by what is in the reference frame in movement (Where is the muon?) is much shorter than the time t0 lived by what is in the reference frame at rest, that is to say in this case the human observer who realizes the experiment.

In other words, the height hv of the Atomium measured by a living being moving at a speed v from the summit to the base is clearly lower than the height h0 measured by a motionless observer if we actually observe that the life of the muon in the laboratory is 2 seconds, it is not the case when it moves at a speed close to that of light where we see a duration of 30 microseconds.

One can also imagine that a muon falling from the sky to the earth at a speed close to that of light would perceive the Atomium with a considerably reduced height.

We have seen that relativistic time was linked to length (or height) :

hv = h0

N.B. h est la hauteur (Ă ne pas confondre avec la constante de Planck qui est tout autre chose)

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Experimental Evidence Two photos that were taken during the exhibition â&#x20AC;&#x153;Einstein un autre regardâ&#x20AC;? (Einstein another look)

Above, the Atomium seen by an immobile muon.

Below, the Atomium seen by a cosmic muon.

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My meeting with Einstein during the exhibition â&#x20AC;&#x153;Einstein, the other lookâ&#x20AC;? at Tour et Taxis in Brussels in 2005 4.9. Experimental checking of gravitational waves A reminder of chapters 3.8 to 3.10.

In these chapters, we learned how Einstein attacked the Newtonian fortress, and especially what the impact of his principle of equivalence had been.

Let us remember that weightlessness corresponds to a system in which we cannot measure any acceleration, caused by gravitation or by any other force, by an observer situated in this system.

We saw that Einstein falling freely in an elevator shaft no longer felt his weight (and any object accompanying him fell at the same speed as him.)

Actually, what is felt like the weight is not the attraction exerted by the Earth on the person of Einstein, but the reaction of the soil of the elevator shaft subjected to this force.

Thus, falling free-fall with the elevator, Einstein feels weightless, as the astronauts feel in a free orbit around the Earth.

We have also seen in chapters 3.8 to 3.10 that, technically speaking, a body is not in a state of weightlessness in free fall if it is sufficiently large, or if the gravitational field is sufficiently intense and non-uniform so that the body is subject to considerable massive forces.

Albert Einstein thus postulated the total equivalence between free fall and the absence of gravity: no physical experience, no measure can differentiate a situation of free fall from a situation of absence of gravity.

It is this principle of equivalence that is at the origin of the theory of general relativity. This equivalence is only local, for punctual objects.

According to Einstein, gravity is not a force, but a geometric property of spacetime.

As we have also seen in the aforementioned chapters, spacetime can be represented as a two-dimensional elastic surface.

The term gravitational wave (or gravitational wave) is used to express the oscillations of the curvature of spacetime that propagate at the speed of light in a vacuum.

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Experimental Evidence On September 14, 201532, LIGO33 researchers announced that they had detected gravitational waves directly from two black holes. This announcement was confirmed on February 11, 2016, at a conference of the National Science Foundation in Washington. The result is published the same day in the journal Physical Review Letters.

It would also be "the first direct proof of the existence of black holes," says Thibault Damour, the French theoretical physicist.

The interferometer LIGO (Laser Interferometer Gravitational Observatory)

We have seen previously that any mass movement in a point of the universe creates a wave propagating through the cosmos. The larger the mass, the greater the curvature produced and thus the greater the gravity. The curvature of the spacetime adjusts to reflecting the change in the position of accelerated objects, and it propagates like "waves on the surface of the water."

The efficient production of gravitational waves requires very large masses and very large accelerations. These are mainly astrophysical systems involving massive and very dense objects like black holes.

32 "Physicists announce that they have detected Einstein's gravitational waves" [archive], on Powerpoint 33 The Laser Interferometer Gravitational-Wave Observatory (LIGO)

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Experimental Evidence pexpĂŠrimentales At the passage of this gravitational wave, a portion of the space expands and contracts before returning to its original shape.

The LIGO detection tool is an interferometer whose laser beam is sent to a mirror that separates it into two beams.

Each one travels a distance of several kilometres at the end of which a mirror returns the captured beam.

After several round trips, which increases the accuracy, each beam out of the arm to cross the other beam with which it recomposes.

If the two beams have travelled the same distance, they return at the same time to the intersection.

If a gravitational wave has shortened or lengthened one of the arms, one of the beams comes out a bit before or after the other.

This phase shift means that the result of the subtraction of the two beams will not be zero. It is this "vibration" that would have detected LIGO.

Schematic diagram of LIGO. Source: LIGO "The interferometer concept is, therefore, quite simple, but to reach the precision required to detect gravitational waves, it is a real feat because these interferometers, which are 4 kilometres long, must be able to measure a difference in distance. 10-18 m, one billionth of a billionth of one meter or the ten-thousandth of the diameter of a proton!

The distance ratio to measure is 1021. It amounts to measure a difference of 1 centimetre between the Earth and the closest star to our solar system (Proxima Centauri located 4,000 light-years away.) It's just amazing!

First of all, LIGO has many 4-kilometre arms but, actually, the light in 1600 between the mirror and the separator because between the 2, the scientists added what is called a cavity of FabryPerrot in which the beam makes 400 back/forth movements artificially lengthen the arms and thus improve the sensitivity of the device."

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Chapter Five Some quotes from Einstein A hollow stomach is not a good political adviser.

The most beautiful thing we can experience is the mystery of things.

The possession of marvellous means of production has not brought freedom, but worry and famine.

The true value of a man is determined first by examining how far and in what sense he has managed to free himself from the self.

My political ideal is the democratic ideal. Everyone must be respected as a person, and no one should be deified.

We will have the destiny that we will have deserved.

I deeply despise those who like to march in ranks on a piece of music: it can only be by mistake that they have received a brain; a spinal cord would suffice them amply.

Imagination is more important than knowledge.

In the effort we make to understand the world, we are somewhat like the man trying to understand the mechanism of a closed watch. He sees the dial and hands moving; he hears the ticking, but he has no way to open the case. If he is ingenious, he may form some image of the mechanism, which he will render responsible for what he observes, but he will never be sure that his image is the only one capable of explaining his observations. He will never be able to compare his image with the real mechanism, and he cannot even imagine the possibility and significance of such a comparison.

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Chapter Six When the devil digs in God ...

6.1. Bohr and Heisenberg in friendly collaboration The two friends are Werner Heisenberg and Niels Bohr before the Second World War.

And the devil is Hitler and the German scholars who have remained faithful to him. The object of the excavations is the bomb.

On Diego Rivera's fresco, entitled Hitler, the Fuehrer of the people, Einstein is recognized on the lower left among the regime's persecutors.

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At the end of the 1930s, it soon became clear that the chain reaction that resulted from the fission of the uranium nucleus could be used for a weapon of extreme power.

The equipment which was to be used by the Germans to obtain the fission of uranium was seized at the end of the war by a special American unit. The Kaiser Wilhelm Institute was evacuated in the hills around Stuttgart. It was in a cellar dug in the rock at Haigerloch that the German physicists realized their first atomic reactor, but fortunately without getting the desired reaction.

Werner Heisenberg, was one of the henchmen of the devil? Did he participate in the construction of the fatal weapon or, on the contrary, braked the research?

I would now like to mention the history and the discoveries of these scientists, who became confused because of the devil.

This chapter will focus on the tragic relationships that Bohr and Heisenberg experienced during the Second World War and my main source of information on this subject is the film written and directed by Mike Smith Mike, Bohr-Heisenberg Atomic Bomb, the failure of Copenhagen, presented by RTBF(Radiodiffusion Télévision Belge de Langue Française).

The world met Werner Heisenberg at a conference Niels Bohr gave at a German university. Nobel Prize in physics since 1922, the Dane was revered in the scientific world. The audience, hanging on his lips, tried somehow to understand. Indeed, he spoke his hand in front of his mouth articulating German with a very pronounced Danish accent. From time to time, he inserted English words. So his speech seemed confused.

He was suddenly interrupted by a young unknown physicist in his twenties who pointed out to him that he had made a mathematical mistake in his remarks. Bohr found this interruption quite relevant and even invited the young man to continue the conversation during a walk that took place that afternoon. During this walk, the two men realize that they share many common passions and really bond with each other.

Bohr was an imaginative physicist who could picture the behaviour of electrons within the atom itself, but Heisenberg had a mathematical skill that could help Bohr formulate and develop his theories.

Bohr's theory was revolutionary since, from ancient Greece, the atom was considered indissoluble (…) And for hundreds of years, students have been learning that physical phenomena are caused by cause-and-effect relationships.

Bohr demonstrated only at the atomic scale. It was not so. He also took his guests to visit the mechanism of the church clock in Copenhagen to show that this beautiful mechanism was absent from the atom in which the electrons jump from one orbit to another unpredictable.

Bohr posited as a first postulate that the energy of the orbits is quantified and that the electrons move around the nucleus in determined and energetically stable orbits. As a second postulate, he stated that when an electron passes from an orbit of energy E1 to an orbit of energy E2, there is emission or absorption of energy in the form of electromagnetic radiation.

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Bohr had gone beyond Newton's physics.

In 1925, Werner Heisenberg asked to become his assistant in Copenhagen, and they became the best friends in the world. This is the beginning of the real boom of quantum mechanics.

The success of Heisenberg made him famous and in 1927, he was offered a place at the University of Leipzig.

At 26, he became the youngest university professor in Germany and in 1932 he was awarded the Nobel Prize in Physics.

That year, at the Solvay Council, Einstein and Bohr really opposed the possible interpretations and philosophical consequences of the discoveries of quantum mechanics.

According to Einstein, Bohr's theory was incompatible with the principle that physics must describe a spatial and temporal reality.

And yet, quanta, which Einstein brought up from the underground worlds, will betray him.

In 1924, with Louis de Broglie, a new generation of physicists came upon the scene. They are less than thirty years old and form a revolution whose main victim will be their spiritual father: Einstein.

Indeed, quantum mechanics made it possible to know the structure of matter and that of the atom in particular. Each spectral line corresponds to the energy of a photon transmitted or absorbed when an electron passes from one energy level to another. The interpretation of chemical linkages has been radically transformed by quantum mechanics and is now based on Schrรถdinger wave equations.

But the problem often mentioned is that of the microscopic world where quantum physics predominate, and the macroscopic world under relativity reign, are two incompatible theories.

About which Einstein and Bohr discussed during the Solvay Council of 1927. This conversation, somewhat adapted, could have been the following one: : 105

When the devil digs in God ...

Niels,lethe worldn’est is Niels, monde settled pas not réglé par by le hachance sard. Dieu ne joue pas aux dés.

Qu’en savez-vous, What do you know Albert ?

Ne dites Albert? Do not tell pas àGod Dieu ce qu’il what to do. doit faire.

Albert, pensez Albert, vous do you really vraiment que Dieu ne think God does not joue pas aux dés ! play dice?

Of course, Niels,

Bien sûr, Niels, tôt sooner or later we ou tard nous le renwill meet him and He contrerons et il will confirm it to us nous le confirmera

34 De Closets, François., Do not tell God what to do, Seuil, Paris, 2004

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As François De Closets writes: "What is this mysterious biatomical reality that responds like an echo to the questions asked of it? Are you a particle? "I am a particle"; "Are you a wave? "I am a wave" It is in fairy tales that the same person changes his appearance from one moment to the next, sometimes prince charming, sometimes hideous toad. But we do not see anything like it in the ordinary world. Double nature does not exist. The answer can only be "extraordinary." It will emerge from two simultaneous approaches that seem very different and converge. (...)

"May God “play” his servants a trick, it must be admitted; that he has built everything on such rules is intolerable "Einstein wants to show that this formalism leads to aberrations that prove the limits of quantum mechanics. He is assisted in this criticism by Schrödinger. Although not a Jew and not directly threatened by anti-Semitic persecutions, the great specialist in wave mechanics did not support Hitler's coming to power, he left Berlin in 1933 and was in Oxford. In 1935, he imagines the paradox of the cat and shows that the animal can be both alive and dead. (35) (See explanation 10 in the mathematical appendix).

The theory seems to lead to nonsense. Bohr is quick to confirm that quantum mechanics in no way allows us to go from microscopic to macroscopic. (…)

This aporia aims to put quantum mechanics back in its place, to curb the interpretative zeal of these theorists. "Realists" like Einstein or Schrödinger believe that it can lead to aberrant situations whose physicists, lost in the calculation, are not aware and who denounce the very limits of the company. In the same logic, Einstein published in this year 1935 an article so striking that at seventy years of distance, it still shakes physics. For this work, he joined two young physicists: Boris Podolsky and Nathan Rosen.

Together they publish in the Physical Review an article with a very explicit title: "Can description by quantum mechanics of physical reality be considered complete? Which will go down in history as the "EPR paradox" for Einstein, Podolsky, Rosen, of course? " The content of this article says in essence that the wonderful and the incomprehensible arise from an incomplete vision of reality and, in a certain sense, denounce this incompleteness.

For Einstein, there must be something that quantum mechanics do not account for, and which allows particles to be both distant and not separated. Bohr spends a sleepless night: he responds to this article with a different but unconvincing interpretation.

When we do not know what to say, we shut up. This is what physicists did. Physicists ended up forgetting the EPR paradox and the quirks of the quantum world, and when Einstein died in 1955 no answer was yet given to the EPR paradox.

It was not until 1964 that the Irish physicist John Bell left the 1935 article and showed that, in many cases, the results are not the same depending on whether the test is governed by "quantum magic" or by the "Einsteinian prestidigitation," that it reflects the only quantum mechanics or uses hidden variables as Einstein imagined it. The probabilities recalculated by Bell do not allow any confusion between the realistic hypothesis and the quantum hypothesis.

In 1982, at the “Orsay Institut d'Optique,” the moment of truth took place. It was the experience of Aspect and his team. He ran "correlated" photons, that is to say ... (I give up explanations here…)

Regularly, we can read articles that bring together quantum physics and general relativity. Laurent Nottale, an astronomer at the Observatory of Paris-Meudon, wanted to reconcile the two enemy sisters: "Faced with so many shortcomings and contradictions, I told myself that there must be a fundamental theory that cannot only remove the inconsistencies of quantum mechanics but also reunite this one with general relativity." (36) "If again the two worlds were separated in the facts, we could be satisfied with this dualism, but it is not true, and all the macroscopic objects have microscopic behaviours, if only the permanent emission and absorption of photons of light."

35 See details of this experience in the biographical appendix to Schrödinger 36 Science et Vie, N ° 936 of September 1995, 50 years after Einstein, a scholar elucidates the mysteries of the universe, p. 48 to 56

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"The strong idea of relativity is spacetime (...) Well, in quantum mechanics, there is no spacetime. More exactly, the latter is flat, that is to say without any influence on the objects it contains. (...) In mechanics, quantum space would be absolute, insensitive to gravitation and ultimately useless. Indeed, on a small scale, gravitation has little influence: between electrons, it is 1044 less strong than the electromagnetic force. It can, therefore, be neglected. (see the demonstration in mathematical appendix) (37) (...)

As energy is linked to gravitation (E = mc2 obliges), on a very small scale, gravitation becomes dominant, so space cannot remain indifferent (without curvature) 38 Laurent Nottale continues: "The current situation has seemed absurd to me, and I have felt the need to introduce a new concept: spacetime has an influence at the microscopic level, provided that we accept that it is fractal."

Compare with the classic world to better understand. In the macroscopic universe, the more one observes with a good resolution, the size, the speed or the energy of a body, the more the measurement is precise. In the microscopic world, the more precisely we measure, the faster the velocity changes. The resolution does not specify the result but changes nature!

"My bet is that there is something that has not been taken into account in the interpretation: the scale we are looking at" A sudden change of course, of "frame of thought." What was unimportant, spacetime or spatiotemporal resolution becomes primordial (...) The microscopic world is fractal, which means that one can always observe smaller resolutions and always find different things corresponding to the resolution one is looking at.

"Thus, the new principle that I add to physics, more specifically, the relativity of scale, emphasizes Laurent Nottale, explains that we can see different things depending on the resolution. The quantum world is no longer insane since the unexplained difference in results according to scale is now necessary and comprehensible. Actually, it is the spacetime itself that is different according to the scales. And it is because its role is essential that it produces different results according to the scales."

However, the bases that make up the long chains of DNA of our genetic code are the level of angstrom size, (10-10 m) that is to say, they have quantum properties. Genetic information was written at the level of the quantumclassical transition, and living beings show a hierarchical fractal structure of this size at two meters. Moreover, adds Nottale, "this continuity of scale can also extend to the organization in society and why not, to the whole Earth" But contrary to what Descartes said, the global is not a mere sum of local information because the exchange of information between the different scales is permanent.

In chapter eight, devoted to Ilya Prigogine and the arrow of time, I inserted a passage from my socio-philosophical essay "The end of men machines" where I ask myself the question of whether societies and their cultures are not also systems composed of men like solids, liquids and gases are composed of molecules?

6. 2.The Bohr atom The construction of the Bohr atom belongs to the history of physics. It is often told by physicists according to a narrative thread that follows the controversies over the nature of light and leads to Einstein's hypothesis of quantum light and the corrugated mechanics of De Broglie and Schrรถdinger. (...)

In 1913, Bohr returned to Copenhagen and he adjusts all the pieces of the puzzle. The periodic nature of Mendeleyev's painting can be explained by the limited number of electrons occupying the same orbit: when an orbit is filled, the line is changed in the table. As for the quantum discontinuity of Planck, it agrees wonderfully with the spectral lines of emission and absorption of light. (...)

Bohr understood that each line of emission or absorption is determined by the orbit change of an electron, and the different orbits have discrete energy values, whose unit is the quantum of Planck. The Bohr atom is born: positively charged nucleus surrounded by electrons arranged in

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                                  

When the devil digs in God ...

successive orbits - each characterized by a quantum number distinct- and capable of "jumping" from one orbit to another by absorbing or emitting a luminescent quantum corresponding to the energy difference between the two orbits (39) The description of the electronic structure of atoms according to Bohr's theory can be summarized as follows. (40) a) Each electron is located on an energetic level characterized by its main quantitative number n. At each level corresponds an orbit on which the electron moves around the nucleus. The electron neither emits nor absorbs any energy when it is on a given energy level. b) When the electron passes from an upper orbit (2) to a lower orbit (1), it emits energy in the form of electromagnetic radiation of given frequency en, using the Planck relation, by the expression:

Where n2> n1 and where Z is the atomic number For hydrogen, Z = 1, the frequency of the emitted radiation is given by:

39 History of Chemistry by Bernadette Bensaude Vincent and Isabelle Stengers 40 Chemistry for the Life Sciences of C. Houssier (Part 1) pages 10.21 to 10.23

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E2 â&#x20AC;&#x201C; E1 = hf

R2

R3

R1

Rn

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6.3. Heisenberg Uncertainty Relation Formulated by the German physicist Werner Heisenberg in 1927, these relations contributed to the development of quantum mechanics.

They indicate that, during the same experiment, the position and the momentum cannot be measured simultaneously with great precision.

By observing nature, we change the world. We choose a way to apprehend it. For example, we choose to consider the electron as a particle or a wave depending on what we want to see.

Uncertainty on position x uncertainty on momentum  h

h being Planck's constant which is 6.626.10-34 Joule.second x being the uncertainty on the position and p the uncertainty on the momentum (m.v) So Heisenberg declares that: :

x.p  h

The consequence of this mathematical formulation becomes a philosophical interpellation expressing that the process of measurement invariably influences the measured quantity. Indeed, experience shows the distance or even the disappearance, of our everyday world when we consider the subatomic scale.

Heisenberg adds that the uncertainty relation holds for other physical quantities, for example, energy E and time t.

E.t  h

For example incompatibility of the lifetime of the observation and the lifetime of a state, since it is both impossible to specify simultaneously the position and the amount of motion of a particle, such as an electron.

He states that a more precise determination of a quantity necessarily results in less accurate measurement of the other and that the product of the two uncertainties is never less than the Planck constant.

In quantum mechanics, probability calculations replace the precise predictions of classical mechanics. The philosophical notions of indeterminacy that Heisenberg implied were at the root of an important current within the scientific community, which viewed this concept as overturning the traditional conception of cause-and-effect phenomena.

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Consider two examples of application (41). a) Suppose that the speed of a lead grain of a decigram (10-4 Kg) is determined with a precision v = 10-8 meters per second. Let's see what will be the uncertainty on its x coordinate. .

Given

x.p  h ,

and

pp- =mv , we can write

108 x 

6,626.1034 10

4

x.vx  h/m

et x  10

22

m

that is, ten-thousandths of a billionth of a billionth of one meter. In other words, practically, the grain position is precisely determined. a) Let's now examine the movement of the electron in the atom. The dimensions of the latter are of the order of 10-10 meters. In the most unfavourable case, the position of the electron could be determined with a precision equal to:

x  1010 m Therefore, for this inaccuracy on the coordinate, given the mass of the electron, 9,109.10-31 Kg, the inaccuracy on the speed will be: 34 1010 vx  6,626.1031 9,109.10

Therefore,

vx 

6,626.1034

 7,2.10 6 meters per second

9,109.1031.1010

But given the speed of the electron in the atom which is of the order of 106 meters per second, it seems absurd to talk about the trajectory and the orbit of an electron given this high level of relative inaccuracy. We must not imagine the electron in the atom as an ordinary particle, but rather as an electronic cloud.

The Heisenberg inequalities set out in the year 1927 of a Solvay Council, show us the limits on the relevance of the use of classical wave and particle concepts to describe phenomena at the atomic scale, such as those involving on electrons and light.

In no case do these inequalities indicate an inaccuracy or a limit to the simultaneous knowledge of the position and momentum of a particle in the classical sense?

They do not reflect a limit to knowledge, but a limit to the application of conventional concepts to describe mechanical phenomena at the atomic scale.

If we persist in describing matter and light in terms of particles and waves, we can do so only by limiting these concepts one by the other and by giving probabilities of observations of this or that classic value of a classical object.

41 Van de Vorst Albert., Introduction to Physics, De Boeck University, page 944

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6.4. Man and places at the source of the Copenhagen Spirit.

Let's summarize Niels Bohr's C.V. We know that he is a famous Dane, known all over the world, and is best known for developing a model of the structure of the atom.

Upper secondary students now know that the atom has different levels of energy, distinct from each other, on which the electrons turn. There are seven of them and the number of electrons varies according to the level.

Born October 7, 1885, in Copenhagen; he died on November 18, 1962, in Copenhagen. In 1922, at the age of 37, he was awarded the Nobel Prize in Physics.

Mr Philippot (see Foreword) had learned of his death in the 13-hour diary, and he devoted his lesson that afternoon to Bohr's famous model of the structure of the atom.

When we finished, what was once called the humanities, we knew well his theory at the base of quantum mechanics: "the electrons have the possibility to go from one layer to another by emitting a photon."

And no one would have dared to say of that time, what this student and this reporter are saying on TV. Enclosed: â&#x20AC;&#x153;The boring world of Niels Bohrâ&#x20AC;?

Below: This lesson is really boring (boring) With boring (boring) replaced by Bohring

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The bust of Bohr decorates the facade of the main entrance of the University of Copenhagen (Our August 20th Square for the inhabitants of Liege).

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We find him smoking a pipe on the 500 Danish kroner banknote.

And on a timbre, we see the formula of the energy of the photon emitted by an electron that changes its orbit.

Then, smoking a pipe, statued with Einstein

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The Niels Bohr Institute was founded in 1921 under the leadership of the Danish physicist.

On the occasion of the 80th birthday of Niels Bohr, October 7, 1965, three years after his death, the institute which was then called the Institute of Theoretical Physics of the University of Copenhagen officially became the Niels Bohr Institute.

I wanted to see these buildings loaded with the history of physics. I touched and photographed them. Seeing my curiosity, a young researcher offered me a visit.

Two pictures at the end of his life.

Enclosed Niels Bohr near the physics institute in the early 60's.

On the following photo, Bohr is 5th in the first row.

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Suggested reading, see the following link: http://www.matierevolution.fr/spip.php?article3807

by Robert Paris Here is a summary: Bohr had been endowed by the Danish state with great organizational and financial means to surround himself with the best physicists in the world whom he invited and offered support on condition that ... they join his group (called "school") of Copenhagen ").

They had to accept his thesis and his scientific direction.

Very great physicists refused to yield to his pressures like Einstein, de Broglie, Bรถhm or Schrรถdinger.

In 1929, two years after the Solvay meeting, I just mentioned, Bohr institutionalized his private conversations with scientists, founding the "Copenhagen Conferences" and taking advantage of them to hire the best researchers at his Institute.

There was no program planned in advance. Oral communications were not published. Everything was informal.

The discussion was open. Debates usually continued in private with Bohr during memorable walks and excursions.

I saw many framed pictures in the offices and corridors, among which are the famous participants in the spirit of Copenhagen.

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When the devil digs in God When the...devil digs in Godâ&#x20AC;Ś This photo was taken at the facade of the Physics Institute, Copenhagen, July 1963, Niels Bohr has died since November 18, 1962.

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Detail of the previous picture: Niels Bohr's son, Aage Bohr sits near Dirac in the front row. (Red arrow)

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r

Above, Copenhagen, 1932. Niels Bohr is in 3rd position standing, sitting in front of him Leon Brillouin, Lise Meitner and P. Ehrenfest.

The staff of the Institute of Physics in 1921. Bohr is in the second row. (red arrow) Following is the 1937 Copenhagen Physics Conference. From the left, in the front row: N. Bohr, W. Heisenberg, W. Pauli.

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Enclosed Bohr in conversation with Heisenberg and Pauli. (back)

To all his visitors, congressmen or observers, Bohr really insisted on the essence of the Copenhagen interpretation by conditioning the reliability of the measurements by the judicious choice of classical physics measurements "because they were the only ones to provide "a language devoid of ambiguity" In other words, Bohr wanted to avoid at all costs possible paradoxes due to the wave-particle duality.

These two concepts mutually exclude each other in classical physics, but not in quantum physics where they are complementary, as is also the case for the position and the speed which, in classical physics, are associated continuously on the trajectory of a particle. Not in quantum physics where these two parameters are measurable only within certain limits of a relationship called indeterminacy.

For more details, read Heisenberg and the Uncertainty Principle, Etienne Klein, Great Ideas of Science.

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The birthplace of Niels Bohr along the canal in Copenhagen.

Below, the plaque on the facade: "In this house, the atomic physicist Niels Bohr was born on 7.10.1885."

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devil When the devil When digs inthe God ... digs in Godâ&#x20AC;Ś 6.5. The Solvay Council of 1927: 17 of the 29 physicists present had received or were going to win the Nobel Prize Let's start with the photo of the October 1927 Solvay Council in Brussels where met the greatest scientists in the world. This famous council opposes the "Copenhagen School" (Bohr in the lead, Heisenberg, Born, Pauli, Dirac) and the proponents of a deterministic interpretation. (de Broglie, SchrĂśdinger, Einstein)

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Remembrance of the 1927 Solvay Council: participants leave Leopold Park for a walk (digestive, it seems, or on the run) on the Grand Place side.

Sc hr รถ di ng e r e t Bo hr

Sc hr รถ di ng e r

Heisenberg

P a u l i e t Ei n st e i n

Dirac

Kramers

B r il l o ui n

D e B r o gl i e

E h r e n f e st e t B o h r

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The Solvay councils have always challenged me. These were mythical moments in the history of physics.

It was the epoch of "quantum theory" where geniuses of science such as Einstein and Bohr competed over the interpretation of quantum mechanics.

The places have changed little. The facade was cleaned in 2007. The soul of the great physicists is still there.

From that date on, according to the subjects treated, there was a resounding series of Nobel Prizes, like that of Louis de Broglie in 1929, Heisenberg in 1932, Dirac and SchrĂśdinger in 1933 and much later, in 1954, Bornâ&#x20AC;&#x2122;s one.

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6.6. Max Planck, the patriarch It is undeniably the resolution of the problem of black body radiation that marked the beginning of quantum mechanics.

It is Max Planck who discovers the spectral law of the radiation of a black body. . In physics, a black body is an object that absorbs all the radiation it receives. Its electromagnetic spectrum depends only on its temperature degrees Kelvin (K). The visible spectrum is between about 400 and 800 nanometers.

Max Planck, through the study of black bodies, discovered the value of a constant that will bear his name. It expresses the threshold of minimum energy that can be measured on a particle. Its value is as follows: h = 6.63. 10-34 joules.second. Planck discovered this constant in 1900, astonishing the physicists of this time who believed that the energy exchanges between matter and radiation were continuous, while the experiments proved the opposite.

He introduced the value of this constant into his calculations and arrived at this formula: E = hf. where E is energy, and f frequency, h being Planck's constant, He will later give the quantum name to this amount of energy.

In physics, a quantum (Latin word meaning "how much" and whose plural is "quanta") is the smallest indivisible measure, whether of energy, the quantity of motion or mass. This notion is central in quantum theory, which gave birth to quantum mechanics.

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Here on the photo of the Solvay Council in 1927, Planck turns 69 Shortly after Planck's discovery, Albert Einstein, following his analysis of the photoelectric effect (see page 45), suggests that the quantity hf is the energy of an electromagnetic particle that will be later called a photon.

This reintroduction of a corpuscular conception of light will incite Louis de Broglie to propose a relation similar to that of Planck, but for the momentum: :

6.7. The wave mechanics of Louis de Broglie Let's first look at Louis de Broglie who had the idea to associate a wave function to each particle by this formula:

λ = h/p = h/m.v where λ is the wavelength and p is the momentum of the particle, that is to say, the product of its mass by its velocity. As for h, this is Planck's constant The shorter the wavelength, the higher the frequency, because λ = c.T = c / f where f = c / λ A particle is a wave that propagates throughout the space whose amplitude of probability allows us to know the position at a time t. .

Above, taken from the photo of the 1927 Solvay Council, De Broglie is behind Langevin, who was his PhD supervisor in 1924.

Translation of the text on the left: After a long reflection in solitude and meditation, I suddenly had the idea, during the year 1923, that the discovery of Einstein in 1905 was to be generalized by applying it. to all the material particles and especially to the electrons.

Einstein appreciated De Broglie's thesis. Experiments were carried out at the Bell Telephone Laboratories and they showed that the electrons hid well undulatory properties. The λ (wavelength) of the formula was of wave type and the momentum m.v was corpuscular. The wave displaced the particle.

Actually, De Broglie was expanding what Einstein had said: if electromagnetic waves had particlespecific characteristics, why would not matter have some of the characteristics of waves? (See explanation n ° 10 in the mathematical appendix)

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There was no equation yet to calculate the dynamics of the waves that guided the electrons.

In October 1925, one year after De Broglie's doctoral thesis, the Dutch Peter Debye (photo left from Solvay Council 1927) asked Schrödinger to produce it. (42) An equation was needed to know the waves emitted by vibrations of all kinds, such as those of guitar strings, or the oscillations of molecules in the air or vibrations of electromagnetic origin.

His equation intervened at a propitious moment when discouragement prevailed among several physicists.

It is said, moreover, that the wave mechanics developed by Schrödinger was born as a reaction against Heisenberg, which seemed too unintuitive in the domain of atoms.

The wave equation illuminated the darkness as the F = ma, Newton’s equation But there was no equation yet to calculate the dynamics of the waves that guided the electrons.

On the photo Solvay 1927, behind Compton and Einstein.

Schrödinger has already formulated the equation and founded his version of quantum wave mechanics. He very recently succeeded Planck as chair of theoretical physics at the University of Berlin.

In six years, he will be nobelled.

What did the famous Psi function mean? Heated fights ensued in which Max Born, who had already developed the function of one in the years 1925-1927, proposed the most satisfying answer: "it corresponds to an amplitude of probability of presence of electrons" Schrödinger even opposed Born's interpretation, having always thought that the Psi function represented the distribution of the charge of the electron as if the electron were dispersed in space as a liquid filling the depressions and avoiding the asperities.

Like Bohr in Denmark, Schrödinger became a famous Austrian and he was also entitled to his picture on a ticket of 1000 Austrian Shillings.

42 See more in Schrödinger and quantum paradoxes, Etienne Klein's collection, Great Ideas of Science

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6.8. Quantum mechanics of Göttingen teachers and students Gottingen is one of the most famous universities, with 26,000 students and 2,500 teachers. 42 Nobel Prize winners taught or studied in Göttingen. The city is home to the Max Planck Institute and the Academy of Sciences.

In 1921 he was appointed to professor of theoretical physics in Göttingen. He focuses his work on quantum physics and develops, with Pascual Jordan, the matrix mechanics introduced by Werner Heisenberg.

The Solvay Council was also an opportunity for Max Born, professor at Heisenberg in Göttingen, to present his vision of quantum theory, in opposition to that of Einstein.

Born wrote in 1923 that his pupil, Heisenberg, had an incredible talent and was proud of him.

Born was a mathematician and astronomer and it took a while for Heisenberg to appreciate his courses, which he believed were based too much on celestial mechanics.

But this doubt was short-lived, for Heisenberg wrote to his father a short time later that in Göttingen he would learn once and for all mathematics and

astronomy.

He became Born's assistant and apparently befriended him, as the lessons often ended informally, with Born and Heisenberg playing the piano alternately or in four hands.

Born in 1923, with Bohr, Pauli and Heisenberg, Born considered that the whole system of physical concepts had to be rebuilt from its foundations and he coined the term quantum mechanics as the title of the new discipline.

Born was also the first to give the square of the wave function module the meaning of a probability density of presence.

Born was also the supervisor of Robert Oppenheimer in 1927 in Göttingen.

The title of this chapter, "When the devil digs in God ...", is not due to chance, when we know that Oppenheimer was one of the fathers of the American atomic bomb.

Born received the Nobel Prize in Physics in 1954.

When the Russell-Einstein Manifesto at Einstein was made public on 9 July 1955, in the middle of the Cold War, highlighting the dangers created by nuclear weapons, and calling on world leaders to seek peaceful solutions to international conflicts Born signed it with 10 other leading intellectuals and scientists. Among them, Albert Einstein, in April 1955 (a few days before his death).

6.9. Heisenberg, the pupil became Nobel Laureate before Born, his teacher Heisenberg behind Born at Solvay Council in 1927 still does not know that 5 years later he will receive the Nobel Prize, but apparently it will not be without some regrets, if it is believed sincerely in the letter he sent to his teacher after that he congratulated him for his Nobel Prize: Dear Mr Born, "The fact that I am the only one to receive the Nobel Prize for the work done in Göttingen in collaboration - you, Jordan and I - is depressing and I do not know what to write to you, naturally I am glad that our joint efforts are appreciated, and I remember with emotion the pleasant time of our collaboration, and I believe that every good physicist knows how important your help and that of Jordan (Photo below Born) have been for the structure of quantum mechanics, and it does not change because of a bad external decision, but I can only thank you again for your valuable collaboration and feel a bit ashamed.

Cordially W. Heisenberg

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6.10. Wolfgang Pauli and his exclusionary principle Pauli's half-profile, next to Heisenberg at the 1927 Solvay Council.

Two years ago, in 1925, Wolfgang Pauli, an Austrian physicist, proposed a principle: electrons cannot be in the same place in the same quantum state.

By quantum state is meant the state of a system is represented by a set of physical quantities from which one can determine all the properties of the system concerned.

(See explanation 12 in the mathematical appendix)

Here we see Pauli, with Bohr, watching a ball spinning on its axis, like the spin of the electron. (45)

45 Fine art America photo: http://fineartamerica.com/featured/wolfgang-pauli-and-niels-bohr-margrethe-bohr-collection-and-a-ip-andphotographers.html

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6.11. Paul Dirac, a conceptual genius Here, between Lorentz and Einstein at the 1927 Solvay Council, Dirac will share his Nobel Prize with Schrรถdinger in 1933.

In 1926, a year before the Council, Dirac had managed to unite in one formula Schrรถdinger's wave mechanics and Heisenberg's matrix mechanics.

But he wanted better still, that is to say, to take into account the Special Relativity of Einstein.

In other words, he wanted to unify science because objects (the electron is one) behave differently at a speed close to that of light. Recall that Schrรถdinger equation is timedependent, but does not take into account the limited relativity associating time and distance travelled in interconnection.

But Dirac also wanted his equation to please. Does he not say: "Every physical law must have a mathematical beauty" He described a new situation of what is happening inside the atom. By observing his equation well, Dirac has a real revelation because behind the symbols of his equation there is the perfect description of reality, there is the secret code which makes it possible to decipher nature and which announces to him the truth. existence of another universe never noticed before.

Actually, instead of having a solution, its equation has two: the first that of familiar atoms, the second a kind of mirror of our universe made up of atoms whose properties are reversed; Dirac announces that, in addition to matter, there is an antimatter and that these particles belonging to these two states must never come into contact, lest they are annihilated by an explosion of energy.

Positive electrons (positrons) that have the same mass as negative electrons, but an opposite charge, are manufactured in our laboratories.

They are used in medical imaging (PET scan = positron emission tomography). They are able to show us all the details of our brain.

In the 1920s, physicists have a hard time believing in the existence of antimatter. But an American, named Anderson, detects particles coming from space and he finds that, subjected to a magnetic field, some particles deviate on one side (the electrons) and others deviate on the other side.

Anderson has just discovered the "electrons" of Dirac, in other words, antimatter particles.

This theme will not be developed in this book. However, we reserve explanation 15 in a mathematical appendix entitled "Roughing the Dirac equation and the existence of antimatter.

The photo : http://www.lindau-nobel.org/ (46)

46 Lindau Nobel Laureate meetings 131

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6.12. Niels Bohr and Werner Heisenberg face apocalypse Let's go back to the events that preceded The Second World War. In the early 1930s, the historical context changed with the arrival of Hitler in power. Most German Jews left Germany. Bohr welcomed several to Copenhagen.

Einstein chooses the United States.

Heisenberg decided to stay in the country, believing that he could better control the evolution of German physics and react if necessary to the dangerousness of the discoveries. According to the testimony of Karl Weiszacher, another atomist scientist who was interviewed in Mike Smith's film, Heisenberg told him, referring to Hitler: "This man, I know him from Munich, he is very dangerous.â&#x20AC;?

Then he added: "I have to compromise to prepare for the future of my country and not leave it in the hands of this bastard" This decision will put a chill on his relationship with Bohr, influenced by his Jewish wife.

The correspondence between Heisenberg and Bohr was abundant, except during World War II when Bohr could not admit that his "ex-friend" remained in Germany "in the service" of the Nazis

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During a trip to Berlin, I spent a whole afternoon in the district of the former Nazi ministries. I followed the old Prinz-Albrecht-Strasse and then met Niederkirchenstrasse with some period buildings, such as the "House of Airmen" and the Martin-Gropius-Bau museum facing each other: I walked around the museum and discovered, on the back, a prefabricated pavilion that covered what was forty years earlier the cellars of the Gestapo. This place full of history gave me a feeling of sadness, but also highlighted the German resistance to this criminal regime. .

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House of Airmen in front of MartinGropius-Bau Museum

Above and below, the Martin-Gropius-Bau Museum.

Below and next photo, on the left, the white pavilion built on the cellars of the Gestapo

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The exhibition was entitled: "Topography of the Terror" It had already recorded 1.3 million visitors end of 1989. It was there that were questioned suspects of all kinds and where torture was practised and even some executions.

Heisenberg was one of them and was questioned in these cellars in 1937 when the Hitler regime suspected him of a connection with the Jewish physicist community. His life was in danger. After months of investigation, the Reich fĂźhrer Himmler wrote a letter to Heydrich where he wrote "We cannot afford to kill this young man" and the physicist was ordered not to teach the theories of Jewish physicists anymore.

I read an article in Das Schwarze Korps ("The Black Corps"), the SS weekly, about the "political bankruptcy of science." The article classified Jewish physicists as "Weisse Juden", the white Jews. Heisenberg was one of them because he considered Einstein's relativity as "the most obvious basis for all future scientific research"

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Here is the translation : "The dictatorship of the Gray theory.

There is a primitive way of being anti-Semitic, it is one that is content to fight the Jews as such. Those who share this attitude are content to draw a precise line of demarcation between themselves and the Germans.

The problem is solved, they say, from the time when intermarriage was ended and Jews were excluded from the political, cultural, and economic life of the nation. The most radical solution they envisage is emigration of Jews to Palestine or elsewhere. When Germany is finally free from the presence of Jews, anti-Semitism will no longer have reason to be, they think.

Such a way of looking at it is appealingly simple, but it is an error of judgment: if we were to fight the Jews by limiting ourselves to the old and unmistakable features, camouflage noses and frizzy hair, we would fight against windmill. Our struggle against the influence of the Jews in political and cultural life, and the unfinished struggle against their economic power, has shown us that it is not so much a question of fighting the Jews as such to attack their mode of thought, or rather their evil spirit, which they spread everywhere through what is called influence. (...) Unfortunately, the truth is this: the constant peril of a judeification of our public life, the power of the Jewish influence that national socialism has had to stem, does not come only from the reduced number of Jews, but in a large proportion, of all who, although of Aryan descent, have been open to the influence of the Jewish spirit and have pledged allegiance to it. The victory of racial anti-Semitism is, therefore, only a partial victory.

We cannot limit ourselves to the rigorous application of the racial laws of Nuremberg or the pursuit of the struggle against the Jewish economic power. We must also exterminate the Jewish spirit, which flourishes with impunity when it has the most beautiful jewels of the Aryan race. (...) It is not the individuals of the Jewish race who represent, by themselves, the greatest danger: the true great danger is the mentality they spread. And those who are bearers of this mentality are not only Jews, there is also, unfortunately, among them, Germans (...)

"

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Jews of feelings" The people have coined a word for these bearers of the Jewish bacillus, he calls them the "white Jews", and the name strikes the heart because it expands the concept of "Jew" beyond even its racial definition. We could similarly say "Jews of character", "Jews of feelings", "Jews of spirit". They are people who voluntarily open themselves to the Jewish spirit, for want of one on their own. ; They have made themselves worshipers of the quibbling intellect because they lack the natural instincts and strength of character that drive men to develop their own qualities and to stick to them closely.

There is above all a sector of national life that this Hebrew spirit of "white Jews" has invaded like a virus and where the spiritual kinship that exists between them and their Jewish masters is irrefutably demonstrated.

Science. To purify the science of the Jewish spirit must be our main duty, because if in everyday life it has become easy enough to fight "white Jews" with the help of legislative and policy measures, a science contaminated by the Hebrew bacillus constitutes for the Jewish mind a key position from which it can continue to exert a decisive influence on all aspects of national life.

Let us take a typical example: today, where the German medical profession has to face new tasks and where research is in a hurry to deliver decisive results in the field of biology and heredity, racial hygiene and health. of the people, today what do we see? In six months, the specialized medical press published 2138 articles on which 1085 emanate from foreign authors (116 of which are of Soviet origin) and do not deal at all with the problems which we regard as the most urgent ones. Under the guise of "exchange of results" lies the thesis of scientific internationalism so dear to the Jewish spirit, which invented and disseminated it, because it conditions the establishment of uncontrolled domination. corn.

But it is in physics that the effects of the Jewish spirit, with its most accomplished representative, Einstein, are most clearly seen. All the great achievements in this field are due to the great capacities of German scientists and to the patient, diligent and creative method peculiar to them in the observation of nature; and the German scholar sees in the theory only one means, which in some cases facilitates the observation of nature, but never becomes an end in itself.

The only goal the German scholar assigns himself is knowledge of the real, and he is ready to sacrifice his personal theories if they turn out to be erroneous or insufficient. But in the last decades, the Jewish mind has succeeded in imposing a theory, of which it has made a dogma, which is completely dissociated from reality. In order to found and impose this theory, we have resorted to a sophisticated generalization of already acquired knowledge, to clever manipulation of mathematical formulas, to the constant fog of ambiguity. It is a theory that corresponds perfectly to the Jewish spirit, its "method of research" and its desire to render diligent, patient and creative observation of nature superfluous.

It was a Jewish professor in Munich, Leo Grätz, who produced this telling statement that, over time, the experimental physicist will regain the rank of a good mechanic to whom the theoretical physicist will delegate certain experiments. Einstein stated in a 1922 lecture: "It is to be expected that the theory will soon be capable of calculating a priori the properties of the atoms of chemicals and the means of producing them, which will make it possible to do without the exhausting experimental work of the chemist, a big eater of time ". After these proclamations rejecting the second level the scientist who works in close contact with the real, we moved quickly to practice. The Jews Einstein and Haber, flanked by their spiritual comrades Sommerfeld and Planck, began distributing the university halls without anything coming to limit their power. Sommerfeld alone could boast of having ten chairs occupied by his pupils. In just fifteen years, Jewish theoretical physicists and their heralds printed nearly 50,000 pages, and the youth was almost exclusively subject to their teaching. If we had continued to tolerate these actions, we would have eliminated in a few decades the category of productive and close-to-reality researchers, in favour of unproductive and quibbling theoreticians. National Socialism, taking power, has removed this danger, but has not yet fully conjured it (...)

Einstein, cornerstone To show how much the "White Jews" feel in the field, let us take the case of the holder of the chair of theoretical physics at the University of Leipzig, Werner Heisenberg, who in 1936 managed to publish in an official organ of the Party an article in which he declares that Einstein's theory of relativity is "the most obvious basis for all future scientific research" and places it among the "most remarkable works of the young generation". German scientists to produce theoretical systems applied to the knowledge of the world ". At the same time, he tried to get the agreement of German physicists on the value of this theory, to impress the most competent circles by refusing any means of debate to who was not of his opinion.

This representative of the Einsteinian spirit in modern Germany was appointed in 1928 to the Leipzig Chair, as a model pupil of Sommerfeld, when he was only 26 years old, that is to say too young to have really done basic research. Upon taking office, he began by dismissing his German assistant to give his post to the Viennese Jew Beck, then to the Zurich Jew Bloch. Until 1933, his seminary had a majority of Jewish pupils and today still the restricted circle to which he addresses is composed of Jews and foreigners.

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The Ossietzky of physics In 1933, Heisenberg and two other pupils of Einstein, Schrรถdinger and Dirac, obtained the Nobel Prize, which was a direct provocation to Germany National Socialist from the Nobel Committee, subject to the influence Jewish.

This reward will be compared to that attributed to Ossietzky (In 1935, Carl von Ossietzky, 18891938, founder of the movement "Nie Wieder Krieg", "Never again the war", and opponent of the Nazis, received the Nobel Peace Prize; Goering increased the pressure to make him give up his price, but Ossietzky did not give in and was put into concentration camps.

Source : Carl von Ossietzky quotes, https://www.azquotes.com/quote/1345278 Heisenberg thanked the Nobel Committee in its own way for refusing to sign, in 1934, a call from the German Nobel Prize winners to support the action of Hitler, Chancellor of the Reich. Here he justified his refusal: "Even if, personally, I am in favour of the yes, I consider that this kind of political declaration is not suitable for scientists, and that, besides, until now, it was not in their habits. That's why I do not give my signature. " This answer is typical of the Jewish spirit that is earned by its author, when he declares that "Does not fit" an act of union with the people and political responsibility on the part of "scientists" In the context just described, it is not surprising that Heisenberg was somewhat hesitant to choose to work for his homeland, even if the regime's leader acted as a terrorist, or to fight it. But did he really hesitate?

In September 1941, Werner Heisenberg met Niels Bohr in Copenhagen in order, he said, to agree on the common position to be adopted by physicists around the world on the construction of the atomic bomb. He is waiting for an answer to his question, but Bohr thinks that the German's mission is not clear and he sees it as a Nazi propaganda operation.

During this interview in Copenhagen, Heisenberg eventually revealed to Bohr that he was working on the nuclear bomb and Bohr immediately ended the interview and Heisenberg would never know the answer to his question.

The two ex-friends are thus opposed and will even communicate more with each other during the years that follow.

When the Germans decide to build the bomb by mobilizing their last resources, because their economy is in free fall, Werner Heisenberg answers to Albert Speer that it would take years to realize such a project. In so answering, Heisenberg gets rid of a heavy moral burden.

In August 1945, Heisenberg and his physicist colleagues, including Weizacker, were imprisoned in England. It's beyond that they learn the atomic explosion on Hiroshima.

But after his release, Heisenberg then faces the rejection of his former colleagues and he is accused by them of collaborating with the Nazi regime. He defends himself by explaining that, on the contrary, he only delayed the manufacture of the nuclear weapon. Niels Bohr's intransigence on him is particularly painful. He wants to know what his ex-friend thinks of him. And in October 1945, this one sends him a letter, for the first time since the interview of Copenhagen, where he writes:

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"Dear Heisenberg, I hope we can resume our collaboration soon. I am sure that the future will bring us all happier days and that the horrors committed on innocents by men blinded by their prejudices will serve as a lesson for all humanity." (47) In 1956, a book (Brighter than a thousand suns, the moral and political history of atomic scientists) revealed that Heisenberg was at the head of a plot to stop Hitler from building the bomb.

Heisenberg would have proposed stopping further German research if Bohr succeeded in stopping the research of physicists from other nations.

In the early 1960s, twenty years after Heisenberg's trip to Copenhagen, he reiterated his explanations in an interview whose details are summarized below.

The fact that Bohr misunderstands his intentions is very painful for him. But Bohr will declare that the subject is no longer relevant He had promised him an interview, but Bohr was rushed to the hospital where he died in 1962. (48)

47 Bohr-Heisenberg atomic bomb, Copenhagen failure, presented by RTBF. 48 Bohr-Heisenberg atomic bomb, Copenhagen failure, presented by RTBF.

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I thought it was good to ask Bohr's opinion Of course, I knew he was Danish

And that Denmark was occupied by the Germans So it was clear that Bohr would react violently on the subject

But at the same time I knew we were good friends And he knew my opinion about this problem from the beginning

So I thought that on this basisâ&#x20AC;Ś

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As far as I'm concerned, Bohr and Heisenberg were very present in my mind: Bohr, because I taught his discoveries for seventeen years and Heisenberg, because he welcomed us in the hall of the Athenee de Huy from 1957 to 1963 by this writing which also testified to the preponderance he attached to the ancient humanities:

Translation of Heisenberg's message: To be able to hold one's place in existence, they say, one must acquire the practical talents of modern life: living languages, technical processes, commercial skill, and intelligence of numbers. The one who, unfulfilled, has the desire to get to the bottom of things in any field, either in technology or in medicine, will meet sooner or later these ancient sources and will find many advantages, by taking from the Greeks their principle of thought and their way of asking the question.

Heisenberg.

6.13. Conflicts and fights between physicists (49) We already set out conflicts between Bohr and Heisenberg.

The war also did a lot of other damages among the collaborations of these physicists who helped or not the Nazi regime.

But there were not only oppositions due to the world conflict, other conflicts, on a smaller scale, took place between these physicists animated by their discoveries, often partial elsewhere, because sometimes initialized or terminated by other.

Often partial also in the sense that, among them, several physicists had participated to advance them before their term.

It is not always easy to differentiate the part taken by one and the other in the finalization of a discovery.

This was the case for all these physicists intertwined in a series of objectives whose definition was often questioned according to unexpected observations or brilliant intuitions.

49 More details in Schrรถdinger and quantum paradoxes (Emile Klein collection: Big Ideas of Science)

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The replacement of Max Planck In May 1927, in Berlin, debates were held on the replacement of Max Planck for the chair of theoretical physics. Einstein was not available, having an activity that relieved him of any academic responsibility.

Heisenberg was apparently too young (he was 26), Sommerfeld refused to leave Munich. There remained two tenors: Max Born and Schrödinger.

Born was very discreet while Schrödinger was a born seducer and was completing his masterpiece: the wave function.

Planck then realized that Schrödinger was going to put physics back on the right path after he got bogged down and he chose him.

Surprising as it may seem, Schrödinger replied: "I am deeply sorry, but I can do it during school hours, it is impossible for me to work in the morning."

The outspoken Pauli Where does the truth begin in everything about Wolfgang Pauli? It was said that his presence in a laboratory disrupted the operation of the devices.

He did not hesitate to criticize Einstein or Bohr, the two luminaries of the time.

Heisenberg endured his affronts: "I do not count the times he called me a fool," he says.

In 1930, he assumed the existence of the neutron and 26 years later the physicists discovered it where Pauli had indicated.

Schrödinger against Born, Bohr and Heisenberg Although the majority of physicists accepted the statistical interpretation of quantum mechanics, some like Einstein, Schrödinger and De Broglie wanted a return to the concepts of classical mechanics.

Einstein's opinion struck the henchmen of quantum mechanics, and some, like Heisenberg, dared to be less respectful of Master. Heisenberg ventured to laugh at Einstein, whom he included in the trio with De Broglie and Schrödinger, calling them all three "Knights of the Continuous", as opposed to quantum, which is the domain of the discontinuous.

On the one hand, the physical institute of Copenhagen and that of Göttingen, and on the other side the advocates of wave mechanics, including Einstein, fiercely opposed The affront of Wien to Heisenberg (50) Wien, which is Wien. A physicist who received the Nobel Prize in 1911 "for his discoveries on the laws of heat radiation". In 1927, at the Solvay Council, he received his Nobel 16 years earlier "for his discoveries on the laws of heat radiation," and he is 63 years old. Heisenberg only has 26.

On July 21, 1926, in Munich, Heisenberg, on vacation with his parents, attended two conferences given by Schrödinger. Sommerfeld and Wien were the organizers.

50 Plus de détails dans Schrödinger et les paradoxes quantiques (collection Emile Klein: Grandes idées de la

Science)

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At the end of a lecture, Heisenberg ventured to ask Schrödinger a question about phenomena of a corpuscular and non-wave nature, after obviously having chosen judicious cases putting the lecturer in difficulties.

Schrödinger was speechless, unable to find an acceptable answer.

Wien intervened and he wanted to put an end to the tension that the question of Heisenberg had provoked, but he did it clumsily saying: "Listen, my young friend (he was indeed 37 years younger than him) ... Understand that the time of these nonsense quantum jumps is over" ' Heisenberg, furious, went out and confided in Pauli with these words: "He hardly made me leave the room" Bohr cordially invited Schrödinger to Copenhagen. Heisenberg later recalled this meeting which he followed with interest but remaining in the background.

The Austrian had to submit to the Dane, who did not stop teasing him and pushing him to his last entrenchments, so much did he want an answer to the deficiencies and faults of his adversary. For it was like an adversary that Bohr considered Schrödinger.

It is even said that the Austrian fell ill so much he had to be exhausted by the demand of his host. But Mrs Bohr served her with tea and cakes, which did not stop Niels Bohr from going to the edge of his guest's bed to continue their conversation.

Bohr nevertheless agreed to tell Schrödinger "that the mathematical clarity and simplicity of wave mechanics is a great advance over the earlier quantum mechanics" Schrödinger returned cured from Copenhagen and confided to Wien in these terms: "There comes a time when you do not know if you should accept the position that Bohr is attacking or you must attack the position he defends"

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Einstein’s myth Chapter Seven Einstein’s myth "One of the most difficult aspects to interpret in the field of scientific mythology is the disparity of treatments reserved for the greatest historical scholars. Most of the illustrious scientists are ignored by the filmmakers, whose attention remains focused only on a few names. Among those who have acquired their right of entry on the screen, we will retain Albert Einstein and Sigmund Freud, who are met seven times each. Louis Pasteur (six times), Pierre and Marie Curie (five times), Benjamin Franklin (five times). Remain among those who make at least three appearances: Charles Darwin, Albert Schweitzer, Thomas Edison and Galileo. In the field of science, Einstein and Freud are certainly the most revealing characters of the extraordinary fluidity of certain myths. Rarely taken in their scientific context, they undergo all the effects of mutation, plasticity and crossover » (...) In addition to the mythical meeting between Albert Einstein and Marilyn Monroe (A Night of Reflection), Freud and Einstein will be particularly drawn to two films (Einstein Junior and the Yellow Submarine). (...) Not to mention the presence of Dr Einstein in Arsenic and Old Lace (a parody of Frankenstein), a doctor El Freud (Lustful Dreams) and even a doctor Freudstein (The house near the cemetery).

Finally, in the field of false confidences and symbolic references, it can be recalled that Dr Brown's dog (Back to the future) is called Einstein. (51) "Pacifist or father of the bomb", modern hero or marginal genius ... In addition to vertigo caused by the theory of relativity, the status acquired by the figure of the German scholar owes much to a historical context that strongly accentuated the ambivalence of the character." (52).

Einstein appears everywhere in popular imagery.

The most famous image is the image he made to a journalist in 1951, a picture that was reproduced in all directions, like here by a cartoonist who chose the trot - as support. Meditative and humorous solitary, selfish husband and unworthy father, amateur violist, pacifist, a supporter of a world government, the inventor of the bomb, Einstein is all that and more. No other scientist of his century can claim so much popularity.

"And yet, says Jean Lopez, his work is reputed difficult, even incomprehensible to the common man! Curious paradox: how to admire what we do not understand? Unless, in Einstein, it is not the scientist but ... the magician who is venerated and feared! Did not this moustached Merlin, in a few equations, upset the most sacred things, those that were believed to be obvious, eternal and immutable: time, space, matter, light?" (53) Einstein was caricatured very early.

51 Jouhaneau, J., Scientists Seen by Filmmakers, in Sciences et Avenir, July-August 1997, page 56 52 Levy-Leblond, JM., A Despicable Hero, in Sciences et Avenir, July-August 1997, pages 22 at 25 53 Science and Life Junior N ° 24 of April 1996, Einstein, you will finally understand

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Einsteinâ&#x20AC;&#x2122;s myth Kaiser Willem II intends to make the German Empire the world's leading power in all military, industrial, economic and scientific fields. With this in mind, he launches the "Kaiser Wilhelm Gesellschaft" In this drawing, the three wise men bring their Christmas presents. They are the Banker Koppel, the industrialist Arnold, and the shopkeeper Simon, who present themselves before the son of God, Wilhelm II, who curiously has the head of Einstein.

The Magi do not present frankincense and myrrh but - more importantly - three scientific institutes: electrochemistry, physics and chemistry. The first director of the Institute of Physics is Albert Einstein.

Einstein the original Einstein was an original man. We see it here without socks

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Einstein’s myth Einstein, equipped with binoculars hung by a simple string. Below, caricatured Einstein presenting the new geometry of space.

aricatures d’Einstein dessinées lors de son voyage au on en 1922

Einstein conversing with Kamerlingh Onnes (1853-1926) who first made liquid helium in his home in Leiden

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Einstein’s myth Einstein found in Leiden a scientific circle very favourable to the development of his research. Here, with fellow physicist Ehrenfest, they share the same love of music.

Drawing by Maryke Kamerlingh Onnes

Below: illustration of the article by Philippe Boulanger, entitled: "Be original! Like Einstein? (54)

Science is like a bicycle ... If it does not move forward, it falls " This is the poster of the exhibition Vélo-sciences which took place at the Museum of Science, Liège, from 4 April to 23 October 2004 54 For Science, No. 326 of December 2004, The Einstein Era, p.1

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Einsteinâ&#x20AC;&#x2122;s myth Birthday card received from a grateful studen

My granddaughter Ella imitating Albert Einstein, without knowing it

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The old king and the flea. Einstein appears in a parody of Faust to present the main precursors of quantum physics and its interpretation. The action takes place in Copenhagen in the prestigious institute Niels Bohr.

Einstein in the features of the king of Thule who received from his beautiful (hear classical physics) a gold cup. Remained faithful until death, he drank one last time before dying. The chip obviously represents the quantum theory of which Einstein can be considered the father since it was he who introduced in 1905 the concept of "Quantum of light". The flea grew old, said the parody. She had a son. The son betrays the father ... Then fleas and fleas escaped from the Berlin Academy ... "

This caricature inspired by "Alice in Wonderland" expresses the astonishment of Einstein noting that the hedgehog Heisenberg has passed through the wall. This is a humorous allusion to quantum physics that makes use of probabilities 151

Einsteinâ&#x20AC;&#x2122;s myth Tie Einstein with the formulas of limited relativity, sold on Belgian restorations at the turn of the millennium

Einstein in Che Gevara and a subscription form of Science and Life

Einstein carved into Mount Rush-more next to the Presidents of the United States.

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Einsteinâ&#x20AC;&#x2122;s myth When Einstein died, his brain was removed and analyzed Photos extraites du film de under all the covers.

Françoise Wolff : Einstein, It weighed 1,320 kg, which un mythe, un homme corresponds to the average weight, but it presented a curious anomaly: a difference in the "fissure of Sylvius", that is to say on the border between the three lobes of the brain.

Einstein had large parietal I l I t i s w e l found in a few jars. It was admired by Kenji The brain was then cut into 240 cubes which were l Sugimoto, thanks to this American professor, Doctor Harvey. k n o w n t h a t t h e s e l o Without knowing it, the Jewish saint b has his relics. e Dr. Harvey, an anatomo-pathologist, s removed the brain after Einstein's death, m sent sections to researchers around the a world. k The only insignificant result: no e degenerative changes as sometimes i some people have. t Today, Harvey is looking for a buyer p of the famous brain. o Einstein's eyes, removed by his s ophthalmologist, without authorization, s are kept in a New Jersey bank i b l Photos from Françoise Wolf's film: Einstein, a myth, a man e t o l o c a t 153 e r e

Einsteinâ&#x20AC;&#x2122;s myth "I am the son of Albert Einstein," proclaims the 65-year-old, who claims to be the son of Albert and Elsa when she was 56 years old. "The important thing for me is to have Einstein's brain, the most valuable legacy, it's his genes that I seek to value through my scientific work" "The resemblance seems obvious to me. When you look at my skull and this one, it's almost identical, "he adds, pointing to Einstein's statue.

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Einsteinâ&#x20AC;&#x2122;s myth This cartoon published in the Washington Post: a bubble lost in hyperbole representing spacetime. Commentary: "If someday, in the distant future, intelligent beings examine the cosmos, all they will remember from this pile of dust we call Earth will be this: this is where Albert Einstein lived"

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Chapter Eight "The Gods need man and men need Gods" Ilya Prigogine The classical science of Newton and Einstein was turned towards stability, equilibrium, permanence. Yet our world presents only fluctuations and instabilities.

Evolution is the transition from science as geometry to science as narrative, where man and nature are included.

Einstein, a proponent of permanence in considering a balanced static universe, was, however, at the root of the explanation of a changing universe. Einstein became Darwin against his own will.

The fundamental concept of classical science is the concept of the law of nature. Newton's law F = m.a. is a deterministic law, since it is enough to give a value to the acceleration of a known mass to know the force that will animate it in the future. And again, since the force is known, it is possible to deduce the acceleration given to it in the past. The future and the past of this classical law are in a reversible situation.

Is it really a model of the universe? What happens to men in this world where there is a break between them and nature?

The answer is that there are two separate cultures. Such a dualism already existed among the philosophers Descartes (Res Extensa and Res Cogitans) and Kant (phenomenon and noumenon).

Prigogine wanted to go beyond these dualisms.

Would we be spectators of a film already shot? No, says Prigogine, the world is under construction, the future is not given in advance What is the link between determinism and contingency?

The notion of probability enters physics with thermodynamics. Boltzmann influenced by Darwin highlighted the fluctuations and chances. Biology became the biology of populations and irreversible phenomena.

Determinism is alienating; it prevents the coexistence of the two projects: that of the intelligibility of the laws of nature and that of the humanism of values, without which there is neither choice nor freedom.

Prigogine then introduces the notion of the arrow of time that appears in thermodynamics with the increasing entropy of an isolated system. When we leave the established equilibrium, we begin new ordered structures, the world diversifies. Human creativity is a good example of how the arrow of time is a universal property of nature and man.

Newton was not wrong, but his theories applied to simple and idealized situations. The arrow of time is expressed in probabilistic terms. Prigogine disagrees with Einstein when he said that time is an illusion. No, time builds the future and time is at the origin of the diversity of the world. The world is a superposition of fluctuations.

What is the meaning of this arrow of time? Are crops also systems composed of men as solids, liquids and gases are composed of molecules?

Here is another quote often heard in cybernetic circles: "Liquids and cultures reorganize when they undergo fluctuations that move them away from their equilibrium state". A kind of non-equilibrium crystallography is then observed.

How far can this analogy between a solid, a liquid, a gas and a society go? Professor Prigogine admits "that life is too complicated to be explained by physics and chemistry. (...) Physics must integrate the overall structures; Since, in the same way, we cannot do sociology from a single individual (...) in the field of physics, we must consider sets: many properties of matter do not occur. do not end up at the level of a particle from which I cannot say if I am dealing with a solid, a liquid or a gas (...) Because before, sociology and the economy had only one model: Newton's laws. (...) Today, the human sciences can take other models: instability, chaos "(...) But, we must remain cautious because the decision-making mechanism, essential element in the description of sociology and economics is obviously very different in the case of molecules and in the case of a man " (55)

55 The Complete Conversations Names of Gods (Noms de dieux) by Edmond Blattchen and Alice Editions, Brussels, 1999, p.36 to p.39

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"The Gods need man and men need Gods" If we go further into the notions of entropy and negentropy, we find that the measure of disorder and order only makes sense if we include the system observed in an environment superior to it. but closed. This image is not difficult to imagine since we now find that our atmosphere is surrounded by an ozone layer that is, in a way, a limit to the closed system that contains us.

Actually, ignoring the troubling hole that has been discovered in this layer, we can say that living beings and the societies they compose (open systems) are imprisoned biologically and "socially" in this closed system.

There is reason to wonder, therefore, about what can happen when, culturally, economically and politically, humans reorganize spontaneously by creating order, negentropy at the level of microenvironments in which they live in small groups (families, villages, companies), that is to say in this multitude of open subsystems interacting with each other.

If this order is made out of a major and collective concern to restore stability, we are not really dealing with a spontaneous reaction, because it is thoughtful and rational and often requires action plans, sometimes restrictive, sometimes austere. But the human, contrary to matter, is moved by thought. As a first approximation, accept the idea that these reactions are spontaneous.

On the other hand, if the disorder is the result of individual or collective discontent resulting in oppositions, uprisings, revolutions and even wars, there is more spontaneity, because in most cases their consequences are not really wanted.

The frequency of spontaneous increase of the disorder is far superior to the spontaneous increase of order.

If "Spontaneously" is the appropriate adverb to express the transition from a defined state (concerning the whole open system and its environment) to a more (or less) disordered state, then we encounter the application of the second principle of thermodynamics in which S (entropy) increases with the disorder and decreases with the order. . dStot ď&#x20AC;˝ dSi ď&#x20AC;Ť dSe ď&#x192;ą0 dStot is the sum of the total entropy (open internal system + closed external system); dSi is the entropy of the internal system and the entropy of the external system.

We find that the sum of the two measured entropy differences is always positive. But it may be that dSi or dSe is negative (negentropy) while the other term is positive (entropy). We must, therefore, create disorder in one system to create order in the other and it is always the disorder created in one that is superior to the order created in the other since the resultant of the sum entropic differences dStot is positive.

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Here are the two books that Professor Prigogine offered me during our meeting on October 10, 1997, on the occasion of the recording of the program "Names of Gods". They really complement each other: one is a scientist and exposes the mathematics proper to the systems studied, the other tackles the essential renewal of the human and social sciences.

Let's go back to the matter and ask ourselves the question of spontaneity. By way of example, a cold steel ingot cannot spontaneously become hotter than the environment in which it is located. But the opposite is true: steel products from hot lines cool spontaneously in halls before cold processing.

Similarly, the solidification of ice water is spontaneous at -1 ° C, the entropy of this system decreases and order is created (formation of geometrically ordered crystals); but the environment in which the water is found undergoes an increase in entropy greater than this decrease (the disorder outside increases more than the order inside the water).

Another experience: ice melting is spontaneous at + 1 ° C; the entropy of water increases in the internal system studied, disorder is created there (water molecules are released from their geometrical order and roll over each other), but the external system in which it there is a decrease in entropy less than the increase in internal disorder.

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"The Gods need man and men need Gods" In the diagram above, on the left, there is a solidification of the water: the heat passes in the external environment where the entropy Sext increases (more of disorder). On the right, there is a melting of the ice: the heat comes from the external environment where the entropy decreases (more order). What analogy can we envisage with the solidification of water in ice? This corresponds to ordered crystallography of the molecules with respect to the relative disorder of the liquid.

It is the same in any human organization that decides to put order in a given system in communication with its own environment. Do not they say, "The spirits are warming up. We must calm them down. "? Or again: "the result of this company is in the red, it will have to restructure"? To calm the spirits in an internal system or to restructure it corresponds to an increase of order, but often induces a great deal of disorder in its environment. In this case, Sint decreased at the expense of Sext which increased.

What analogy can we envisage with the melting of ice in the water?

The melting of the ice causes, in the internal system, analyzed, an increase of the disorder which will be greater than the simultaneous increase of the order of the external system.

It is the same in any human environment that gives priority to the quality of life of the population to the detriment of the profitability of internal systems, including businesses.

Labour forces, for example, have struggled to improve their financial situation. It is true that the disorder created in some companies has made them collapse and many of them have even disappeared because their costs began to exceed their profits. In this case, Sext declined at the expense of Sint which increased.

Globally, at the scale of our planet, the resultant of order increases, that is, the sum of negentropies, is less than the result of increases in disorder. But it is necessary to ask the question about the importance of the disorders and the orders generated. For example, in the case of the solidification of water in ice, it is also important to measure the disorder caused to the environment. It can be seen that the external environment will become all the hotter and more disordered than it was initially ordered, because it is well known that if the external environment is cold rather than warm, the same amount of heat emitted towards this environment will have the effect of "disordering" more, a bit like the bowling player who easily kills nine pins perfectly ordered from the start, rather than three disordered pins

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Thermodynamics tells us about the trends, but it remains silent on the speeds. Spontaneous transformations are sometimes very fast (as is the case with the expansion of a gas), but this is not a general rule. A viscous oil has a spontaneous tendency to flow slowly. Any process causing disorder can occur at a very low speed and sometimes even imperceptible. When, for example, disorders occur in our populations and societies, it is often late.

This was the case in the economic field, where liberalism gradually wanted to move order to areas of interest (to increase profit and profit) by not accepting the disorder caused by the quality of life of the people by the consequences of its excesses. This liberalism began slowly but surely to destabilize us but today, its speed is galloping and it has no limit.

He is constantly exculpating himself from the disorder he has provoked. This is the case in the United States, which prefers to pay for their pollution rather than to bring real remedies that might slightly compromise their economy. It is also in the United States that created this dual society where only the rich have the right of citizenship: 50 million citizens are deprived of social security. Thus, the economic wants to save the economy to the detriment of the planet and men.

Are capitalist networks of multinational corporations not similar to this orderly crystallography of ice molecules, and do they not want to constantly restructure themselves so that their "machine" can run at full capacity, without paying too much attention to the negative repercussions that they will produce on the global system?

For humans, the disorders induced by hyper-ordered systems are measured in suffering, slavery, pollution, malnutrition, disease, poverty; in short, in physical and spiritual destruction. Work absenteeism increases; alcoholism sets in; divorces are legion because the family unit is shaken and disturbed by the crazy schedules and by the importation of the daily conflicts and problems from the workplaces to the heart of the households.

Professor Prigogine (for whom I am using the present tense, in spite of his recent death) is also about the interactions between men and God if we judge the choice of the symbol he chose for the program "Names of Gods".

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When he presented his pre-Columbian statuette, Meczala, he told us: "I really like this sculpture because it represents an interrogation, even certain anxiety (...) In the civilizations of South America and Central America, the reigning conception (of art) is that of a "biological" world in which the movement of the planets and the brightness of the sun require energy: we must feed the gods; the gods need man and men need the gods " (56) The time to be and to become.

The bifurcations of a system occur when its imbalances are such that this system passes from the elastic state to the state of irreversible deformation. This obligatory passage allows the interactive elements that make up this system to reorganize to find a new balance.

Civilizations do not escape this fundamental law. And they know, they also, "Dissipative structures" Where are we now? In the elastic phase or in the deformation phase close to rupture? Since the beginning of the modern era, we have witnessed the development of science, where rigorous, objective, incontestable knowledge reigns supreme. During the twentieth century, scientific thought has been led to replace the classic image of the world of Newtonian physics - world determined rigorously and whose necessity makes its law an image of a world in the making, where the contingency takes place next to the need.

Although we cannot deny the good brought by the sciences, we must ask ourselves why, at the same time, the cultural values that man has so long been building up have collapsed one by one. "Because it is life itself that is affected, it is all its values that stagger, not only aesthetics but also ethics, the sacred and with them the opportunity to live each day" (57) This upheaval has been accentuated by the specialization of tasks and by the proliferation of all-out searches in order to be the first in the exchange market, which does not necessarily go hand in hand with usage values. Scientific methods have woven their web in all fields, including those concerning the management of men that is administration and management.

This is commonly known as a single thought, which has reduced us to being only producer-consumers subject to developments in techno-science. "Whereas, like the swell of the ocean, all the productions of the civilizations of the past ascended and descended together, as by common accord, and without dissociating themselves - the knowledge producing the good, which produced the beautiful while the sacred illuminated everything-here before us, what we had never seen before: the scientific explosion and the ruin of man. Here is the new barbarism of which it is not sure this time that it can be overcome.â&#x20AC;? (58) 56 Ibid, p. 61-62 57 Henry, M., La Barbarie, Grasset, Paris, 1987, p.9 58 Ibid. p.10

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"The Gods need man and men need Gods" This barbarism is the technical universe that proliferates like cancer, self-proclaiming itself, in the absence of any norm, in its perfect indifference to everything that is not itself, c that is, the life of him whom he devours. The problem of the problems of our time must be set out in the following terms: will the Western elite succeed in detaching itself from this civilizing form which is not concerned with culture, with working for a new form, or with will she fascinate on a corpse that she will apply to mummify in order to hide her nothingness from an illusion of survival? After having "succeeded" in its development, capitalism has trouble creating the next chapter, so that the chances seem to be in reality against the "favourite" and in favour of the unknown horse.

"The human being never has time to be, he never has time to become," said Georges Poulet. And Paul Rostenne expressed this thought through the metaphor of the Chrysalis and the caterpillar: "As the caterpillar needs to be a caterpillar and the Chrysalis to be Chrysalis, modern man needs to be modern and to take all the forms and all the contents that he gives himself. As life destroys successively the caterpillar form then the chrysalis form targeting the butterfly, life also brings man to its fullness through a series of steps that are not only physical - as was the case with 'insect, but above all spiritual' (59) Culture is a culture of life; it is transformed like the caterpillar, it is at once what transforms and what is transformed into an incessant movement. And his whole organism, in perpetual transformation, constantly interacts with that of his fellow beings. Human life, during its evolution, generates new experiences; the human thus encounters new qualities of life, new altitudes of values that aspire to know it no longer as a utilitarian value, but as an absolute value.

"Culture is what remains when we have forgotten everything" (60) This is the system that includes all the others, it is a container without which the content has no flavour. This is not a misleading packaging, as is often the case with packaging found on the capital, goods and services market; it is, on the contrary, the first truth, that which prevents barbarism from settling down as hermetic packaging, prevents bacteria from attacking the product it protects. But this protection is fragile if we are not careful at all times, because "the most civilized peoples are as close to barbarism as the most polite iron is rust" (61) Man does not really have a past, because his consciousness makes him live, permanently and in the present, the events that marked his life. Only the man hic et nunc really exists, and to live the present, he constantly needs to remember. Constantly, the man remembers and extrapolates. Its past and future are assembled together to form on the timeline two cones of opposite sense, contiguous in their summation to a desertified point: its present. These two cones express the spatiotemporal fluxes of the events of the past and those of the projections towards the future.

Since, according to Aristotle, the past is no longer, since the future is not yet, since the present itself has already finished being as soon as it began to exist, how could there be a "being of time"?

59 Rostenne, P., The barbarism of the elite, Editions DesclĂŠe et Cie, Tournai, 1954 60 Quotation of Edouard Herriot 61 Count of Rivarol (1753-180156 Ibid. p.10

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"The Gods need man and men need Gods" The time to be and to become (Following).

Some maxims relative to the "Present" in ascending chronological order of birth dates of the authors Pick the present day, relying as little as possible on the next day. Carpe diem quam minimum credula postero.

Horace 65-8 BC J.-C Odes, I, XI, 8 And remember that everyone lives only the present, this infinitely small.

Marcus Aurelius (121-180) Thoughts, III, 10 Life is pleasure or nothing. ... Let's enjoy today, no one knows tomorrow.

Palladas of Alexandria Fifth century Palatine Anthology, V, 72 (translation R. Brasillach) When one is too curious about things that were practised in past centuries, one usually remains very ignorant of those practised in it.

RenĂŠ Descartes (1596-1650) Speech of the method Men who, by their feelings, belong to the past and, by their thoughts in the future, find it difficult to find a place in the present.

Louis de Bonald (1754-1840) Letter to Joseph de Maistre, March 22, 1817 Duration is essentially a continuation of what is no longer in what is.

Henri Bergson (1859-1941) Duration and Simultaneity (P.U.F.) May God preserve you from sacrificing the present in the future!

Anton Pavlovich Chekhov, (1860-1904) The Privy Councilor My past is three-quarters of my present. I dream more than I live, and I dream back.

Jules Renard (1864-1910) Journal, March 23, 1901 The extremes touch me.

AndrĂŠ Gide (1869-1951) Selected Pieces, Epigraph (Gallimard)

The days may be equal for a clock, but not for a man.

Marcel Proust (1871-1922) Chronicles, Easter holidays Published in Le Figaro, March 25, 1913.

On earth, two things are simple: telling the past and predicting the future. Seeing it clear day by day is another business.

Armand Salacrou (1899-1989) The earth is round When one is still what one is, one is already what one will be.

Georges Poulet (1902-1989) The Inner Distance, Marivaux The true generosity towards the future is to give everything to the present.Albert Camus (1913-1960) The Revolted Man

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"The Gods need man and men need Gods" The time to be and to become (Following and end).

If the vital function of a healthy 75-year-old man’s life seen by a mathematician is f (x). The integration of this function, which is, actually, the activity that he produced during his life, can be expressed as an accumulation of infinitesimal presents corresponding to 2,366,820,000 seconds.

2.366.820.000



f (x)dx

0 The integral from zero to two billion three hundred and sixty-six million eight hundred and twenty thousand seconds is a way of representing the life of a 75-year-old man as the vital function f (x) accumulating an infinity of present moments, each from them (dx) tending towards 0.

The past truly exists only to the extent that it haunts our present. It is not surprising, then, that the culture of men is imbued with the luminaries of the past, as revealed by the poll conducted by the B.B.C. to her listeners at the end of 1999, where she asked them who were the most famous Englishmen of the millennium. The answers were obvious: William Shakespeare took first place, followed by Winston Churchill, the youngest of these celebrities, then William Caxton (1422-1491), the printer of the first book in England, and the two scientists, Charles Darwin and Isaac Newton.

But culture is also ready to accept new concepts to give itself the illusion of progress so that it accepts innovations without asking too much about their consequences.

Towards the next system bifurcations The evolution of physicochemical systems is explained by their "self-organization". This is done whenever, far from their equilibrium position, these systems undergo fundamental and irreversible fluctuations. It then happens like a symmetry break that Professor Prigogine calls "a bifurcation".

Between two bifurcations, systems evolve deterministically; at the bifurcation, their behaviour becomes probabilistic. This is why any hypothesis of extrapolation beyond what seems to be the state of maximal entropy is vain.

Before humanity reaches the next organizational junction point, beyond the globalization that is under way, there are still many areas where our corrective actions can take place, starting with the establishment of a democratic world government.

The capitalist and bureaucratic experiences of the twentieth century have taught us that if we forget the meaning of man in the application of the ways and means of these policies, we end up with a system of alienation. And that we do not want it any more at any price. However, these two systems had their glory days and could still have them if we approach them differently from the Americans, for some, Russians and Chinese, for others.

Hans Jonas explains that "central planning" avoids the mechanism of competition and, therefore, "the aberration of a market production aimed at exciting the consumer. Since waste is one of the plagues of our civilization, planning would have the advantage of an economic and social order not motivated by a gain on the condition of avoiding "misdirection from above, servility and reign. Sycophants coming from the base (62)

Les systèmes qui intéressent les sciences sociales sont articulés les uns aux autres et s’influencent en fonction de leur prépondérance dans la motricité de l’ensemble.

62 Jonas., H., The Responsibility Principle, Les Editions du Cerf, Paris, 1990

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"The Gods need man and men need Gods" This set appears to us as a complex mechanical structure formed of gears driven either directly by the main flywheel, or by other gears actuated by it. By analogy, our society suffers the resultant of various forces and lives the events produced by their reciprocal interactions: it is the history of men.

From blocking situations to crisis situations, sometimes embellished by a few fundamental discoveries that make humanity leap towards real progress, the history of our societies does not unfold as a programmed digital machine works. The bio-social system, the political system, the economic system, the cultural system, the system of beliefs, values, ethical and aesthetic codes, all these systems have only relative autonomy with respect to each other.

What is today the one that represents the driving wheel of our company? The answer is obvious: the economic system. And how could we change our society by not giving primacy to other systems closer to the human? This is the fundamental question to which it is more difficult to answer. Indeed, as Julian Huxley points out: "In the language of causality, the naturalist can sometimes discover a single definite cause for a phenomenon; the social scientist must always be content with several partial causes. It needs to develop a system based on the idea of multiple causalities."

Human harmonic frequencies and willpower The various quotations from La Mettrie - the author of the machine man - which I had occasion to recall in this essay, would leave us with a bitter taste if we limit ourselves to what they state in the first degree because we would then accept as a fatality our state of man-machine. On the contrary, we must bounce back on these affirmations and discover the ways of humanization of it.

We want to be something other than a malleable material to thank you. But, that does not mean that we are distancing ourselves from the matter, because this too poses its conditions. She herself does not allow herself to be manipulated without rules, and she does not act at all under the impulse given her.

Let us refer to the theory of photoelectricity that Einstein enunciated in 1905 and which awarded him the Nobel Prize. He demonstrated that when the energy of a luminous quantum "h" reaches a precise value, equal to the work of extracting an electron from a precise metallic surface, then, and only then, this electron leaves this surface. For the phenomenon to occur, the frequency "" must be equal to that of the electronic vibration of the illuminated metal. If this is not the case, the increase in light intensity will have no effect.

It is, therefore, the frequency that must be aimed since it only depends on the nature of the metal chosen. This frequency cannot take all the imaginable values, but it is limited to the quantified values specific to the target metal Physicists also try to find, in their discipline, the equations, the ideas, which will best describe the reality of finance, the discipline that produces the agitation of all speculators. To describe the fluctuations of the markets, and the fluctuations of the men who animate them by their offers and their demands, one can also refer to the physics of turbulent flows whose deep analogies with the life of the Bourse have intrigued Jean-Philippe Bouchaud: "A few years ago, I was interested in so-called tropical, extreme disorders; most of the time, nothing happens, then we have big events, accidents. The financial markets also have intermittent flashes of activity which, in time, are organized in the same way. In appearance, it has nothing to do with it, but what is a turbulent flow if not a system where molecules interact with each other?” (63) Of course, the human being is also conditioned by his own material against which nothing is possible; we know that, for example, it is born with a genetic potential which it will be difficult to stop the effects during its existence. And the neural structure of his brain, progressively constituted according to his experience and the conditions of the environment in which he evolves, will also have the effect of making him comprehend life in a specific way.

63 Barthélemy, P., The world of Friday, September 1, 2000, Today, p. 19

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"The Gods need man and men need Gods" Would our subject be limited to a few excitations peculiar to our species which give it the same physical reactions as the phenomena perceptible to the laboratory by means of some simple, even banal experiments? Would we be determined as much as Einstein thinks? That is, to do what we want, but not to want what we want? For example, when you drive, you have the individual impression of mastering your vehicle while the strength of statisticians "demonstrates" what you do, collectively, the road will kill in France several thousand people every year. In spite of everyone's desire that it be nothing, your conduct will be, in its way, only the confirmation of this "natural law."

(64) Would we only be variously modified materials? We do not think so. For the man, it is also necessary that these are worthy of interest because if living beings do not seek anything, they will not perceive anything. As Georges Ganguilhem writes: "A living being is not a machine that responds with movements to excitations, it is a machine that responds to signals by operations" (65) Since it is enough for the herbivore to see and smell grass to start grazing it, without it being necessary to detect the action of sunlight on its nutritional properties, I note that There exists in the animal a sensory consciousness of the world, strictly proportional to the activity required of it to satisfy its bodily need for food and well-being, as well as the necessity of the species to reproduce itself Of course, consciousness is essential "attention," and attention is "interest," that is, perception, not of the object as such, but of the object as necessary. Without this consciousness, the object is perceived vaguely, as in a marginal vision. And since the consciousness is aware of what matters to me, and the precision of the perception of the object is limited to the need that I have, if I choose a fruit to taste it, its colour will reach me only if it means its succulence. In the same way, the female, after the time of the loves, returns, for the male, in this marginal reality where also move, for the others, the passers-by of the urban streets or the travellers of the public transport. And for a female body or face to detach itself precisely from this confused mass, it will be necessary for a man, for example, to manifest a sexual attraction or an aesthetic interest. But this one or that one, by awakening the consciousness, only allows him to sharpen sensory perception in strict accordance with his requirement.

Consciousness, therefore, appears in the beings who are endowed with it not as the instrument of apprehension of the real, but as the use of the instruments of apprehension at its disposal. And it is not forbidden to think that the mismatch between perception and consciousness, which constantly detaches the "interesting" real from an uninteresting real, "determines, even in the most elementary consciousnesses, the less confused feeling of a distinction between the given and its truth.

The truth of the grass for the herbivore is strictly its food quality as perceived by its sight and taste. But when he goes to bed, his truth becomes what his touch perceives. The alternation of these two truths of grass corresponds to the alternation of the two needs of food and rest. And if only these two needs manifest themselves to the herbivore in front of the grass, this one will never have for it any other truth. I want to believe that an action performed by a man requires on his part, in addition to this-sensory awareness, a knowledge of the object to which its action relates, and a knowledge of the influence of this object on all other objects - belonging to the same system or different systems - that could, in a way or another, produces an unfortunate consequence on the course of events that this man will be called to live.

It goes without saying that the majority of men have a more developed consciousness than the herbivore and far from me the thought of wanting to discredit our species to this point. Nevertheless, I would like to be certain that this majority acts with sufficient perspicacity and restraint, and that the necessities of the human species, for this majority, are accompanied by the medium and long-term welcome and fulfilment of future generations

64 Ibid 65 Ganguilhem, G., Consciousness of life, Hachette, Paris, 1952, p 180-181

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"The Gods need man and men need Gods" Now the human consciousness looks in two directions, one of which has nothing to do with the body and its needs. Something becomes conscious in the man who appears more essential, it is the call to the perfection of another order which envisages on his part activity and efforts incommensurate with the activity and the physical efforts and which cannot wait for any help from the bodily dynamism, on the contrary.

From now on, the struggle is triggered in humanity between its conservatism which animalizes it and this trans-corporal dynamism which tends to tear it from its animality. Nowadays, it becomes more and more difficult to live, since between consciences no longer plays a simple imitation of the same, but a tapping emulation that worries those it does not entail. Today, every thought, every feeling, every individual act is carried by the conformity that is sufficient for its justification. The truth is no longer to remain what we are but to become what we must be.

Let us not fear marginality when we are different from what the mould of the unique thought expects of us. Long live our singularity and our rebelliousness to become like others And here comes this turbo engine, which can be called "Will" And even if this engine is beautifully designed and maintained, it cannot avoid some paradoxical sources that radiate to him and condition it by hiding behind the discrete frequencies that he agrees, other subliminal frequencies that no longer vibrate in sync with him, but insidiously provoke in him irreversible deformations: they are the destructive stimuli of humanism, the conditioning, the producers of reflexes.

Man is not an improved metal plate nor a diversely modified material, nor an animal polarized on its necessity. It is, first of all, a being endowed with a unique mind capable of finding the way to his own happiness if his will works and if he is taught to develop it and to challenge corrupting signals.

Man is matter, born of matter and unable to ignore it, but above all, he is a free being who can decide his own destiny by his own choices. Contrary to what Einstein said, the man can want what he wants. It is no longer just a chemical compound formed from the combination of basic elements of the planet, in precise proportions, but it is above all a thinking material capable of modifying everything including itself

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"The Gods need man and men need Gods"

Chapter Nine Man, the finality of creation or product of chance and necessity?

This chapter brings together other archaeologists of God who have wondered about the mysteries of creation.

T he an th rop ic p rin c ip le The anthropic principle would consist in recognizing in this fine adjustment of the properties of the universe a cosmic conspiracy whose purpose is the appearance of intelligent life. Did the universe, from the first moment, possess the properties required to elaborate complexity? This is the fundamental question that shares our contemporaries.

This principle concerns as much the physical origin of the men as their social relations insofar as it does not seem to me possible to make the part of the things between the man, biological product of the Big Bang, and the human activity that follows. The man lives and acts. He is what he does.

Why should we separate the biological evolution and the activities of the human species, since these are themselves creators of biological change and certain circular causation has been established in the world and explains the evolution of the human species, in particular?

No matter what name is given to this prodigious initial energy, it is called: Big Bang, God or "The Vital Moment".

We must first ask ourselves whether, from this first fraction of a second when creation started, this initial power was or was not an end.

The growing "complexity" of matter and the spirit in which it is articulated (or generated) are indeed the fundamental questions that any scientist, philosopher or theologian must ask one day.

Pascal had not already understood this complexity when he said: "All this visible world is only an imperceptible trait in the vast bosom of nature. No idea approaches it. Although we inflate our conceptions beyond the imaginable species, we only build atoms at the cost of the reality of things. (...) This is our true state; that is what makes us unable to know for sure and to ignore absolutely. We sail on a vast environment, always uncertain and floating, pushed from one end to the other. Whatever term we think we may attach and strengthen, it shuts and leaves us; and if we follow him, he escapes our catch, slips and flees from an eternal flight. Nothing stops for us. (...) So all things being caused and causative, aided and helped, mediately and immediately, and all being held together by a natural and insensitive link that binds the most distant and the most different, I want impossible to know the parts without to know the whole thing, as well as to know everything without knowing particularly the parts." (66) In this complexity, it seems to me essential to consider what is at the origin of the human species and to find a logic between its creation and its actions. When Brandon Carter spoke of the "anthropic principle," according to which the laws of nature must allow the existence of intelligent beings capable of questioning them, I seem to have given to the universe and to the man an equally innovative sense, just as powerful as that of the divine incarnation in the person of Jesus. Except for the fact that the anthropomorphic Christian conception of God is more attractive, more comfortable, warmer, more optimistic than the conception of the man marked with "cosmomorphism" which sees in it only a specificity that appears today, revealing general characteristics of life; themselves of the general characteristics of universal matter.

66 Blaise Pascal, PensĂŠes, Brunschvicg edition, Paris, Hachette, 1953, II, p348, 354, 355-356

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"The Gods need man and men need Gods"

Man, the finality of creation or product of chance and necessity?

But today, the anthropic principle is more and more contested, as is the incarnation of God in Jesus. Because the biological man, as the finality of life and spearhead of the Big Bang, is it not as questionable as the man Jesus as the son of God? Was it necessary for the universe to make sense? Is man the thinking element of the universe? In this world, he is, in any case, an animal capable of judgment, socialized, educated and civilized with an expressive capacity superior to other species: the diversity of the sounds emitted by his voice and their combination is considerable.

Already, according to the philosopher Kant, everything happens "as if" nature intentionally pursued ends. According to Kant, the "as if" process, "als ob", qualifies a regulating use of the ideas of reason.

The idea of finality, therefore, has no objective reality. It is a methodological rule.

And many were his predecessors to make some reflections on this subject. Descartes said, "One would presume too much of oneself if one undertakes to know the end which God has proposed in creating the world". For Spinoza, the "finalist doctrine totally overthrows nature and leads us to conceive of God in imitation of man", whereas Leibniz saw the system of general harmony as "the reigns of efficient causes and final causes parallel to each other ".

And Bernardin de Saint-Pierre did not hesitate to say: "Do not look at the storms of the atmosphere (...) like disorders of nature: everything is well in a plan infinitely wise".

Anthropogenic statements can be divided into two broad categories: weak statements and strong statements The weak statements assume no finality and are simply the expression of the principle of causality: human life exists, then there must be conditions necessary for its emergence. Strong statements are explicitly prescriptive since they state that the universe is such that life must necessarily appear there because of a final cause (purpose, project, intention, plan, etc.).

In a strictly deterministic perspective, one might suppose that life must necessarily appear in the universe for reasons connected with the very nature of certain physicochemical determinisms.

"We are not born alone. To be born, for all, is to be born. Every birth is a co-birth, "wrote Paul Claudel:" We are part of a homogeneous whole, and as we co-born to all nature, that's how we know it " (67) (...) "In the broad sense, to know is to exist at the same time. Thus, all that is born, mind or body, co-born according to its mode. There is harmony at every moment of duration, between all the parts of creation, from the Seraphim to the worm.â&#x20AC;? (68) Our times are extraordinary because this knowledge is far superior to that experienced by our ancestors.

First, the place of the planet in the cosmos. It was only in 1965, after the discovery of radio waves from our galaxy, that the hypothesis of an isotropic universe born of a huge explosion was consolidated, and that we were only a portion even smaller than the one we had imagined. It was established by this very fact, in convergence with other previously hypothetical theories, that our universe was indeed expanding. As if we were on a tiny surface of a balloon swelling, each portion of this surface representing a galaxy. The universe has also so swollen that we no longer perceive its curvature: it has become flat.

It is also at this time that earth sciences unify: we understand that the planet is a living system, which has its life and history, and where all the elements interact with each other. Ecology then realizes that there are not only ecosystems next to each other, but that there is a biosphere whose problem has arisen since the 1970s with all perils that threatened it if we continued to pollute it.

And it is also at the same time that we discover that Africa is the cradle of modern man; which, until then, was almost unthinkable since it was believed that there were only 30,000 years ago that very archaic human forms - with large bony margins around the orbits - were still widespread in Africa. New dates have led to the conclusion that modern man could have evolved on this continent several million years ago .

67 Paul Claudel, Poetic Art, p53 68 Ibid., p 72

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Man, the finality of creation or product of chance and necessity?

The seventies was also the time when systemic analysis became unavoidable for a wise mind. We are convinced that there are fundamental laws of complex systems. They are laws of structure, organization and scale, and simply disappear when we focus on the individual components of a complex system because they do not stand up when we individually question each participant.

According to Edgar Morin, humanity emerged from the biosphere and we must become aware of the link in life, ours connected to the earth, the earth connected to its sun and its sun connected to this immense cosmos. Here is the basic idea: to believe that a man is a supernatural being is an error that led to the mad idea of the master of nature, who was going to conquer and master it. There is no biological substance different from physicochemical substances.

To think of isolating the life of matter is a crazy idea that today is a misconception.

Philosopher s, scient ists, theologians, what do they think of the human link?

Two words dominate the literature concerning the evolution of the cosmos, in general, and living beings, in particular. These two words are: "Chance" and "Necessity".

According to the knowledge and beliefs of the men who pronounce them, a series of definitions emerge, and among them, fundamental differences. Thus, with regard to the "Chance", it is: "the character of an inexplicable fact by the final causes, while it is thought to observe a certain finality in it" (69), "The measurement of the ignorance" (70),"The mechanism behaves as if there was an intention" (71) As for "Necessity", it expresses what cannot be, and whose essence implies existence. It is a word whose meaning is a function of the faith and culture of the person who pronounces it. "If there is one trait of the French temperament particularly striking (...), that's what I will call the need of necessity. The French hate chance, accidental and unexpected,"said Claudel. (72) Is the vital link that is a man in the development of the cosmos due to chance or is it necessary?

And if this necessity exists, is it teleological? In other words, does it have a real purpose?

Has not this fundamental awareness already been hatching intuitively for several centuries? When Julien Offroy de La Mettrie wrote "Man is a machine, and there is only one substance in the Universe which has been variously modified", did it not mean, in its own way, that everything that followed the Big Bang had its source in him? And others, did they not deduce from this original explosion, from this brutal energy conversion in the matter, a finality: the man? Is this the effect of chance or necessity?

By making a re-entrant curve in relation to its fundamental principles, the Catholic Church gradually came to recognize evolutionism, but it was a long and painful struggle against itself. In 1909, when the Catholic University of Louvain took part in Darwin's centenary celebrations, Canon Henri de Dorlodot, a geologist and theologian, endeavoured to demonstrate "that one cannot find in the Sacred Scripture, interpreted according to Catholic rules, no argument against the theory of natural evolution even absolute.”

(73) Twenty years later, Georges Lemaître, another Belgian ecclesiastic, (Picture on the left) did not hesitate to declare between 1927 and 1933 that the universe was expanding and that this implied a warm and dense past, which he called the Primordial atom. Which positioned him as the current precursor of the Big Bang model.

Pope Pius XII, astonished by his remarks, however, avoided the dismissal adding that they were quite in agreement "with the original singularity included in the models of the Big Bang".

Then it was Teilhard de Chardin who issued the theory of coexistence of spirit and matter since the birth of the universe, as if, from the Big Bang, energy and matter were already traversed by a force spiritual creator. In other words, man is a product of evolution whose original consciousness is the cause of the molecular complexification of the human organism, in particular. (73) 69 Paul Foulquié, Dictionary of the Philosophical Language, p.313 70 H. Poincaré, Sciences et meth., P. 71 H. Bergson, Both Sources, p. 155 72 P. Claudel, Positions and prop., I, 18-19 73 Darwin, Ch., The Origin of Species, GF-Flammarion, Paris, 1992, introduction of Drouin, p.28

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Actually, Teilhard espouses the theory of evolutionary philosophers who do not hesitate to extrapolate to the things of life the theories they have constructed to explain the phenomena of raw matter.

Since then, the evolution of the Church itself has allowed "The Great Forgiveness" and that of Darwin, particularly

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The philosopher Henri Bergson (On the left), winner of the Nobel Prize for Literature in 1927, sees in life, since its origins, that it "is the continuation of a single impetus that has been shared between lines of divergent evolution. Something has grown, something has developed through a series of additions that have been so many creations.

Bergson did not dissociate being from acting, and he explained their interaction: "It is, therefore, correct to say that what we do depends on who we are; but it must be added that we are, to a certain extent, only what we do, and that we are continually creating ourselves. (...) For a conscious being, to exist is to change, to change to mature, to mature to create itself indefinitely." (74) What Bergson calls "Vital Momentum" Teilhard prefers "Radial Energy". And Teilhard, it is usual to oppose Jacques Monod (below) who published, in 1971, "Chance and Necessity" where he denounced "Vital Momentum" and "Radial Energy" by explaining that biological evolution was a function of chance mutations and the need for natural selection The notions of "chance" and "necessity" are also systematically expressed by Joel de Rosnay (75): "At the root of the genesis of all new forms, we thus find a random generator of variety and a system of stabilization. The random variety generator plays the role of "Chance ". (...) The system of stabilization and selection represents the "Necessity" It involves the environment. (...) The environment acts as a filter while retaining only the most suitable forms. The sanction is elimination. The death ".

74 H. Bergson, The Creative Evolution, p 7-8.

75 Joel de Rosnay, The Macroscope, Points, p. 260-261

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But the "Necessity" of Monod does not necessarily lead to a finality, a teleology (76) in the evolution of the universe. Which is to say that no mind has ever taken control of the material since the Big Bang.

"The universe was not big about life, nor about the biosphere of man," he wrote. We are thus far from LemaĂŽtre's "initial singularity", Bergson's vital impetus and Teilhard's radial energy. Monod's conception of the universe does not exclude, however, that living beings are finalized objects: "One of the fundamental properties that characterize all living beings without exception: that of being objects endowed with a project (underlined in the text) that they both represent in their structures and perform through their performances." (77) This project is the conservation and multiplication of the species. But it is not a question of a co-presence of mind and matter, as believing philosophers think.

The biologist, Jean Rostand, says: "Of course, there is finality in nature, since there is some in the mind of man, but the problem is to know if nature can "finalize" without going through a cerebral cortex Âť.

And if the cerebral cortex was a means chosen by God to bring his project to a successful conclusion?

The whole question is there: is the finality of living beings and of nature an obligatory passage leading us to an end of the universe?

In "Dust of Life" (78), Professor Duve, Nobel Prize in Medicine, (Photo RTBF, taken during the show Names of Gods), disagrees with the statement of Monod and argues instead that the universe was, from the start, fat about life: "You are wrong. He was, "he writes.

While attributing the same role to chance, he asserts that "the universe is not void of meaning and that this meaning lies in the very structure of the universe, which happens to be capable of producing thought through life and brain function. Thought, in turn, is a faculty through which the universe can reflect on itself." (79)

76 telos = end, the study of ends 77 Jacques Monod, The Chance and Necessity, Threshold 1970, p. 22 78 Christian de Duve, Dust of life, Fayard, p. 495 79 Ibid., P. 49674 telos = fin, ĂŠtude des fins

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However, de Duve, despite his apparent inclination for Teilhard by opting for a "Meaningful and non-meaningless universe" is said to be closer to Monod, on a scientific level, but with a "different reading of the same facts".

It "assigns the same role to chance, but makes it intervene in the case of constraints so strict that the production of life and thought becomes mandatory, and this, on many occasions." (80) The theory of chance is also developed by Stephen Jay Gould who states: "It is almost impossible for humans not to believe that we have some special relationship with the universe, that human life is not just the result more or less grotesque of a series of accidents going back to the first three minutes (...) The more the universe seems comprehensible, the more it seems also meaningless " (81) Gould described the unpredictability of fluctuations for large families of animals: reptiles began to fly, while others remained on the ground; among the mammals, the whales have returned to the water and others have not left the earth; some monkeys became men while others remained monkeys.

Close to Monod's conception, Steven Weinberg, Nobel Prize in physics, dreams of an ultimate theory (82): "In this spirit, it seems to me that if the word God must have any meaning whatsoever, it is to signify a God interested, a creator, a dispenser of laws, who has not only established those of nature and the universe, but also standards of good and evil, an entity that cares about our actions, in short something we have reason to love.

This is the God who, throughout history, has counted for men and women. Scientists, and many others, sometimes speak of "God" to evoke something so abstract and so clear that it becomes difficult to distinguish it from the laws of nature. (...)

Will we find God in the laws of nature? (...) But as premature as this questioning may be, it is hard not to wonder whether we will find an answer to our deepest questions, any sign whatever .of an interested God, in an ultimate fundamental theory.

I think not"

80 de Duve, op. cit., p. 495 81 The First Three Minutes, New York, Basic Books, 1977, p148.

82 Dreams of a Final Theory, Pantheon, New York, 1992

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This unpredictable evolution can be found in Pascal Picq, a paleoanthropologist at the Collège de France, who does not see in man the goal of evolution and summarizes his point of view in an article entitled "The cemetery of accepted ideas".

And he goes on: "For it would be necessary to admit that there was a little shrew, Purgatorius, our ancestor, 70 million years ago, who exterminated the dinosaurs with meteorites and gigantic volcanoes; that the flowering plants arrived at the right time to celebrate the event; that Africa has split a large Rift and that the ice caps have brought a refreshing final touch. This symphony of events worthy of Fanastria merely aligns a series of contingencies. If everything were to be redone, the score would play a different tune, but not for men, any more than for monkeys, horses or snakes." (83) We would never cease quoting great scholars as famous as the others, who have on the coexistence mind-matter, in the heart of the universe, different or very nuanced opinions; some, moreover, expressed more affirmatively than others, where subjectivities and beliefs are not foreign.

I would be incomplete if I did not quote Professor Prigogine, Nobel Prize in Chemistry in 1977, (RTBF photo taken during the show Names of gods): "What emerges today is, therefore, a median description, situated between two alienating representations, that of a deterministic world and that of an arbitrary world subject to chance alone. Laws do not govern the world, but it is not governed by chance (...) " (84) Prigogine locates the history of men in this set of ensembles that is the cosmos: "There is a cosmological story, within which there is a story of life, in which there is finally our own story (...) it is the idea of a universe under construction." (85) On the subject of who or what has built the universe, Prigogine does not venture. Like Bergson, he thinks that "the creation of the universe is above all a creation of possibilities, some of which are realized and others not." (86) Hence this pathetic dialogue between Einstein and Bergson, the one determinist and the other supporter of Evolution, the Creative Evolution.

Bergson's basic idea was an Oriented Time, and if he turned to metaphysics, it was because there was nothing in the physics of his time that allowed him to envisage a Time Oriented. But Einstein did not want it, because for him the sense of time is an illusion. But Prigogine wants to reconcile the philosopher and the physicist or at least find in them a common value. This value is choice, freedom and responsibility. Or we are the product of self-organization that is built up from within, by what we call "the laws of nature" or the cosmos (Bergson) or we are the product of a "program" "(Einstein)," but in all cases, there is choice, freedom and responsibility. " Among the scientific thinkers of this end of the millennium, there are other high-level physicists who have understood that the philosophy of science deserves our full attention.

83 Special Historia No. 50 p. 24 84 Emission "Names of Gods" RTBF and Edmond Blattchen 85 Ibid 86 Ibid

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This is the case of Jean Charon who inserted himself between matter and spirit because he considered them as two inseparable pictures of the real: "We believe that our body is a frozen state in which each particle has its place once and for all. Now, this is only an appearance, for 98 per cent of the atoms of our body change in a year; our skin changes every month; our skeleton every seven years. Everything that constitutes our organism is therefore changed in full in seven years. However, the form remains the same or almost. Obviously, a kind of know-how seems to be at work." (87) This same Jean Charon had not already written: "I know that I am the child of the most conscious that I, with whom I live physically in symbiosis as the cells of my body do it with me; I know that this Shepherd who watches over me will know, if I am able to hear it, to tell me if my freedom distances me too far from the path that evolution builds with me and for me, towards the most. I know that the Lord is my Shepherd. I repeat it often today, as a positive affirmation to prelude every day, every night. (...) I have lived for 15 billion years. Because I was born with these first electrons created from the original light, at the beginning of the world. » (88) To study all the physicochemical phenomena that govern the cosmos, humanity has created the exact sciences; but the way in which men have reflected in the course of their history and how they have used their knowledge is the domain of philosophers and sociologists.

According to Marx, the worker no longer has the freedom of his choices, his tools and his ends and he has become "an appendage of flesh in a steel machine". Its materialistic determinism, however, feels the need to clarify that there is no acquired cause, that the innate is secondary, and that only "historical materialism" and class struggles are involved in the creation of all objects. of this world. This is why Marx emphasized the project and the human finality by considering that objects were not all created by evolution, but by man: "The objects of the simplest sensible certainty are themselves only given by social development, industry and trade (...) We know that cherries, in almost all fruit trees, have been transported to our latitudes by commerce and this it is only thanks to this action of a determined society at a given period that it was given to the sensible certainty of whomever.” So even the tree that seems to be given there from all eternity is an inseparable object of man's production.

To limit the evolution of the world and of humanity in particular to the dynamics of class struggle is an outdated theory today. Why wouldn’t it be the opposite: the innate, the main cause, and the class struggle, the second? Nobody can weight a priori the influence of one and the other. Marxist theory reached dramatic proportions in the Soviet Union under the action of the geneticist Theodore Lysenko, who fought the notion of a gene whose invariance he regarded as totally incompatible with the themes of the "dialectical materialism of nature" for which the innate is a negligible quantity. The principle of the influence of the environment was to be preponderant, and there was no question of showing the opposite. A fanatical and unscrupulous man, Lysenko will drag the USSR into an economic catastrophe by his disastrous initiatives that will prevent any development of genetics in his country.

The term "genetics" was also forbidden by power, and many scientists paid with their lives for their refusal to "politicize" chromosomes.

Current sociobiologists including O.E. Wilson bridges the gap between natural and social sciences, and the phrase "genes to culture" (89) deserves an explanation: "How can one claim to speak of a gene that would control culture? Actually, no scientist has done it. (...) All biologists talk about the interaction between the environment and heredity. But except in laboratory notebooks, they never talk about a gene that "causes" a given behaviour, and they never take it literally. It would not make more sense than the opposite, the idea that behaviour would proceed from a culture without the intervention of brain activity. The explanation of the action of genes on culture, like that of genes on any product of life, does not lie in heredity alone. And not the environment, but the interaction between the two (90) (...) And Wilson gives an example: "The case standard of reaction is the shape of the leaf of an amphibian plant. When a specimen of the considered species grows on the mainland, its leaves resemble arrowheads. When it grows in deep water, the leaves on the surface are shaped like lily feet; and when it is submerged in deep water, the leaves grow like stalks of grass floating at the mercy of the current. No known genetic differences in these plants underlie this extraordinary variation. These three basic types are variations of the expression of the same type of genes caused by different environments. Together they form the standard for genereaction controlling leaf shape. " 87 Jean Charon, And the divine in all that?, (Et le divin dans tout ça ) Albin Michel, p.41 88 Jean Charon, I lived fifteen billion years, Albin Michel, pp. 154 and 155 89 Wilson, EO, The uniqueness of knowledge, Robert Laffont, Paris, 2000, p.180 90 Ibid, p.180-181-182

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After Wilson's explanations, it seems to me that all the evolutionary theories are entirely compatible with the existence of God, that it takes the name of Big Bang (LemaĂŽtre), Elan vital (Bergson), Radial energy (Teilhard) ... Man is indeed an instrument of propagation of the mind, but it is not in itself the finality of the mind.

Hominization is an organization among others One must be indulgent to a man if one thinks of the time at which he was created.

Alphonse Allais The actions of man and the knowledge he has accumulated over the centuries - which represents so much for us and which Einstein emphasizes in his profession of faith - are not unrelated to evolutionism. The objects of knowledge and the human actions are not pure products made directly by God - whatever the name was given to Him - but come from a biological and psychological evolution such that man had to be created so that they themselves can exist.

Biological hominization is measured on three main parameters: the erected walk, the liberation of the hand and the "cerebralisation" taking into account their functional interrelations. It took four hundred thousand to five hundred thousand generations, or 20 to 25 million years for biological evolution to build the current anthropomorphic.

It is thanks to their prehensile hand that the precursors of the hominins could appreciate the directions, the distances and locate the place where they were. This "central representation of space" - as Lorenz says - allows not only hominids to move in this one, but also to move objects from their environment. Thus, they save as much energy as they would if they acted in a probabilistic way by repeating the same actions over and over again until they found the one that matched the goal. From this biological hominization, the conditions of reasoned thinking and the methodical manufacture of tools emerge.

This is where the systemic analysis once again comes in: it teaches us that through a series of interactions and feedbacks, the parameters that gave rise to hominization enriched each other and greatly increased the skills species concerned.

Sexuality and family integration, parental care and domestication are particular forms of natural selection, while the reduction of instinct and freedom of action are modes of behaviour that have adapted over time. At the same time, the selection correlated personal experiences with the real world by transmitting knowledge from generation to generation. The accumulation of these has led man to become aware of his brain potential and use them as a creative power capable of modifying his environment. In biological evolution, cultural evolution has gradually been added.

This is not a reason to think we are "gods": we are only advanced monkeys The less stupid of our species know that compared to other animals, great apes, for example, we cannot really exalt our superiority. Their expressive potential astonishes us and their morphology constantly reminds us of our common ancestors. Have we not often wondered what they could tell us if they had the ability to make more nuanced sounds?

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Man shares with chimpanzees and bonobos 98 per cent of his genes. According to Frans de Waal, (91) today, the discipline has turned its back on dogmatic and monolithic approaches to the "all-genetic" or "all learning" and the old feud between the innate and the acquired is now out of date. Subjectivity has given way to more reliable and more nuanced balance sheets.

Of a sulphurous sexual reputation, Bonobos remain the least known of great events. They live in the rainforest of the Zaire River Basin (Democratic Republic of Congo), and it is thought that they have never left their country of origin. The Bonobos population is difficult to assess, given the difficulty of accessing their territory, but it is estimated to be between 2,500 and 10,000.

Even if we add a few hundred who are captive in the European and American zoos, the species is fragile and threatened. These animals have the particularity of defusing their conflicts with frequent, intensive, heterosexual and homosexual sexual activity. While chimpanzees mate more canum (in the manner of dogs) bonobos have the particularity of faceto-face sex (more humum, in the manner of humans); these being favoured by the localization of the sexual organs of the female, more between the legs than the chimpanzees.

Ideal company? It can be described as tolerant, sensitive or intelligent. It is surprising not to see bonobos using tools in their natural environment; primatologists say they do not need it. However, many examples prove that these animals are capable of empathy: they sometimes put themselves in the place of their fellow creatures and help them (92).

As the naturalist, E. W. Wilson writes: "In animals, great apes are the closest to true linguistic ability. (...) Their champion is called Kanzi, a bonobo, the most intelligent animal that has been observed in captivity. I met this primate genialist when he was still very small (...) I played with him and shared a glass of grape juice, and I was struck by his general attitude, surprisingly similar to that of a child of two years. Years later, Kanzi acquired a rich vocabulary, with which he indicates his desires and his intentions on a keyboard of images-symbols. He builds phrases that are lexical, if not grammatically correct. One day, he said "Ice Water Come" (Give me water with ice) and he was brought his drink." (93.

The fact that humans use language to designate objects and express specific feelings is a considerable asset. And even though most animals know how to express their hunger in one way or another, they can hardly tell by their sounds the type of food they want. This property of language has allowed the human species to distance itself more and more from the most advanced animals by transmitting from generation to generation the products of its thought, such as tools and its experiences.

It is the existence of the "cumulative tradition" and the tools that have allowed a man to become the dominant species of the entire animal world. Would I dare to repeat the analogy that once provoked a few bursts among my readers: "The man is cheating what the computer of the year 2000 is to that of the sixties: a product that has developed more". Just as it is impossible for me to ignore this reflection that I launched to a student after waiting for a certain time the answer to the question I asked her: "Even the Bonobo could answer that. ! ".

It was a basic notion of chemistry and my remark was badly accepted. But, what the student did not know was that I really thought - not that she was a great ape - but that the monkey named Bonobo - if he had had an MCQ in symbolic images - would have responded to this question.

Man is nothing more than a thinking organism, a product of nature that has evolved more than other products. Nietzsche's "Es denkt in mir", â&#x20AC;&#x153;It thinks in me", is certainly the tradition, but it is also the biological molecular organization that has become so complex that it has secreted the thought or that it is co-present since the beginning of the formation of the cosmos.

If the chimpanzee, the gorilla, the Bonobo and the Ourang-Outang had a configuration of the larynx different from ours, perhaps they could also express themselves as man, and perhaps they would also say â&#x20AC;&#x153;Es denkt in mir"?

91 De Waal, F., Lanting, F., Bonobos, the happiness of being a monkey, Fayard, Paris, 1999 92 See article by Michel Febvre in Pour la science March 2000 (French edition of Scientific American), 93 Wilson, EO, op. cit., note n ° 50, p.172-173

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While morphological similarities between humans and great apes account for 60 per cent of the characters studied, molecular biologists found that only one per cent of the genes in the entire human genome were different from the monkey genome. But, small causes, great effects.

Morphological evolution is controlled by the "architect" genes, which decide on the speed and, therefore, the duration of species development. This discovery is revolutionary if one compares it to the old synthetic conception of the middle of the twentieth century, which combined small morphological differences with small mutations and large morphological differences with thousands of mutations.

Do we become restless as simple ants?

Is not this the height of men's machines? The observation due to Major Hingston is worth recalling because it illustrates the finalized direction of the collective action of the ants in the removal of prey of a certain size. "When you throw some food at a Cremastogaster auberti ant that lives on the fig trees in the Baghdad region, you see it immediately go to the nest and come back with a team. After discovering where the loot is, the team forms a circle around it, the species and fragments it into the nest.

If you cut a grasshopper into three fragments - the first having a length of 5 millimetres, the second being twice as large as the first, and the third three times larger than the second - and being deposited the three fragments in front of three ants on the same tree, but at different points, all three rush towards the nest. Each one sends a team to his fragment. The experimenter leaves them alone for ten minutes, after which he counts the number of ants forming part of each team: they are 28 in front of the small fragment, 44 in front of the fragment of intermediate length and 89 in front of the largest one. Roughly, each number is double that which precedes it, in other words roughly proportional to the size of the fragment.

The collective action of Crematogaster auberti is supposed to manifest according to the author, a certain kind of 'intelligent' estimate of the work to be done. Without discussing the legitimacy of this qualifier, there is no doubt that the behaviour observed assumes that the recruiting ants have transmitted to the community differential information about the goal to be attained: they have memorized and transmitted to the group external data by means of 'a special code. The finalization is, therefore, obvious.

The depersonaliza tion of men for the benefit of a few Certainly, the twentieth-century experiences have revealed stubborn failures whose repercussions are still strong today. This is the case of Communism practised by a Nomenklatura who has only reproduced an alienating and as totalitarian system as the Tsarist monarchy which it had suppressed.

The moulds of vanity and power have quickly been renewed over time. Their forms are different, but the models that emerge are cast in the same material whose founding principles privilege an extreme minority sooner or later. What one can believe sincerely too often gives way to selfishness, despotic powers, personal interests that end up prevailing on the merit.

Marx and Jesus, at one time or another, were betrayed by men who took them hostage to build the system that suited their own interests. In the twentieth century, Mao Tse Tung and his successors did not seek a universal Marxism, but theirs.

Differences between particularisms often have a greater role than similarities in the overall system. This is also the reason why the papacy struggled for a long time to refuse a universal Christianity which was different from what it wanted.

But today, the majority of particularisms agree to accept the current economic and social thought as being the only one capable of giving men the happiness of living. It is not uncommon that people claiming to fight for the social are themselves undermined by the unique thought and the need to find in the human a selfish deposit rather than a shared purpose. This is often the case in this economic war that we live permanently for almost thirty years where many business leaders and their executives are called to "degrease" the structures they have in charge by getting rid as much as possible their useless content: men and women.

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But you must know that such wor ds animat e the ant -men.

We must, at all times, protect ourselves from insidious currents of ideas that are always ready to kill the innovative powers that aim at human well-being, because it is too easy to discredit common sense and to call Utopia what we refuse to consider. Of course, the whole question is to agree on the very relative notion of "well-being".

The politics of the supplies of which we have just spoken is obviously controlled by their reign, and it is not uncommon to hear human leaders articulate sentences that go so far as to advocate the depersonalization of the men they serve, have to manage, which gives each of them a sense of power in abandoning oneself for a system that encompasses it.

In that vein, I read in a corporate journal the words of a director who said, "We have managed to create a system where there is no hierarchical silo. Nobody is in the service of anyone, everyone can be helped by everyone. These words sound so much the more false that the one who pronounced them wanted on the contrary to be noticed and thus individualized by concealing in the shadows the mass of those who had helped him to reach his own objectives including that which was not the least - to succeed personally.

But you must know that such words animate the ant-men.

The gr eatest current knowledge is to t ell ourselves that we do not know anything For thousands of millions of years, the universe we know today was lifeless. This, at the beginning of the 21st century, seems insignificant from the point of view of the space it occupies in the cosmos, and infinitely recent compared to the time when the Big Bang took place.

Starting from Purgatorius, the first primate listed to date, which lived 70 million years ago, then through the Ramapithecus (14 million years ago), evolution has spawned the Australopithecus (there are five million years for Australopithecus anamensis and three for Australopithecus africanus). Then Homo Habilis (2 million years), Homo Erectus (1 million years) and finally the current man, the Homo Sapiens Sapiens (there are 100,000 years).

At the end of the millennium, not a day goes by without us learning something new about our ancestors. And besides, we who speak willingly of millions of years in palaeontology and millions if not billions of light-years in astronomy, ask us about the fragility of our knowledge, since it is a hundred years ago that we began to understand how our hereditary traits were transmitted to our descendants.

We are, therefore, only at the dawn of human history, and the theories developed over a hundred years cannot pretend to explain everything. The greatest current knowledge is to tell ourselves that we do not know anything.

In the preceding subchapters, we have sounded the alarm about the easy comparisons that can be made between certain behaviours of man and society, on the one hand, and the molecules and states of the matter, on the other hand. We warned the reader of the need for caution when making such comparisons.

Admittedly, "consilience" brings new elements capable of "restoring moribund humanities," (94) and in particular by encouraging the reconciliation of school subjects in such a way that the current partitioning between them disappears in favour of new creativity. We must dare to remove the intellectual boundaries to acquire a complete vision of the world. Otherwise, everything is fragmentary and wobbly.

But this is also not a reason for conditioning one science by another, and in this sociobiology must be careful not to refer to options that are too much of Cartesian objectivity. The naturalist E. O. Wilson believes that the humanities and medical sciences are both facing urgent problems and he realizes that the first ones do not develop as fast as the second ones. Why? He asks himself, and he replies: "Physicians rely on the coherent foundations provided by molecular and cellular biology (...) and on social scientists who refuse the idea that knowledge is governed by a hierarchical order, a belief that unites and animates the sciences of nature. (...) Social scientists as a whole have neglected the foundations of human nature and have had little interest in its origins.â&#x20AC;?(95) 94 A rare English term close to that of "coherence" used by E.O.Wilson in "The unity of knowledge", and which expresses the character of reconciling different apparently foreign disciplines .Op. cit.

95 Wilson, E.O., op. cit. p.21

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"Utopias are taken into consideration by the social sciences, which is not true for the natural sciences, and utopias must, of course, be based on existing trends. Although we are now convinced that there is no future certainty and that there can be none, conceptions of the future can, however, influence the way humans act in the present.

The University cannot refrain from such a debate in a world where, with certainty being excluded, the role of the intellectual changes necessarily and the idea of a neutral scientist is severely questioned (...) We come from a social past of conflicting certainties, that they are related to science, ethics, social systems, to arrive in a present of considerable questioning, including even the questioning about the intrinsic possibility certainties.

Perhaps we are witnessing the end of a type of rationality that is no longer appropriate to our time (...) We invite the social sciences to open up themselves to these questions (... The responsibility to go beyond these immediate pressures is not unique to those who work in the social sciences; it also falls to the intellectual bureaucracies - university administrators, research associations, foundations, and government agencies - in charge of education and research.

We must recognize that the main issues of a complex society cannot be solved by breaking them down into small parts that seem easy to master analytically, but rather by trying to deal with these problems, treating people and nature in their own way of complexity, and their interrelations." (96)

96 Wilson, E.O., Ibid. p. 238-241

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Conclusion "I never understood," wrote Einstein, "why the theory of relativity, whose problematic is so far removed from everyday life, was able to find such a lively and enthusiastic echo in the most diverse segments of the population."

The answer seems simple: "The theory of relativity gave theoretical physics the importance that philosophy had held until then, and the impression could only be enormous among all educated minds." (97) Relativity has undoubtedly become a marvellous intellectual construct, in which the physicist was and remains "the archaeologist of God", certainly the pantheistic God, that of Spinoza, thus advocating a philosophical theory in which the mind and the universe do not one.

Although I became a professor of mathematics for electromechanics, in the theory of general relativity I am only an amateur anxious to discover the mysteries of the cosmos. During the writing of this book, I became aware of the mathematical abyss I was in before.

But I also thought that at sixty, it was not too late to partially fill it. This is my current profession of faith and it is my way of doing digs in God. Max Born gave a speech on the fiftieth anniversary of the annus mirabilis: "The foundations of general relativity then appeared to me, and even today, as the greatest feat of human thought in Nature, the most astonishing combination of philosophical penetration, physical intuition, and mathematical skill. But his connections to the experience were tenuous.

It seduced me like a great work of art that one must appreciate and admire from a distance."

(98)

97 Sugimoto, K., Albert Einstein, Illustrated Bibliography, Belin, traduct. French, 1990, p.167 98 Physics and Relativity, in Fßnfzig Jahre Relativitätstheorie, Bern, 11-16 Juli 1955, Verhandlungen, A.Mercier and M. Kervaire Êds., Helvetica Physica Acta, Supplement 4, 244-260 (1956)

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Conclusion And T.Damour writes: "Today, a hundred years after the mirabilis annus, the situation is very different. General relativity plays a central role in a broad field of physics, ranging from primordial cosmology to black hole physics (...) It even has daily practical applications via satellite positioning systems (like GPS and soon its system European Galileo).

Many ambitious (and expensive) experimental projects aim to test it (...) or use it as a tool to decipher the distant universe (...) Far is the time when its links to experience were tenuous.

However, it is remarkable to note that the fascination, evoked by Born, for the structure and the physical implications of the theory remains intact." (99) Besides the wonder of Einstein's discoveries, let us not forget the pacifist contribution of the scientist, even though he contributed to the "progress" that led to the atomic bomb.

May the last words of Einstein, written in April 1955, inspire each one of us: "In matters of truth and justice, there are no small or big problems, everything is of equal importance when it is is the human. To anyone who does not take the truth seriously about unimportant matters, one cannot trust the great » (100) Remembrance of a physics lesson on electromagnetism in 2002 and in 1962

In 2002

In 1962

99 Leduc Michèle., Director of the « Savoirs actuels collection », Einstein today by Aspect Alain, Bouchet François, Brunet Eric, CohenTannoudji Claude, Dalibard Jean, Damour Thibaut, Darrigol Olivier, Derrida Bernard, Philippe Grangier, Laloë Franck, Pocholle Jean-Paul ...

CNRS Editions, EDP Sciences, Paris, 2005, p.316. 100 Ibid 3097

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Glossary Absolute Identical in all reference frames Absolute (space) Newton's conception of the three-dimensional space in which we live, according to which the notion of absolute rest has a meaning. In this absolute space, the lengths of the objects do not depend on the movement of the reference frame in which they are measured.

Absolute (time) Newton's conception of time as universal, everyone agreeing on the simultaneity of events and on the interval of time between two events.

Big Bang Explosion at the origin of the universe Big Crunch Hypothesis of the final stage of the collapse of the universe on itself Atomic bomb A bomb whose explosive energy comes from the chain reaction of uranium 235 and plutonium 239.

Constant of Planck Constant fundamental (symbol h) which intervenes in the laws of mechanics. It is worth 6.64.1034 joules Contraction of lengths Contraction of the length of an object resulting from its movement with respect to an observer who measures this length. This contraction only appears in the direction of movement.

Curvature of space and time Ownership of space or spacetime which leads him to violate the notions of Euclid's or Minkowski's geometry: initially parallel straight lines may eventually cross each other.

A spacetime property that leads free-falling particles along initially parallel universe lines to move toward or away from each other. Curvature of spacetime and tidal forces are synonymous.

Deviation from light Deviation of the direction of a light beam when it passes near the Sun or other mass. This deviation is due to the curvature of spacetime around this mass.

Photoelectric effect Effect by which a metal, subjected to a swarm of photons of precise frequency, releases electrons.

Point event without spacetime, that is to say, a position in space at a given moment. It can also be something that happens at a point in spacetime, for example, the explosion of a firecracker.

Galaxy Rally of billions of stars orbiting a common centre. The galaxies have a diameter of about 100,000 light years.

Matrix A mathematical structure in the form of a table with rows and columns.

Wave mechanics The initial form of quantum theory, created in 1924 by Louis de Broglie, according to which every moving particle is associated with a periodic wave.

Quantum mechanics Laws of physics that govern the kingdom of the infinitely small (atoms, molecules, electrons, protons) and which are also underlying the realm of the infinitely great whatever they are rarely revealed. Quantum mechanics foresees phenomena such as the uncertainty principle, the wave-particle duality and the vacuum fluctuations.

Photon Particle of light associated with wave-particle duality to electromagnetic waves.

General Relativity The set of Einstein's laws of physics in which gravitation is described by a curvature of spacetime.

Reference frame of inertia Frame that does not rotate and on which no external force acts. The movement of such a frame is solely due to its own inertia.

Special Relativity Einstein's set of laws of physics in the absence of gravitation

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Glossary Tensor: this is the mathematical generalization of the idea of a single vector to a system that contains several vectors at a time.

Einstein Curvature Tensor: The mathematical construct used by Einstein to describe the part of the curvature of spacetime.

Pulse Energy Tensor: Einstein knew he could not just use mass density as the sole source of gravity. Also, he introduced a tensor expressing mass density and pressure. This tensor takes into account both matter and energy Metric tensor: the mathematical structure that makes it possible to calculate the distances in a curved space. It can be represented by a matrix of values that can change places in place.

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Biography of the archaeologists of God Bohr, Niels, (1885-1962) was born in Copenhagen, Bohr entered in 1912 at the Rutherford laboratory in Manchester. Bohr's theory of atomic structure, for which he will receive the Nobel Prize in physics in 1922, is published between 1913 and 1915. His work is inspired by the model of the Rutherford atom, in which the atom is considered to be formed of a compact nucleus surrounded by a swarm of electrons.

In 1916, Bohr joined the University of Copenhagen to work as a professor of physics. His institute will become, until the Second World War, the center of a remarkable theoretical activity and will see the birth of the most fruitful developments of quantum theory.

During this same period, Bohr is also invited as a teacher in many universities.

In 1939, he became aware of the importance of fission experiments. In the United States, at a conference, he convinced physicists of the importance of these experiments. He later demonstrates that uranium-235 is the isotope of uranium that undergoes nuclear fission. He returned to Denmark, where he was forced to stay after the German occupation of the country in 1940. However, he eventually fled to the United States, where he participated in the realization of the first atomic bomb (Manhattan project), in Los Alamos, New Mexico.

Max Born (December 11, 1882-5 January 1970) was a British naturalized German physicist and mathematician. He has played an important role in the development of quantum mechanics. The Nobel Prize in Physics was awarded in 1954.

His real passion in physics was Einstein's early theory of relativity. He will become a close friend of the father of the theory of general relativity, but their opinions will diverge as to the interpretation of quantum mechanics.

With Heisenberg, he will expose his vision of quantum theory, in opposition to that of Einstein, during the mythical Solvay Council in 1927. Council that many consider as the founding act of quantum mechanics Max Born migrated to England because of the Nazi regime. He became a British citizen and taught at Edimburg University for a long time before retiring to Germany where he died in 1970.

Marya Slodowska Curie was born in Warsaw in 1867. In 1891 she studied chemistry at the Sorbonne. In 1903 Marie Curie and her husband Pierre Curie shared the Nobel Prize for physics with Becquerel. Marie Curie receives in 1911 a second Nobel Prize, the chemistry, is honored and becomes a global personality. In 1994, the atomic number element 96 will be called curium (Cm) in tribute to Marie and Pierre Curie.

Albert Einstein said: "Madame Curie is, of all the famous beings, the only one whom glory has not corrupted"

186

Biography of the Archaeologists of God De Broglie, Louis, Duke of (1892-1987), French physicist who made an essential contribution to quantum theory with his studies of electromagnetic radiation.

He began studying history at the Sorbonne. In 1924, he obtained the title of State Doctor with a thesis on Research on the theory of quanta.

Influenced by Einstein's work, he states that, in the same way that waves can behave like particles, particles can behave like waves. He proposes, for example, that an electron can behave like a wave of wavelength h / mv where h is the Planck constant, m the mass and v the speed of the electron.

E. Schrรถdinger will use De Broglie's ideas to formulate his theory: wave mechanics.

De Broglie was elected to the French Academy in 1943, appointed Professor of Theoretical Physics at the University of Paris (1928), Perpetual Secretary of the Academy of Sciences (1942), and Counselor at the Office of the French Sec- Atomic Energy (1945). He received the Nobel Prize in Physics in 1929 for his discovery of the wave nature of electrons (1924).

Pauli, Wolfgang, (1900-1958), is a physicist born in Vienna.

"Spiritual Son of Einstein", linked with Heisenberg, he trained in Munich and Copenhagen, at Bohr. After writing at the age of 20, a remarkable presentation on the theory of relativity, he participated in the development of quantum mechanics.

Around 1925, he formulates the exclusion principle that bears his name and for which he received the Nobel Prize in physics in 1945: a fundamental principle according to which two identical fermions, such as electrons, can not occupy the same state (State of energy) in an atom. This principle partly justifies the regularities of the periodic table. In 1931, he introduced a new particle, the neutrino. It took twenty-five years to see the experimental confirmation of the existence of the neutrino.

Planck, Max, (1858-1947), was born in Kiel (Northern Germany). After the University, in mathematics and physics, at Munich. The problem of the "black body" is insoluble by classical mechanics, which professes that the nature of fact does not "jump".

Planck emits, almost in spite of himself, a revolutionary hypothesis: the exchanges of energy take place discontinuously. He thus creates the theory of the "elementary quantum of action", hence the adjective "Quantum". The constant "h" is the basis. It will also be called "Planck's constant". In 1918, he received the Nobel Prize in Physics.

The theory develops rather under the action of Bohr and Schrรถdinger, because Planck himself turns his interest towards the "relativity" of Einstein, which he defends as he defends other Jewish colleagues, under the rule of Hitler. He had lost one of his sons during the First World War and he lost the last in the repression that followed the attack against Hitler in 1944.

187

Biography of the Archaeologists of God Poincaré, Henri, Jules (1854-1912), mathematician, astronomer, theoretician and philosopher of sciences, influenced cosmology, relativity and topology. Poincaré followed, from 1872 to 1875, the Ecole Polytechnique of Paris where he obtained mathematical successes. He obtained a doctorate at the Ecole Supérieure des Mines in 1879 thanks to a thesis on differential equations. In 1881 he became professor at the University of Paris at the age of 30.

In 1889, the King of Sweden awarded him an award for his contribution to the theory of orbits.

In 1906, he was elected president of the Academy of Sciences and in 1908, member of the French Academy. As Minkowski did, Poincaré contributed to the explanation of spacetime S ch röd ing er, E rw in , (18 87 -19 61 ) est né et mort à Vienne.

Il a une carrière brillante lais troublée par deux guerres : officier d’artillerie, professeur à Iéna, Stuttgart, Breslau, Zurich, Berlin, Edimbourg, retour à Graz(Autriche), exil à Dublin jusqu’en 1956. Il reste un philosophe qui pense que « la forme remplace aujourd’hui la subs- tance ». Le sommet de cette carrière se situe en 1926, quand il complète la mécanique ondulatoire créée par Louis de Broglie et lui donne une base mathématique abstraite en établissant une équa- tion d’onde qui portera son nom. En 1933, Schrödinger partage le prix Nobel de physique avec Dirac.t

188

Mathematical Appendix Annexe mathématique Explanat ion 1. The photoelectric effect .

1. Will the copper surface (ejection work = 4,4 eV) emit photoelectrons if it is illuminated by

visible light?

The frequency of light corresponding to the critical value at which electrons begin to be ejected can be deduced from this formula with WA = 0

Ecin  hf WA

Ecin  hf

or and

Answer to the question asked

Conclusion: visible light (400 to 700 nanometers) cannot extract photoelectrons from copper 2. To be able to break a chemical bond in the molecules of human skin and thus cause sunburn, a photon must have an energy of about 3.50 eV. How long does it fit?

Conclusion: ultraviolet rays are responsible for sunburn Explanat ion 2. The Twins Paradox The spaceship clock, seen by the twin, which is in space, gives a travel time of 6 years.

The twin who stayed on Earth sees her brother age 6 years, but her clock tells her that a time of 18 years has really passed; therefore, the speed at which the space twin travelled is:

Namely

189

Mathematical Appendix Annexe mathématique Explanat ion 3. Exam ple of conversion between mass and energy Consider an example of an application.

The sun radiates energy isotropically in all directions. At the level of the Earth (r = 1.50.10 11m), the power delivered by solar radiation is 1.4 kW / m2. What mass does the sun lose per day as a result of the radiation emitted?

The surface of a sphere centred on the Sun and passing through the Earth is given by Surface  4r2  4(1,50.1011m)2  2,83.1023 m2 On each square meter of this surface, the Sun radiates an energy per second of 1.4kW. Therefore, the total energy radiated by the Sun per second is:

Energy / s  (surface) (1400W / m2)  3,96.1026 Watts The amount of energy radiated per day (86400s) is:

Energy / Day (3,96.1026W ).(86400s / jour)  3,42.1031 Joules / Day In conclusion, the mass lost per day by the sun is::

Explanat ion 4. Demonstration of the constancy of the speed of light propagation Now that we know the Lorentz transformations, let us go back to Einstein's text on the constancy of the speed of propagation of light.

"It is easy to see by the following example how the law of propagation of light in a vacuum is, by virtue of the Lorentz transformation, satisfied both for the reference body O and for the reference body O '. Suppose we send a ray of light along the positive axis of x and propagate according to the equation x = ct, that is, with velocity c. In accordance with the equations of the Lorentz transformation, this simple relation between x and t has a simple relation between x 'and t'.

Indeed, substituting, in two equations of the Lorentz transformation, for x the value ct: becomes

becomes

Which means x’=ct’ According to this equation that the propagation of light takes place. It can thus be seen that the speed of propagation is also, relative to the reference body O, 'equal to c. It is the same for the light rays that propagate in any direction. "

190

Mathematical Appendix Annexe mathématique Explanation 5. What is Poincaré -Minkowski's spacetime? Anecdotal approach Either a driver strolling in a big avenue with a platform on his roof with a series of firecrackers bursts as the rear of the vehicle passes in front of me. (100)

The movement of the driver is identified by a system of axes whose abscissa corresponds to the movement of the car. The time of the driver and that of the observer are resumed on the ordinate.

On the left, the spacetime graph is drawn by the driver with explosives on the roof. On the right, my spacetime, as I see and hear the explosion as the rear of the vehicle passes in front of me. The dashed verticals represent the universe lines of the front and rear of the car.

The spacetime of the driver perceived by the observer at the moment of the detonation

The spacetime perceived by the driver at the moment of the detonation

The observer’s space

The roadhog’s space

In the graph on the left, a horizontal displacement corresponds to a displacement in space at a fixed moment.

The driver becomes one with the vehicle, and his firecrackers are running at the same time. As for the fixed observer, he finds that the explosives do not explode at the same time from his point of view the rear firecracker, closer to him, explodes before the firecracker foremost.

Thorne (101) continues his thought experiment by taking precise figure this time. Here is the summary.

You drive a sports car, whose length is 1 Km and that rolls at 162.000 km / s (54% of the speed of light). By the time the back of your car passes me, the exhaust fizzes and gives a puff of smoke. This event is noted B on the diagrams.

100 Thorne Kip S., Black Holes and Distortions of Time, 'The Sulfurous Legacy of Einstein), Flammarion, Paris, 1997, p.72 101 Thorne Drawn in Schutz Bernard, Gravity from the ground up, an introduction guide to gravity and general relativity, Cambridge University Press, 2003, p.322

191

Annexe mathématique Mathematical Appendix You hear two microseconds later (2 millionths of a second) a firecracker at the top of your front bumper. This event is noted D on the diagrams.

We do not agree either on the intervals of time between the puff and the detonation or on the distance which separates them.

Ecarts constatés For you For me

Time

Distance

2.10-6 s

1 Km

4,51.10-6s

1,57 km

Yet, despite these temporal and spatial disagreements, we have agreed on the absolute interval along the spacetime line that separates these two events Explanat ion 6. Existence of an absolute d istance thanks to the tale adapted from the book of Taylor and Wheeler (102) by Thor ne (103) Here is the summary of Thorne's book whose sentences are in italics.

Every year, in June, on Mledina Island, the longest day of the year, men barge on a ship and go to a sacred island, named Serona, to talk with a huge toad.

All night long, the toad charmed them with stories nightlights of galaxies and stars, pulsars and quasars. And the next day, men returned to Mledina, filled with an inspiration that would comfort them for a whole year.

Each year, in December, during the longest night of the year, the women went to Serona to talk to the same toad all day long and came back the next night, also full of inspiration and comfort. Neither women nor men could tell the story during their journey or what the toad had told them.

In the autumn of 1905, a radical young man of Mledina, named Albert, (104) who had little interest in the taboos of his culture, discovered and showed two sacred cards to all men and women of Mledina. These were the cards used by the priestess, guide of the women and the priest guide of the men during their stay in Serona.

This betrayal of the oath of Mledina's men and women caused a great shock, as the cards did not agree on Serona's location. The women sailed east for 10 miles, then north for 21 miles, while the men sailed east for 16.5 miles, then north for 16.5 miles.

Many of the inhabitants claimed that the maps were false, except for an elder of Mle-dina, named Hermann (105), who believed in them. One day in 1908, he discovered the truth: Mledina's men sailed by compass, and women guided themselves on the stars.

The men spotted the north and the east magnetically, the women by the rotation of the Earth, spinning the stars over their heads.

On arriving at Serona, the two directions taken by men and women made an angle of 20 °.

Hermann used the formula of Pythagoras: the sum of squares on both sides of the right angle is equal to the square of the hypotenuse (the longest side)

102 Taylor E.F. & Wheeler J.A., Spacetime Physics: Introduction to Special Relativity, (W.H.Freeman, San Francisco, USA,1992 103 Thorne Kip S.., Black holes and distortions of time, 'Einstein's sulfurous heritage, (Trous noirs et distorsions du temps, ‘L’héritage sulfureux d’Einstein), Flammarion, Paris, 1997, p.187 to 190.

104 Allusion to Albert Einstein 105 Allusion to Hermann Minkowski

192

Annexe mathématique Mathematical Appendix For men, the straight line between the two islands was the hypotenuse, and this distance was equal to 212 102  23,2 miles

For women, the straight line between the two islands was also equal to:

16,452 16,452  23,2 miles The story does not tell how the people of Mledina, with their tawous culture, reacted to this wonderful find.

Conclusion: Just as, there is an absolute distance in a straight line at the surface of the Earth between Mledina and Serona, there exists between any two unspecified spacetime events an absolute straight-line interval, computable from a similar formula to that of Pythagoras, using lengths and times measured in any referential, mine or yours. It is the equivalent of this formula of Pythagoras, which I will call the formula of Minkowski, who discovered the latter to discover the absolute spacetime.

What is surprising in Minkowski's formula is that the squared separations are subtracted whereas in Pythagoras, they are added together.

Let us use Minkowski's formula (explained in the appendix for four dimensions) and apply it to the unidirectional diagram corresponding to our thought experiment: S 2  L2 c2 (t)2  (X1 )2 If S is the length of the segment separating two spatiotemporal events but taking place on a one-dimensional path, the time interval for the pilot, indicated on the diagram "your space" is: t = 2.10-6 seconds, from where c = 0.6 km My time interval, indicated on the diagram "my space" is: t = 2.10-6 second of which cte = 1.35 km Since for you, the pilot, L = 1Km and for me it is 1.57 Km, For you, S is equal to For you, S is equal to

Minkowski proves that, according to the observers, time and space are indeed relative, but in fact, the spacetime interval is absolute for each of them.

However, unlike Thorne who, at the risk of provoking your anger, does not explain to you the difference between Minkowski's formula and that of Pythagoras, let me explain it to you in the mathematical appendix included in this book.

106 Ibid,p.90

193

Mathematical Appendix

Annexe mathématique

Minkowski was Einstein's professor at the Polytechnicum in Zurich, from whom Einstein was studying.

"When Einstein publishes relativity, Minkowski holds the chair of mathematics at the University of Göttingen. He discovered with astonishment and admiration the work of his former student, whom he had always considered a "slacker"; In the founding article, the mathematical treatment of relativity is rather sketchy, it is essentially the Lorentz transformations. For Minkowski, this continuum of spacetime could be treated much more elegantly. Mathematicians know how to construct abstract spaces with more than three dimensions. He, therefore, imagines making the relativist spacetime of the algebra move to geometry by giving it the form of a four-dimensional space."

Minkowski believes that this construction is not only a mathematical game, but that it corresponds to the deep structures of reality.

At the time, Einstein considers that it is unnecessarily complicated and prefers to stick to his equations.

And now, working on gravitation, he discovers all the advantage he can derive from this formalism. Does he not stick to reality as his old master said? Without the important conceptions of Minkowski, the theory of general relativity may have remained in the swaddling; he will admit."(107) Explanation 7. Mathematical reminders useful for understanding the Minkowski diagram. What is a hyperbole ?

A hyperbola is the locus of points whose fixed two-point distances have a constant difference in absolute value (ignoring the + and - signs). The two fixed points F and F ', called foci are located on the x-axis at a distance equal to the half-diagonal of the rectangle having sides 2 a and 2 b.

The 2

equation of a hyperbola is as follows: 2 b

Since its asymptotes are perpendicular, it is called "equilateral".

And in this case, the attached hyperbole has for equation:

or: From this previous mathematical reminder, let's analyze this Minkowki diagram where we can only represent one-dimensional movements (along the X axis).(108) An event is represented by its universe point (x, t) in a plane where x is the abscissa and ordinate is its time t.

The scales of the axes were chosen in such a way that a movement at the speed of light (x = c.t) is represented by a line at 45 °.

106.De Closets, François., Do not tell God what he must do, Seuil, Paris, 2004, p.202 107.Stöcker H., Jungt F., Guillaume G., All Physics, Dunod, 1999, p .146

194

Mathematical Appendix Annexe mathématique

What does this hyperbole of Minkowski mean? We are actually considering the trajectory of a parti-cule on a one-dimensional path on the x-axis.

The hyperbola is the place of the "event-points" that can be reached from the origin of the axes in a clean time of 5 meters light by several particles moving unidirectionally at different speeds.

The displacement times of the particles are measured by a fixed observer when the proper time of it has reached 5 meters light. The durations are calculated from the Lorentz transformations.

It can be seen that the time measured by the observer in his own system of axes is greater than the natural time of the particles. The one moving at the speed of 0.3c is recorded in 5.5 meters light, and the one moving at the speed of 0.7c is recorded at 10 meters light.

If these particles were cosmonauts traveling at these speeds, they would find that their own time is less than the time measured in the tertian axis system. Therefore, when they return to Earth, they would discover that they have aged less than the earthlings they find.

The universe line of a particle contains the information needed to calculate its speed.

The following diagram shows that the speed between two events is the inverse of the slope of the universe line joining the events.

Since the diagram has for ordinate T = ct and for abscissa x, and the speed is equal to x / T, the slope is the inverse of the speed: T / x.

T Universe line of a particle in motion T

X

x

195

Mathematical Appendix Any line through the origin of the axes represents the universe line of a particle moving at speed v in the x direction.

These lines have for equation T = 1 / vx If v is expressed in units c (3.108 m / s), x is the distance traveled in meters and T is the elapsed time since departure in light meters.

This means that the universe line relating to the particle moving at the speed of light c will be bisector of the right angle formed by the two axes.

Indeed, in this case, v = 1, 1 / v = 1 and t = x. If the particle has a velocity lower than c (for example 0.7 c), T = 1 / 0.7 x and the angle formed by its universe line with the x-axis is greater than 45 °.

At the limit, when the velocity tends towards zero, 1 / v tends towards infinity and the angle tends towards 90 °, which explains that the axis T corresponds to the universe line of the motionless observer.

Let's extend the diagram above into the four quadrants of Minkowski. What do we see?

If we consider the trajectory of a particle on a one-dimensional path, with a structure of equilateral hyperbolas where a = R, we find that:

where R is expressed as a function of the units x and y.

Now, in Minkowski's scheme, "ct" is a function of x and x is a function of "ct". Mathematically, from the following diagram, we can conclude that the angular coefficient The line of dotted lines passing through the origin of the axes is equal to 1. This means that these lines are "bisectors" of the quadrants and asymptotes of the hyperbolic curves. They represent the time line of a particle moving at the speed of light.

Given the equation of a hyperbola, we conclude that

If there are, in addition to the axes of the previous graph, two other axes, "ct" and x respectively measuring the speed of propagation of another mobile (in meters light) and the distance traveled by it in the x 'direction, we find that ct=R and ct’=R. In other words, as we saw earlier, the hyperbola covering quadrants 1 and 2 is the place of the "event-points" that can be reached from the origin of the axes in a clean time (in meters light) identical for all these points in their own system of axes. But if one places oneself in the system defined by the axes ct and x, one finds that the time measured on t 'has dilated with respect t.

This observation is also true for the hyperbolic curve relative to the past, which covers quadrants 3 and 4.

How to interpret the hyperbolic curves covering the quadrants 2,3 and 1,4?

Since x = R and x '= R, these curves can be considered as the locus of equidistant "event points" of the origin of the axes, for mobiles moving in different directions, as is the case of the axes x and x '.

2

1

3

4 196

Mathematical Appendix Annexe mathématique

Explanation 8. What is Poincaré -Minkowski's spacetime in 3D? Mathematical approach Let us generalize the Euclidean geometrical structure of ordinary space.

X3

X3

L

X1 X1 X2 If L is the length of the segment separating two events in the X1X3 plane, this distance can be calculated as follows: L2  (X1) 2  (X3) 2 If the line segment is measured by the 3 spatial coordinates, X1, X2 and X3, then the length L separating two events is calculated as follows: L2  (X1)2  (X 2 )2  (X3 )2

X3

X3 L

X1 X1 X2 X2

197

Mathematical Appendix Annexe mathématique

But we see that the temporal dimension is not yet taken into account. It is therefore necessary to introduce the moments of time "when are" these two events separated by a duration T = t.109 If we call S the interval between the two four-dimensional events, then: S)2  (X1 )2  (X 2 )2  (X 3 )2  (X 4 )2 (S)2  L2  c2 (t)2  (X1 )2  (X 2 )2  (X 3 )2  c2 (t)2

where c is the speed of light (or more exactly the maximum signal propagation speed) Explanat ion 9. Einstein' s equations of general relat ivity Let's now move on to Einstein's equations of general relativity using new mathematical concepts. As Einstein writes: "We have good reason to think that the Minkowski space is" free of field " represents a possible normal special case, and certainly a simplest particular case that can be imagined. Such a space is, as regards its metric property, characterized by the fact that:

dx12

dx2 2

dx3 2

is the square of the spatial distance, measured with a ruler, of two points infinitely close to a three-dimensional cross section of a spatial character (Pytha-gore theorem), while dx4 is the time interval, measured with a measure of the appropriate time, of two events having (x1, x2, x3) in common. All of this comes down to this - as it is possible to show with the help of the Lorentz transformation - that the magnitude

dS 2

dx12

dx2 2

dx3 2

dx4 2

a une signification métrique objective. (…)

By now subjecting this space, in the sense of the principle of general relativity, to any arbitrary continuous transformation of coordinates, the objective significant magnitude is expressed in the new coordinate system by the relation dS 2  gik dxi dxk

où il faut sommer par rapport aux indices i et k et par rapport à toutes les combinaisons 11,12 ;…jusqu’à 44.

The gik are not now constants, but functions of the coordinates, which are determined by the arbitrarily chosen transformation. In spite of this, the gik are not arbitrary functions of the new coordinates, but functions such that the form dS 2  gik dxx dxk can, by a continuous transformation of the four coor-data, again be transformed into the form dS 2  dx12  dx2 2  dx3 2  dx 4 2 » What is gik? A diagonal matrix whose only non-zero elements are

g00 1

and

g11  g22  g33 1

In this equation, we have used the Einstein summation convention (in other words, every index is supposed to be summed over all its possible values) The chrono-geometry of the spacetime of Poincaré-Minkowski can be visualized by representing around each point x of the spacetime the place of the points which are separated from the point x by an interval (square) unit, c ' that is to say the set of points x 'such that: Sxx '2  gik (x'i xi )( x'k xk ) 1 106 Leduc Michèle., Director of « Savoirs actuels collection », Einstein today, page 270, CNRS Editions, EDP Sciences, Paris, 2005 107 Einstein, Albert., The theory of Special and General Relativity, translated into French by Maurice Solovine for Gauthier-Villars in 1923; Preface by Marc Lachièze-Rey, Dunod, Paris 2004, p.170 108 Leduc Michèle., directrice de la collection Savoirs actuels, Einstein aujourd’hui , page 270, CNRS Editions, EDP Sciences, Paris, 2005 109 Einstein, Albert., The theory of Special and General Relativity (La théorie de la relativité restreinte et générale), traduit en français par Maurice Solovine pour Gauthier-Villars en 1923 ; Préface de Marc Lachièze-Rey, Dunod, Paris 2004, p.170.

198

Mathematical Appendix Annexe mathĂŠmatique This place is a hyperboloid (unit) at a web. (111) The spacetime represented here has only three dimensions (a temporal dimension represented vertically) and two XY spatial dimensions represented horizontally.

We also visualize the spacetime line representing the history of the movement of a particle.

A reminder of the hyperbola equations is essential

Let's apply the basic formula,

dS 2 ď&#x20AC;˝ gik dxi dxk

in the plane of Euclidean geometry. The distance "dl" between two infinitely neighboring points of Cartesian coordinates (x1, x2) and (x1 + dx1, x2 + dx2) is given by the relation of Pythagoras dl2 = dx1 2 + dx2 2 If the surface is not flat or if the coordinate system is not Cartesian, the distance will generally be given by a relation of the form: dl2 = g11 dx1 2 + 2 g12 dx1 dx2 + g22 dx2 2 where g11, g12 and g22 are possibly variable coefficients depending on the considered point.

X2 +dX2

dl X2 X1

X1 +dX1

111 Einstein today, chapter of Thibault Darmour, CNRS Editions, EDP Sciences, Paris, 2005, pages 207 to 319

199

Mathematical Appendix nnexe mathématique Mathématical Appendix Similarly, in the geometry of general relativity, the spacetime points x are identified by four ordinates X1, X2, X3 and X4 (with X4 = ct), and the infinitesimal spacetime distance "ds" is given by the relation: ds2 = g11 dx1 2 + g12 dx1 dx2 + g21 dx2 dx1 +…..+ g34 dx3 dx4 + g43 dx4 dx3 + g44 dx4 2 (Expression that can be positive, negative or null).

The coefficients g  (, = 1,2,3,4).vary a priori in space and in time: they are functions of the point x considered.

They define the metric of spacetime, of which gravitation is the physical translation.

The symmetry group of this time-geometry is the coordinate transformation group (X1, X2, X3, T) in (X1 ', X'2, X'3, T') leaving the shape of the S-interval invariant .

We end up with Einstein's formula: where G is the constant Newtonian of gravitation, c the speed of light, and R  g  R where R is the Ricci tensor. T is the impulse energy tensor. (See glossary) As for  and , these are indices allowing to consider 10 different combinations (See mathematical appendix and glossary) The left-hand side of the equation is relative to the curvature of spacetime; it is the curvature tensor of Einstein. The term on the right is the pulse energy due to matter, pressures and voltages. it is called impulse energy tensor (T) In the equation above, Einstein proposed in 1917 that we add to the left-hand side the term  g  where  is a constant called the cosmological constant to obtain a globally homogeneous and stationary cosmological solution. After the discovery of Hubble of the expansion movement of all galaxies, and after the work of Friedmann, who developed expanding cosmological solutions, Einstein rejected the term.

If we go back further and further to the origin of our universe (in expansion), we find that the distance separating the points of the space tended to zero and the density of the spacetime was infinite. We can assume that at a time in a finite past:

LimR  0 t 0

et

Lim  t0

It is the big-bang that is a necessary consequence of the cosmological principle and Einstein's gravity equation. The radius of the universe, at its origin, about 15 billion years ago was zero and the energy density was maximum.

The famous cosmological constant of Einstein Neither Einstein nor any of his contemporaries imagined an expanding universe, but at that time the philosophical a priori defended the notion of a universe that resembled itself.

To counterbalance the attraction of matter, Einstein modified his field equation by including a cosmological constant ( 0) whose objective was to introduce a repulsive force allowing to consider a static cosmological space. This cosmological constant causes an acceleration while the density and pressure of entraînetot causes a deceleration.

Friedmann also added a cosmological constant, but not to show that the universe is static, but to consider various possibilities of expansion of which he will retain the last as being representative of the current situation.  

With R being the distance between two galaxies; G, the gravitational constant (6,672.10-11), tot, the density of matter, , the cosmological constant and k, the sign of the curvature.

The critical density.

For  0 and k  1, the universe will begin to contract after an initial expansion phase. This is called a closed universe that will lead to the "Big Crunch".

For  0 and k  0, the universe is called flat, there is neither expansion nor retraction.

For  0 and k 1, the universe is said to be open, there is expansion but no acceleration.

For 0, the universe is expanding rapidly. This is the new hypothesis confirmed in the 21st century.

200

Mathematical Appendix Mathématical Appendix

Annexe mathématique

Explanation 10. Applications of De Broglie's law on wave mechanics Calculation of the wavelengths associated with the following particles (112)

Macroscopic particle Tennis ball, mass 0.05 kg and speed 40 m / s.

Microscopic particle Electron mass = 9.10 -31 kg and speed 107 m / s

Quite measurable value that corresponds to the wavelength of x-rays

Explanation 11. Schrödinger's law and the cat's paradox, both dead and alive.

Many thanks to Professor Victor Desreux who taught my wife and I about physical chemistry during the sixties. We have preserved an excellent memory of him.

If I quote him here, it's because he asked me in 1966 about the Schrödinger equation. Here's what I told him: Einstein's concept of dual light exhibits both wave and particle behavior. A function called wave function (denoted ) describes the states of a particu-le or a physical system.  depends on position and time. It makes it possible to determine probabilities on the position and on other quantities of the system described.

From a strictly mathematical point of view, this can be written in the form :

If we are interested in the only spatial variable at a given time t, the partial second derivative of this wave function with respect to x is calculated as follows: First partial derivative: we are only interested in x

Second partial derivative

112

Voir site scribd : https://fr.scribd.com/doc/21990580/9/I-Hypothese-de-Louis-de-Broglie

201

MathematicalAppendix Appendix Mathématical Annexe mathématique Taking into account the relationship of De Broglie and kinetic energy:

where m and v are respectively the mass and velocity of the particle, Ek its kinetic energy, and h, and the Planck constant, we deduce that:

after replacing kinetic energy by the difference between total energy and potential energy

Ek  E  E p By substitution in the relation of the second derivative above, we finally obtain:

2 



8 2 m

(Etot  E p )



2

Each atomic orbital is associated with a form and an energy that makes it possible to answer the two absolutely crucial questions: • Where do I have a chance to find the electron around an atom?

• What is his energy? (113) Victor Desreux then alluded to the "Schrödinger’s Cat" which is an epistemological experience.

We can imagine many paradoxical experiences, such as this: we lock up a cat in an armored box equipped with the infernal machine here (designed in such a way that the choice can not touch it): in a Geiger counter is a quantity very weak radioactive substance, so tiny that in a period of one hour, one of the atoms may be disintegrating and operate a small hammer that will break a bottle of cyanide. If the system is left to itself for an hour, it will be said that the cat is still alive if no atom is disintegrated in the meantime, but that it is dead if there has been a disintegration.

The wave function of the whole system must express the double probability of the living cat and the dead cat.

113

http://jlamerenx.fr/orbitales-atomiques/ Site Marcelin Berthelot 202

Mathematical Appendix Mathématical Appendix Annexe mathématique Explanat ion 12: Demonstrat ion of the time - independent Schrödinger's law Let's start from the formula of total energy equal to the sum of kinetic energy and potential energy

µ We know, on the other hand, that the momentum p for the particle is equal to m.v Let's raise p squared and divide by 2m, we get

= kinetic energy

The total observable energy is often called the Hamiltonian H Determination of E as a function of k (the number of waves)

= the number of waves on a circumference = angular velocity of the wave, T is the period

f, its frequency The Planck-Einstein relationship can be expressed in terms of wavelength h-bar = h/2 ħ is derived from h with the addition of a bar. In quantum mechanics, an ℏ with a line, represents the reduced Planck constant. In this context, it is pronounced "h-bar".

With h, the Planck constant, and c the light velocity in the vacuum

We can also assign a number of waves to a material particle of average pulse P using the de Broglie relation

It’s no longer h-bar

203 203

Mathematical appendix Mathematical Appendix Mathématical Appendix

Annexe mathématique Mathematical Appendix

ħ

=

=

or Etot = Ecin + Epot pot We multiply two members On two multiplie les deux membres The members are the multiplied by  by par Given that

Etot

= ħ

et or

We get

Donc

pot

tot

+

tot

This is the time-independent Schrödinger equation. It is sometimes written: Ceci est l'équation de Schrödinger indépendante du temps. On l'écrit parfois

+

tot

pot

Explanation 12 bis : demonstration of the time -dependent Schrödinger

Explication 12bis : Démonstration de la loi de Schrödinger dépendante du temps

equation

Détermination de E en fonction de Now consider the time impact. Determination of E according to ω Envisageons maintenant l'impact du temps π= π

π = 2π x

E = ħ d'où P= ħk d'où

=ħ k=

And let’s start again from the wave function et repartons de la fonction d'onde et dérivons cette fois-ci par rapport au temps: And let us differenciate this time with respect to time

Etot= ħ car Etot= Etot

=ħ

Etot Etot

= hf

=

=

= =

204

=

Mathematical Mathematical Appendix Appendix 198

Mathématical Appendix

Let us substitute in Schrödinger equation : Let us substitute in Schrödinger equation :

Annexe mathématique Substituons dans l'équation de Schrödinger This is time-dependent Schrödinger equation If we replace Dirac’s constant (h-bar) by Planck’s constant (h), the equation becomes

+

tot

pot

We obtain

+

The quantity « Kinetic energy + potential energy » is called « Hamiltonian » ofpot the system and denoted H. By making the correspondence between H and the partial differential equation, We create an operator, called "HAMILTONIAN’ Ceci est l'équation de Schrödinger dépendante du temps with Si on remplace la constante de Dirac (h barre) par la constante de Plank (h), l'équation de vient Schrödinger equation can be written ;

+

pot

la quantité « énergie cinétique + énergie potentielle » est appelée Hamiltonien du système, et notée H. En faisant la correspondance entre la grandeur physique H et l'équaThe Hamiltonian appears as an operator acting on the wave function.

In summary: respectively, the two equations of Schrödinger, tion aux dérivées partielles, on crée un opérateur noté :as a function of space and as a function of time, are : H= L'équation de Schrödinger s'écrit :

L'hamiltonien apparaît ainsi comme un opérateur agissant sur la fonction d'onde.

205

Mathematical Appendix Mathématical Appendix In classical physics, a particle is described by its position x. The evolution of its position (the trajectory of the particle) is given by the Newtonian equation F = m.a (see page 57) that one writes mathematically according to the second derivative of space as a function of time In quantum physics, by virtue of the wave-particle duality, the particle is now described by a wave function Ψ (x, t) What does Ψ represent? We give here the interpretation of Born. This interpretation relates the quantity Ψ (x) 2 = Ψ (x) Ψ * (x), (Ψ * = complex conjugate of Ψ) to the notion of density of probability of finding the particle in x.

The knowledge of Ψ (r, t) then allows (in Born's interpretation). 1.3 Schrö-dinger equation Now the question is: if we continue the parallel with the movement of a particle, we must find an equation to describ e Explanat ion 12ter: Another pr oof of the t ime -dependent Schrödinger's law

Starting from The first derivative (time-independent) The second derivative (time-independent) t The first derivative (time-independent)

The wavelength and momentum p of the wave in De Broglie's relation are related as follows: By placing the value deduced from this last relation in the previous second derivative

And the kinetic energy is therefore worth:

By placing the value deduced from this last relation in the previous second derivative

200

206

Mathématical Appendix Annexe mathématique Mathematical Appendix By replacing Ek (Kinetic energy) with Etot - Epot

Explanation 13. Quantum numbers and the exclusion principle of Pauli.

114 1. The main quantum number: n This quantum number corresponds in the Bohr model to the numer of the electronic layer.

It is therefore an integer n ≥ 1 and it is also the number of each period (line) of the classification of elements: n

1 2 3

4

5

6

7

Niveau K L M N O P Q

Note that n only intervenes in the radial component of the wave function 2. Secondary quantum number: l Also called azimuthal quantum number, it is defined with respect to n: l is a positive integer that can take the values included in 0 and n - 1: n - 1 ≥ 1 ≥ 0

  



For n = 1 : l = 0,



For n = 2 : l = 0 ou l = 1



For n = 3 : l = 0 ou l = 1 ou l = 2



etc.

At each value of l corresponds an "atomic orbital" term defines a little later.

This atomic orbital has a name: l

114

0

1

2

3

4

http://hrsbstaff.ednet.ns.ca/schof/chimie/chimie11/nombres_quantiques.htm

207

Annexe mathématique Mathematical Appendix Orbitale atomique

s

p

d

f

g

3. Quantum magnetic number: m It is defined with respect to l: m is an integer which can take (2.l + 1) framed values l and - l: +l≥m≥-l

 For l = 0 : m = 0,  For l = 1 : m = -1 ou m = 0 ou m = 1,  For l = 2 : m = -2 ou m = -1 ou m = 0 ou m = 1 ou m = 2,  etc. Each value of (n, l, m) corresponds to an atomic orbital (O.A): n 1

2

3

l 0

0

1

1

1

0

1

1

1

2

2

2

2

2

m 0

0

1

0

-1 0

1

0

-1

2

1

0

-1

-2

3dx²-y²

3dzx

3dz² 3dyz

3dxy

O.A. 1s 2s 2px 2pz 2py 3s 3px 3pz 3py

208

Mathematical Appendix Annexe mathématique 4. Quantum number of spin: s Its value for the electron is s = 1/2. The kinetic momentum of spin ms can take two values: ms = 1/2; ms = -1/2 If m s = 1/2, it is customary to represent the electron by a vertical arrow pointing up: ↑.

If ms = -1/2, the electron is represented by a vertical arrow pointing downwards:↓.

209

Explanat ion 14: Using the four quant um numbers These four quantum numbers make it possible to characterize an electron in an atom or an ion. In the periodic table of elements, also called Mendeleyev's table, are all the chemical elements.

Their sequential order is based on the atomic number (increasing number of protons) and on their electronic configuration, which underlies their chemical properties.

The periodic table has undergone readjustments since its first version, taking into account the discoveries made during the last century.

It has become an universal repository where one discovers all types of physical and chemical behavior of the elements that compose it. In November 2014, its standard form consisted of 118 elements. Today, each element contains its electronic configuration. Iron, below, has the configuration of the Argon symbolized [Ar], but the outer orbitals have respectively the quantum number 3 and 4.

On the layer 3, there are 6 electrons which gravitate on an orbital d. On layer 4, there are two electrons that gravitate on an orbital "s"

Les différentes formes d'orbitales ont déjà été abordées visuellement lors de l'explication After the Pauli Exclusion Principle, we are now in a better position to understand the following summary table:12.

Signification originale Orbitale s

Nombre quantique secondaire

Forme

Quantité(2l+1)

sharp

Boules symétriques

1

principal

Haltèr e

3

Orbitale p Orbitale d

Double haltère croisée (entre autres)

diffuse

Orbitale f

fundamental

5

Rosace (entre autres)

7

Orbitale g

(continuation alphabétique)

?

9

Orbitale h

(continuation alphabétique)

?

11

210

Mathematical Appendix

Annexe mathématique Explication 15 : Ebauche de l'équation de Dirac et de l'existence de l'antimatière

=

=

=

Conclusion :

the mass of the electron Nous différencions

from m de

lorsque l'énergie est positive ou négative et t enons compte de la

masse de l'électron

=0

-

with avec

= with

+

= 0 avec

=

+

(Equation de Dirac en 1928)

Same equation with Même équation avec

Solutions à cette équation Dans le développement de l'équation de Schrödinger, on a vu que : And et que Etot

=

ħ

=

This leads to =

c'est-à-dire

Which implies d'où

ħ

-

211

ħ

=

ħ

=

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Bueche, F.J.,Hecht, E., Physique générale et appliquée, MacGraw-Hill International (UK) Ltd.1997 De Closets, François., Ne dites pas à Dieu ce qu’il doit faire, Seuil, Paris, 2004 de Duve, C., Poussière de vie, Fayard, 1996 Durand, Stéphane., La relativité animée, Belin ; Pour la science Einstein, Albert., La théorie de la relativité restreinte et générale, traduit en français par Maurice Solovine pour Gauthier-Villars en 1923 ; Préface de Marc Lachièze-Rey, Dunod, Paris 2004.

Grundmann, S., Einsteins Akte (Wissenschaft und Politik-Einsteins Berliner Zeit), SpringerVerlag, Berlin, 2004 Hermann Joachim., Atlas de l’astronomie, La Pochothèque, Le Livre de Poche, Paris,1998 Hoffmann, Banesh., La relativité, histoire d’une grande idée, Belin, Pour la science.

Houssier, Claude., La chimie pour les sciences de la vie (1ère partie) 1995 Infeld, Eryk., L’été indien d’Albert Einstein, dans “Les génies de la science, N°21 trimestriel novembre 2004-février 2005 » Journal La Dernière Heure du 19 avril 1955 Journal La Libre Belgique du 19 avril 1955 Journal Le Soir du 8 août 2002, p.15, Anton Vos, Albert Einstein et la théorie de la relativité

restreinte

Klein, Etienne, Heisenberg et le principe d'incertitude, Le monde existe-t-il quand o ne le regarde pas? Grandes idées de la Science, 2014 Klein, Etienne, Schrödinger et les paradoxes quantiques, L'univers réside dans l'onde, Grandes idées de la Science, 2014 Lachièze-Rey Marc., Au-delà de l’Espace et du temps (La nouvelle physique) , Le Pommier,2003 Lapierre, J-W., L’analyse de systèmes - L’application aux sciences sociales - Labor, Bruxelles, 1992 Leduc Michèle., directrice de la collection Savoirs actuels, Einstein aujourd’hui par Aspect Alain, Bouchet François, Brunet Eric, Cohen-Tannoudji Claude, Dalibard Jean, Damour Thi-

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Leduc Michèle., Dir ector of the « Savoir s actuels collect ion », Einstein today by Aspect Alain, Bouchet François, Brunet Eric, Cohen-Tannoudji Claude, Dalibard Jean, Damour, Thibaut, Darrigol Olivier, Derrida Bernard, Grangier Philippe, Laloë Franck, Pocholle Jean-Paul, CNRS Editions , EDP Sciences, Paris, 2005 Le Figaro Magazine N°965 du 24 avr il 1999 -La pensée d’Einstein a pesé sur l’Histoire Levy-Leblond, J-M., Un héros malgré lui, dans Sciences et Avenir de juillet-août 1997, pages 22 à 25 Ludvigsen, Malcolm., La relativité générale, Une approche géométrique, Dunod, Paris, 2000 par J.M. Levy-Leblond Moor e Pete , Les grandes idées qui ont changé le monde, Acropole, septembre 2003 Pour la science, N°326 de décembre 2004, L’ère Einstein Reinhardt Fr it z et Soeder Heinr ich , Atlas de Mathématiques, La Pochothèque, Le Livre de Poche, Paris,1997 RTBF Liège et Blattchen, E., Emission Noms de dieux, Invité : I. Prigogine, diffusée le 23 novembre 1997 Schut z Bernard , Gravity from the ground up, an introduction guide to gravity and general relativity, Cambridge University Press, 2003 Science et vie, N°63 de juillet 1922 , Les théories d’Einstein et leur vérification expérimenta-les, par Léon Brillouin Science et Vie d’avr il 1927 Les progrès de la Physique allemande dans les dernières années, par Marcel Boll Science et Avenir -- Hors sér ie-- N°99 --Décembre 1994--Janvier 1995-- Comprendre la ma-tière, Science et Avenir -Hors sér ie-N°105-mars 1996-Comprendre l’infini Science et vie Junior N°24 d’avril 1996 , Einstein, vous allez enfin comprendre Science et Vie, N°936 de sept embre 1995 , 50 ans, après Einstein, un savant élucide les mystères de l’univers Science et Vie, N°970 de juillet 1998 - Pourquoi y a-t-il quelque chose plutôt que rien ? Science et Vie, N°978 de mars 1999, Einstein et le Big Bang Science et Vie , Tr imestriel N°189 , décembre 1994- Le Big Bang en questions Science et Vie, Trimestriel N°205, décembre 1998- L’univers de la gravitation Sm ith M ike , Bombe atomique Bohr-Heisenberg , l’échec de Copenhague, RTBF Spektr um der Wissenschaft, 1/2005, Biographie, Das neue Weltbild der Physik, Einstein St öcker H., Jungt F ., Guillaume G., Toute la physique, Dunod, 1999j Sugimoto, Kenji., Albert Einstein, Bibliographie illustrée, Belin, traduct. française, 1990 Teilhard de Chardin, P., Le Phénomène Humain, Editions du Seuil, Paris, 1955 Taylor E.F. & Wheeler J.A., Spacetime Physics: Introduction to Special Relativity, W.H.Freeman, San Francisco, USA,1992 Thorne Kip S.., Trous noirs et distorsions du temps, ‘L’héritage sulfureux d’Einstein), Flammarion, Paris, 1997 Van de Vorst Albert., Introduction à la Physique, De Boeck Université Wolff Fr ançoise, Einstein, un mythe, un homme, textes d’Einstein lus par Jean -Marie Dusso-lier, Coproduction La Sept ARTE-Unité THEMA et ON LINE Productions, 1997 Wünschm ann Andreas , E=mc2 , Eine Formel verändert das physikalische Weltbild, Studien-Verlag Wünszchmann,Kirchheimbolanden, 2003

213

Photos credits Am erican Institut e of Physics Niels Bohr in front of an audience.

Heisenberg in front of an audience.

Einstein with Onnes in Leiden Einstein and Ehrenfest drawn by Maryke OnnesP. Am erican Jewish Archives, Cincinnat i Einstein on a bike.

Albert Einst ein Gesellschaft, Berne: The house occupied by Einstein in Berne.

An excerpt from a Bern newspaper where Einstein offers lessons in mathematics and physics.

Ar chiv des verfassers Archiv des verfassers, Thalwil near Zurich, May 28, 1899,

Einstein and his comrades whose Marcel Grossmann.

Benjamin Couprie, Brussels , Solvay Institute Brussels: The Solvay Council of 1911.

The Solvay Council of 1927 (colorized)

Einstein Archives, New - York:Lotte Jacobi, Deer ing : With Tagore: Einstein Archives, New York: Lotte Jacobi, Deering; Einstein in 1930

Francis Baldewyns, personal photo s:

Ulm Town Hall and the banks of the Danube.

The entrance to the Jewish cemetery in Prague and the Jewish graves.

Einstein subjected to gravitation during braking of the elevator.

Einstein in weightlessness during the free fall of an elevator.

Einstein observes the computer with a gravitational lens: "The Einstein Cross" My meeting with Einstein during the exhibition Einstein, the other look Einstein Interview - Bohr Einstein in conversation with Bohr during a private meeting ...

2007 photos at the University of Copenhagen and the Bohr Institute Birthplace of Niels Bohr 2007 photos on the meeting place of the Solvay Council The former district of the Nazi ministries and the museum "Topography of Terror" Heisenberg's greeting at the entrance of Athénée de Huy Ella, little girl of the author of this book, imitating Einstein.

Tie with special relativity formulas and Einstein's photo

Jewish Nat ional and University Library, Jér usalem : Lotte, Einstein and his American colleagues, including Hubble Jacobi, Deer in g : Einstein at Princeton in 1938 or 1939: Moos and Partner Archi ve, Munich: The birthplace of Einstein in Ulm. The house where Einstein lived on the outskirts of Prague.

Albert Einstein in New York in 1921.

With Albert I, the King of the Belgians.

Helen Dukas, Albert Einstein and his beautiful daughter Margot taking the oath of American citizenship.

Einstein and Bohr photographed by Paul Ehrenfest.

RTBF Liège.

Francis Baldewyns, Paul Rostenne and Ilya Prigogine, in 1997, after the recording of the program Names of Gods commemorating the twentieth anniversary of his Nobel Prize.

Christian de Duve, during the show Names of gods.

Ilya Prigogine while recording the program Names of Gods.

Science Photo Libr ary Ilya Prigogine, at the time when he received the Nobel Prize.

Movie Mike Smith, Bohr Atomic Bomb - Heisenberg, the failure of Cope n-hague, RTBF Last interview of Heisenberg Françoise Wolff film, Einstein, a myth, a man.

Einstein's brain The man who thought he was Einstein's son 214

Afterword Since 1957, when I had this crazy idea to ask my parents a bust of Einstein, a lot of water has flowed under the bridges of Liège, Professor of Mathematics and Science, I sincerely hope to have challenged younger generations by suggesting them a more judicious positioning in our Universe full of mysteries, in the humble, respectful and passionate manner of archaeologists.

Not only, I did study physics at the university level, but I taught it to a generation of students who did not fail to thank me despite the rigour I imposed on them.

On a personal level, I can say, as Einstein said: "Realizing that behind all what we can discover, there is something that escapes our understanding, and whose beauty and sublimity can only reach us indirectly, is the feeling of sacred, and in that sense, I can say I am religious."

However, I remember that in 2005, some sorrowful spirits had refused to present my book in the valves of the university, seeing that the word "God" was in my title.

I could explain to them that it was not the God of the Bible, but the God "Big Bang" I present to you "in French" the article of the newspaper La Meuse which appeared after this refusal.

The title “No Archaeologist of God” At the Liège Science Museum, it is out of question of a book with "God" in the title.

Let's laugh because it's amazing ...

215 215

Afterword

As a final, here are some more photographs of my playful approach with Einstein, which also confirms that I remained a great child, respectful of this great man who has deciphered a lot of mysteries of the world.

216

Table of Contents Foreword First chapter. The profession of faith of Einstein Chapter two. Illustrated biography of Albert Einstein Chapter three. The main theoretical discoveries 3.1. The constant of Planck 3.2. Photoelectricity 3.3. Special relativity and the speed of light 3.4. The relativity of simultaneity 3.5. The transformations of Lorentz 3.6. The behavior of rulers and clocks moving.

3.7. The theory of relativity applied to the mass 3.8. General relativity and the Newtonian fortress 3.8. bis. Basic problems relating to the Principle of equivalence 3.9. The spacetime 3.10. A paradox from Paul Ehrenfest, Austrian physicist, a friend of Einstein, 3.11. Einstein's answer to Ehrenfest's paradox 3.12. The contribution of Friedmann and Hubble 3.13. Einstein calls on Marcel Grossmann, his mathematician friend 3.14. Putting into equation the dynamics of the universe (Friedmann's equations) 3.15. Essay of real representation of the universe. Non-Euclidean geometry 3.16. Revealing the light Chapter four. Experimental evidence 4.1. Checking the mass variation with speed 4.2. The mass defect of atomic nuclei 4.3. Evidence of relativity and gravitation. "General Relativity" 4.4. Gravitational shift of Frequencies following the attraction of light 4.5. Checking the photoelectric effect by Millikan 4.6. The discovery of cosmic radiation in 1965 and the Big Bang.

4.7. Checking the Twin Paradox 4.8. Experimental checking of time dilation 4.9. Experimental checking of gravitational waves Chapter five. Some quotes from Einstein Chapter six. When the devil digs in God ...

6.1. Bohr and Heisenberg in friendly collaboration 6.2. The Bohr atom 6.3. Uncertainty relations of Heisenberg 6.4. Man and places at the source of the Copenhagen Spirit.

6.5. The Solvay Council of 1927 6.6. Max Planck, the patriarch 6.7. The wave mechanics of Louis de Broglie 6.8. Quantum mechanics of teachers and students from Gรถttingen 6.9. Nobel student before teacher 6.10. Wolfgang Pauli and his exclusionary principle 6.11. Paul Dirac, a conceptual genius 6.12. Niels Bohr and Werner Heisenberg face apocalypse 6.13. Conflicts and fights between physicists Chapter Seven: The Einstein Myth Chapter Eight: The Gods Need Men and Men need God Chapter nine: Man, the finality of creation, or product of chance and of necessity?

Conclusion Glossary Biography of archaeologists of God Mathematical Annex Explanation 1. The photoelectric effect 217

5 17 22 48 48 48 50 51 52 56 61 63 70 71 72 73 73 77 79 81 86 89 89 89 90 93 94 95 95 97 99 102 103 103 108 111 113 122 126 127 128 129 130 131 132 142 146 156 168 182 184 186 189 189

Table of Contents Explanation 2. The paradox of twins Explanation 3. Example of conversion between mass and energy Explanation 4. Demonstration of the constancy of the speed of light spread Explanation 5. What is the spacetime of Poincare-Minkowski? Anecdotal approach Explanation 6. Existence of an absolute distance Explanation 7. Mathematical reminders for understanding of the Minkowski diagram Explanation 8. What is spacetime of Poincaré-Minkowski in 3D? Explanation 9. Einstein's equations of general relativity Explanation 10. Applications of De Broglie's Law on wave mechanics Explanation 11. Schrödinger's Law and the Cat Paradox both dead and alive.

Explanation 12. Schrödinger's law independent of time Explanation 12bis. The Schrödinger law depends on time Explanation 12ter. Another demonstration of the Schrödinger law Explanation 13. Quantum numbers and the exclusion of Pauli Explanation 14. Using the four quantum numbers Explanation 15. Explanation of the Dirac Equation and Existence of antimatter Bibliography Photo Credits Afterword Table of Contents

218

189 190 190 191 192 194 197 198 201 201 203 204 206 207 210 211 212 214 215 217

Niels, le monde n’est thepar world pasNiels, réglé le ishanot settled by sard. Dieu ne joue pas aux dés.chance

Qu’en savez-vous, What do you know Albert ?

Ne dites Albert? Do not tell pas àGod Dieu ce qu’il what to do. doit faire.

Albert, pensez Albert, vous do you really vraiment que Dieu ne think God does not joue pas aux dés ! play dice?

Of course, Niels,

Bien sûr, Niels, tôt sooner or later we ou tard nous le renwill meet him and He contrerons et il will confirm it to us nous le confirmera

219