MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRETATION

MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRETATION

Vasil Penchev • Bulgarian Academy of Sciences: Institute for the Study of Societies and Knowledge (Institute for Philosophical Research): Dept. of Logical Systems and Models • Vasildinev@gmail.com Modal Metaphysics: Issues of the (Im)Possible IV ⦁ Bratislava, Slovakia (Klemensova 19) ⦁ August 30-51, 2016 ⦁

More than impossible? • What might mean “more than impossibleâ€??

For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⌠• Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability Furthermore, the same effect is interpretable as re-ordering and thus as a certain quantity of information ⌠• One can write a very intriguing equation: .

đ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š = đ?‘‡đ?‘‡đ?‘‡đ?‘‡đ?‘‡ đ?‘†đ?‘†đ?‘†đ?‘†đ?‘†đ?‘†đ?‘†đ?‘† đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸đ??¸ = đ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??ź

Information Relation of probability (distributions)

(Re-ordering) Relation of orderings

Synchronic viewpoint

Diachronic viewpoint

Definition in Shannon

Definition in Kolmogorov

The space-time interpretation of quantum information

The concept of curved space-time

My presentation now

The concept of physical force

More than impossible?

Of course, quantum mechanics • Quantum mechanics introduces those fluctuations, the physical actions of which are commensurable with the Plank constant They happen by themselves without any cause even in principle ⦁ • Those causeless changes are both instable and extremely improbable in the world perceived by our senses immediately for the physical actions in our world are much, much bigger than the Plank constant

The problem: NEGATIVE AND COMPLEX PROBABILITY LINKED TO FORCES IN SPECIAL AND GENERAL RELATIVITY FAQ: What is the intrigue?

That cherished bridge between quantum mechanics and general relativity (including special one, or more exactly special relativity including general one) built by stones of quantum information How or how far?

Absolutely, for complex probability implies quantum information and thus quantum mechanics

Kinematics for dynamics • Meaning that negative and complex probabilities which have been already linked to physical forces in quantum mechanics valid in the Plank scale, one should research that way for them to be introduced in special and general relativity, which should be valid in both macroscopic and microscopic (Planck) scale This implies one to use only the kinematic formulation neglecting the dynamical one for the latter involves mass and energy right distinguishing the scales from each other practically as the distances are unified as macroscopic according to the real apparatuses for quantum phenomena âŚ

‘Reference frame’ as the key to kinematics • Particularly, ‘force’ is defined per a unit of mass (energy), and therefore equated to acceleration after kinematic consideration ‘Reference frame’ is the key concept as it is properly kinematic ⦁ • Still one restriction is representability in terms of quantum information, and more especially, by the concept of qubit One needs it for the consistency and coherence of the considerations in quantum mechanics (and information) and both special and general relativity ⦁

What a qubit is: • A qubit is defined as đ?›źđ?›ź 0 + đ?›˝đ?›˝|1â&#x;Š, where đ?›źđ?›ź and đ?›˝đ?›˝ are two complex numbers so that đ?›źđ?›ź 2 + đ?›˝đ?›˝ 2 = 1, and 0 , |1â&#x;Š are two orthogonal subspaces of the complex Hilbert space (abbreviated as “cHsâ€? further) For any two successive axes (đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–đ?‘–đ?‘– , đ?‘’đ?‘’ đ?‘–đ?‘– đ?‘›đ?‘›+1 đ?œ”đ?œ” ) of cHs can be interpreted as those 0 , |1â&#x;Š, cHs or any point in it can be represented as a series of qubits (đ?‘„đ?‘„đ?‘›đ?‘› ), correspondingly “emptyâ€? or “fulfilledâ€? by the values đ?›źđ?›źđ?‘›đ?‘› , đ?›˝đ?›˝đ?‘›đ?‘› ∈ đ?‘„đ?‘„đ?‘›đ?‘› âŚ

Qubit as space-time and thus kinematics • Any qubit is isomorphic to a unit ball in the usual 3D Euclidean space if two points are chosen in that ball: the one in the ball (including its surface, which is a unit sphere), and the other in the surface Thus, a qubit (being a 3D ball) means the same what Minkowski space is a certain moment of time ⦁ • That isomorphism is both elementary and crucial for our consideration Indeed, it guarantees the equivalent transfer of negative and complex probabilities between quantum mechanics (the former, “left side” of isomorphism) and both special and general relativity (the latter, “right side”) ⦁

1

β

Imβ Reβ

∅ = 2đ?‘?đ?‘?đ?‘?đ?‘?

1

1

0 �� 0 + �� 1

0 0

Îą

ImÎą

Minkowski space

ReÎą The past Imaginary subarea

A qubit as an inertial reference frame • Indeed, a qubit, already as a unit ball with two points “recordedâ€? in it, allows for another interpretation as an inertial reference frame đ?’“đ?’“đ?&#x;Žđ?&#x;Ž , đ?’—đ?’— : The point (vector) within the ball (đ?œśđ?œś = đ?›źđ?›źđ?‘Ľđ?‘Ľ , đ?›źđ?›źđ?‘Śđ?‘Ś , 0) corresponds to the zero of frame (đ?’“đ?’“đ?&#x;Žđ?&#x;Ž = đ?‘Ľđ?‘Ľ0 , đ?‘Śđ?‘Ś0 , đ?‘§đ?‘§0 ) and that on its surface (đ?œˇđ?œˇ = đ?›˝đ?›˝đ?‘Ľđ?‘Ľ , 0, đ?›˝đ?›˝đ?‘§đ?‘§ ) to the speed of inertial frame đ?’—đ?’— = đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ , đ?‘Łđ?‘Łđ?‘Śđ?‘Ś , đ?‘Łđ?‘Łđ?‘§đ?‘§ ⌠• The one-to-one mapping of the components of a qubit and those of an inertial frame is what is implied: đ?‘Ľđ?‘Ľ0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Ľđ?‘Ľ đ?‘Ąđ?‘Ą0 ; đ?‘Śđ?‘Ś0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Śđ?‘Ś đ?‘Ąđ?‘Ą0 ; đ?‘§đ?‘§0 = 0; đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘Ľđ?‘Ľ ; đ?‘Łđ?‘Łđ?‘Śđ?‘Ś = 0; đ?‘Łđ?‘Łđ?‘§đ?‘§ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘§đ?‘§

1

β

Imβ Reβ

1

1

0 �� 0 + �� 1

Relative velocity: đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘Ľđ?‘Ľ ; đ?‘Łđ?‘Łđ?‘Śđ?‘Ś = 0; đ?‘Łđ?‘Łđ?‘§đ?‘§ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘§đ?‘§ Îą

ImÎą

0

ReÎą

0

This means: complementarity interpreted as independence (orthogonality)

Space position in đ?‘Ąđ?‘Ą = đ?‘Ąđ?‘Ą0 : đ?‘Ľđ?‘Ľ0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Ľđ?‘Ľ đ?‘Ąđ?‘Ą0 ; đ?‘Śđ?‘Ś0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Śđ?‘Ś đ?‘Ąđ?‘Ą0 ; đ?‘§đ?‘§0 = 0

Thus complementarity refers to the system as a single 1 one whole

1

0 �� 0 + �� 1

Relative velocity: đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘Ľđ?‘Ľ ; đ?‘Łđ?‘Łđ?‘Śđ?‘Ś = 0; đ?‘Łđ?‘Łđ?‘§đ?‘§ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘§đ?‘§ Thus entanglement refers to the system as composed by subsystems 0

This means: complementarity interpreted as independence (orthogonality)

Space position in đ?‘Ąđ?‘Ą = đ?‘Ąđ?‘Ą0 : đ?‘Ľđ?‘Ľ0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Ľđ?‘Ľ đ?‘Ąđ?‘Ą0 ; đ?‘Śđ?‘Ś0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Śđ?‘Ś đ?‘Ąđ?‘Ą0 ; đ?‘§đ?‘§0 = 0

Thus complementarity refers to the system as a single 1 one whole

1

0 �� 0 + �� 1

Relative velocity: đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘Ľđ?‘Ľ ; đ?‘Łđ?‘Łđ?‘Śđ?‘Ś = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘Śđ?‘Ś ; đ?‘Łđ?‘Łđ?‘§đ?‘§ = đ?‘?đ?‘?đ?›˝đ?›˝đ?‘§đ?‘§ Thus entanglement refers to the system as composed by subsystems 0

This means: entanglement interpreted as dependence (nonorthogonality)

Space position in đ?‘Ąđ?‘Ą = đ?‘Ąđ?‘Ą0 : đ?‘Ľđ?‘Ľ0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Ľđ?‘Ľ đ?‘Ąđ?‘Ą0 ; đ?‘Śđ?‘Ś0 = đ?‘?đ?‘?đ?›źđ?›źđ?‘Śđ?‘Ś đ?‘Ąđ?‘Ą0 ; đ?‘§đ?‘§0 = 0

Another representation of a qubit as an inertial frame • Any qubit have three independent variables, e.g. đ?‘…đ?‘…đ?‘…đ?‘… đ?›źđ?›ź , đ??źđ??źđ??źđ??ź đ?‘Žđ?‘Ž , đ?‘…đ?‘…đ?‘…đ?‘…(đ?›˝đ?›˝), which can be interpreted e.g. as c. đ?‘…đ?‘…đ?‘…đ?‘… đ?›źđ?›ź = đ?‘Łđ?‘Łđ?‘Ľđ?‘Ľ , đ??źđ??źđ??źđ??ź đ?‘Žđ?‘Ž = đ?‘Łđ?‘Łđ?‘Śđ?‘Ś , đ?‘…đ?‘…đ?‘…đ?‘… đ?›˝đ?›˝ = đ?‘Łđ?‘Łđ?‘§đ?‘§ • Then two options appear as the initial position of the inertial reference frame: ďƒźđ?‘Ľđ?‘Ľ0 = đ?‘Śđ?‘Ś0 = đ?‘§đ?‘§đ?‘œđ?‘œ = 0 (accepted as a convention) An additional and complementary qubit is necessary to represent any initial position of the inertial reference frame at issue ⌠• Even more, the former and latter (this) representation can be unified as follows visualized:

Subsystems System In Lagrange

Independence

Dependence

1

0

�� 0 + �� 1

Position qubit

0 A bit A bit 0 1 01

Disjunction

In Hamilton Complementarity

Overlap

Speed qubit

1 �� 0 + �� 1

Position qubit

Entanglement

Subsystems System In Lagrange

Independence

Dependence

Ψ

Ψ Nonentangled A set of inertial RFs

Entangled A set of noninnertial RFs for đ?‘Łđ?‘Ł = đ?‘Łđ?‘Ł(đ?‘Ľđ?‘Ľ)

A bit A bit 0 1 01

Disjunction

In Hamilton

Ψposition Ψspeed Complementarity

Overlap

Interaction or potential force field in classical physics

Ψ speed Ψposition Entanglement

Subsystems System In Lagrange

In Hamilton

General relativity

Dependence

Ψ

A world line in the smoothly curved Entangled Minkowski space A set of noninnertial RF to pseudo-Riemannian for đ?‘Łđ?‘Ł = đ?‘Łđ?‘Ł(đ?‘Ľđ?‘Ľ) space Interaction or potential force A world field in line of classical physics position A world line of speed speed position Entanglement Minkowski space

Ψ

Ψ

The sense of the conventions • The convention "��0 = 0; ���� = 0" means that the qubit is correspondingly oriented according to the reference frame unambiguously Any nonzero rotation of the unit ball would define a different inertial frame ⌠• The parameter "��0 " is a conventionally chosen ordinary moment And thus a new and more than intriguing equation:

đ??´đ??´ đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„đ?‘„ = đ?‘Žđ?‘Žđ?‘Žđ?‘Ž đ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??ź đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘… đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š

A connection to kinematics • Further, the probability "đ?‘?đ?‘?đ?‘? associable with the inertial frame may be conventionally specified as "đ?‘?đ?‘? = đ?›źđ?›ź 2 " so that đ?›źđ?›ź corresponds to the module of wave function just as in the Max Born interpretation of it Indeed, then "đ?‘Łđ?‘Ł = đ?’—đ?’— = đ?›źđ?›ź " or as “kinematic momentumâ€? per a unit of mass (energy) might be the “lengthâ€? of an elementary permutation defined as above, and its change in time would represent acceleration as “kinematic forceâ€? ⌠ A bird’s eye view to the same:

đ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??źđ??ź = đ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒđ?‘ƒ đ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??śđ??ś = đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´đ??´ đ???đ???đ???đ??? = đ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??žđ??ž đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š: đ?‘°đ?‘° = ∆đ?‘ˇđ?‘ˇ = đ?’‚đ?’‚ = đ???đ???đ???đ???

The demarcation of general and special relativity • Further, the unity of ‘pure imaginary probability’ and ‘force’ as above allows of still one interpretation of the relation of special and general relativity The new interpretation is consistent to the standard one, but different from it ⌠• According to the latter, the demarcation line between special and general relativity is right the quantity of acceleration (đ?’‚đ?’‚) of the studied reference frames: zero in inertial reference frames (special relativity) and nonzero in noninertial reference (general relativity)

All you need is tachyon â&#x20AC;˘ According to the new interpretation, one should complement that distinction by the identification of any hypothetical superluminal inertial frame (đ?&#x2019;&#x201C;đ?&#x2019;&#x201C;đ?&#x;&#x17D;đ?&#x;&#x17D; , đ?&#x2019;&#x2014;đ?&#x2019;&#x2014;: đ?&#x2019;&#x2014;đ?&#x2019;&#x2014; = đ?&#x2018;Łđ?&#x2018;Ł > đ?&#x2018;?đ?&#x2018;?) with just one certain noninertial subluminal reference frame đ?&#x2019;&#x201C;đ?&#x2019;&#x201C;đ?&#x;&#x17D;đ?&#x;&#x17D; , đ?&#x2019;&#x2014;đ?&#x2019;&#x2014;, đ?&#x2019;&#x201A;đ?&#x2019;&#x201A;: đ?&#x2019;&#x2014;đ?&#x2019;&#x2014; = đ?&#x2018;Łđ?&#x2018;Ł < đ?&#x2018;?đ?&#x2018;?

The hypothetical particles with superluminal velocity were called â&#x20AC;&#x153;tachyonsâ&#x20AC;?. The new interpretation would add the identification of the tachyons as accelerated subluminal particles âŚ

Now: non-standard Standard General relativity interpretation interpretation Interpretation in Hamilton: Speed Interpretation in Lagrange: and position are two independent st derivative of Speed is the 1 variables: space-time is “straight”, position: space-time is smooth, but consists of two discrtely divided but curved: pseudo-Riemannian subareas: Minkowski space Both subareas of it are necessary, The real subarea of it is redundant, but but there are no accelerated RFs there are arbitrarily accelerated RFs That viewpoint implies “reThat viewpoint implies “forces” & “force orderings” as “forces” being fields“: gravitational field is the unified and mappings between universal background force field, then the two subareas

Now: non-standard Standard General relativity = interpretation interpretation quantum mechanics Interpretation in Hamilton: Speed Interpretation in Hamilton: the and position are two independent qubit Hilbert space is the normed nonstandard equivalent of variables: space-time is “straight”, Minkowski space: each of both but consists of two discretely divided identical subareas is transformed in any of both dual identical spaces subareas: Minkowski space Both subareas of it are necessary, Both dual spaces are necessary being but there are no accelerated RFs “complementary” to each other That viewpoint implies “reThe “forces” & “force fields“ are understood orderings” as “forces” being in an equivalent but opposed way (like in a mappings between “negative photo”): as symmetries and thus the two subareas conservations (what is not re-ordered)

Forces & Force fields

Asymmetries & Re-orderings Quantum mechanics

General relativity Symmetries & conservations Interactions

A new fundamental symmetry in cognition, which already was visualized on the previous slide:

That is the axis of The symmetry to the diagonal: what else is necessary to be transformed once general relativity is transformed in quantum mechanics

It implies the symmetry of general relativity and quantum mechanics

An observer of a tachyon â&#x20AC;˘ Indeed, special relativity identifies the pure imaginary values of speed with those of a reference frame moving with any superluminal relative velocity to an observer The term â&#x20AC;&#x153;superluminalâ&#x20AC;?, which means a real value ( đ?&#x2019;&#x2014;đ?&#x2019;&#x2014; = đ?&#x2018;Łđ?&#x2018;Ł > đ?&#x2018;?đ?&#x2018;?), refers to the relative speed of a hypothetical inertial reference frame to an observer in any usual, subluminal inertial reference frame ⌠ď&#x201A;§ One can identified the physically interpreted gap between the sub- and superluminal the mathematically interpreted one between the real and imaginary dimensions of the complex numbers

Minkowski space

No any difference!

You’re here!

The mathematical gap between real and imaginary numbers I’m an accelerated subluminal particle

I’m an angry tachyon!!!

The physical gap between tachyons and subluminal particles

The observer seeing both physically and mathematically • That observer should register pure imaginary values as to the velocities in the other, observed reference frame According to the generally accepted model of special relativity in Minkowski space, time is purely imaginary unlike distance, which is real ⦁ • This implies for speed to be pure imaginary as time, and acceleration to be real as distance The “scholia” is: one and the same gap is seen as that between different dimensions whether mathematical(ly) or physical(ly)⦁

Dimension 2

Dimension 2

Mathematically Dimension 1

Mathematically

Dimension 1

Physically

Superluminal velocity as subluminal acceleration â&#x20AC;˘ Then, an observer in an inertial subluminal reference frame might not distinguish pure imaginary values of velocity from accelerations in other reference frames for both superluminal velocity and acceleration mean one and the same though expressed in two different kinds of terms: correspondingly mathematical or physical Acceleration being a quantity different from velocity means a new dimension expressed physically ⌠â&#x20AC;˘ Superluminal velocity equated to pure imaginary velocity according to special relativity means a new dimension expressed mathematically, namely that of imaginary axis in relation to the real one

Gravitational field â&#x20AC;˘ Further, the accelerated inertial frames already according to general relativity implies a force field indistinguishable from the gravitational one in turn represented by curving Minkowski space to pseudo-Riemannian one Any tensor associable with a point in pseudo-Riemannian space is representable as the tensor product of vectors of Minkowski space as in its real as in its imaginary domain ⌠â&#x20AC;˘ Particularly, the tensor of curvature in a point transforms a vector to another between the imaginary and real domain

In terms of Minkowski space â&#x20AC;˘ Then, the formalism of general relativity is interpretable as presenting transformations within both domains of Minkowski space separately or together unlike that of special relativity restricted only to the one: that associated to the subluminal area usually identified with the imaginary cone (domain) â&#x20AC;˘ The pair of contra- and covariant 4-vectors as to pseudoRiemannian space is isomorphic to that of 4-vectors in each of the real and imaginary domain as to Minkowski space

THE PHILOSOPHICAL INTERPRETATION: THE UNITED NATURE OF FORCES AND PROBABILITIES IN: Ψ QUANTUM MECHANICS AND INFORMATION Ψ SPECIAL AND GENERAL RELATIVITY Ψ PROBABILITY AND INFORMATION THEORY

The forces in physics as probabilities in mathematics • The introduction of complex probabilities unifies forces and probabilities as two dimensions, whether mathematically or physically interpreted, of one and the same nature, that of complex probabilities Then both “more than impossible” and even the “squire root of that more than impossible” acquire a clear mathematical and physical meaning: • This means that minimal force able to reorder the entities in that more than impossible way, which is observeed

One and the same, universal observer • All physical forces (interactions) as in quantum mechanics (and therefore in the Standard model) and in special or general relativity are a particular case of the generalized probabilities and relative to the classical, one-dimensional probabilities Furthermore, the two dimensional (or complex) probabilities unify the subjective probabilities of the observer and the objective probabilities of the observed, and even the one dimension might be ascribed to the former, the other to the latter ⦁ • This allows of unifying further the concept of ‘observer’ in relativity and quantum mechanics.

Hmm, what ‘observer’ is: • The concept of observer whether in quantum mechanics or special & general relativity means two dimensions and thus a gap between them, which in modern Western philosophy are designated as “subject” and “object” One can even think of ‘observer’ as ‘bit’ or ‘qubit’ of information, the two or infinitely many alternatives for choice of which are interpreted or renamed philosophically as “subject” and “object”: disjunctive for the bit(s) of information or for Descartes’s dualism; and entangled for the qubit(s) information or for any philosophical doctrine investigating the interaction of subject and object⦁

The generalized observer as the philosophical â&#x20AC;&#x2DC;subjectâ&#x20AC;&#x2122; as â&#x20AC;&#x2DC;totalityâ&#x20AC;&#x2122; observing â&#x20AC;&#x2DC;objectâ&#x20AC;&#x2122; inside or outside of it â&#x20AC;&#x2DC;Totalityâ&#x20AC;&#x2122; in definition is what is the same both inside & outside: i.e. topologically, that mathematical object the internality of which coincides with its externality đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;

đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021; â&#x2030;?: đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013; đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x153; Information and its unit philosophically: TOTALITY â¤&#x201C;TIMEâ¤&#x201C; SUBJECT (ITS INTERNALITY) OBJECT (ITS EXTERNALITY)

One can conclude that (quantum) information is the quantity of totality

The observed “inside” and “outside” • Those quantum mechanics and special & general relativity, which are unified on the base of quantum information and qubits, should unify also their concepts of ‘observer’ The intention of observer is the invariance of both viewpoints, “outside” and “inside”, of the subjective and objective, and particularly, of subjective and objective probability as in quantum mechanics ⦁ • The following metaphor might visualize that invariance: the observer in special & general relativity observes the other reference frame “outside”, and that in quantum mechanics observes the quantum entity “inside” the apparatus That invariance implies that both should observer one and the same in the final analysis by means of quantum information ⦁

Generalized observer (from the viewpoint of quantum information) đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;đ?&#x2018;&#x2013;

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What is observed are smooth motions and discrete (deterministic) probability leaps Observer (from the view point of S & G relativity: reference frame)

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Generalized observer (from the viewpoint of quantum information) 𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛

𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

The concept of qubit as the normed superposition of two successive axes: 0 1 = 𝑒𝑒 𝑖𝑖𝑖𝑖𝜔𝜔 𝑒𝑒 𝑖𝑖(𝑛𝑛+1)𝜔𝜔

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

The concept of qubit as the unit ball with two its points chosen by a certain rule

𝑒𝑒𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞

0 1 : two its circles, one of which great, and the circle “0+1” is great as well

𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

The border melting in information â&#x20AC;˘ In that final analysis, the border between the physical theories of quantum mechanics and those of special and general relativity melts in probability and information theory turning out to underlie both That seeming maybe ridiculous viewpoint can be visualized so: â&#x20AC;˘ What is (i.e. [the] being) is (quantum) information. It implies the kinematic viewpoint as universal. In turn, it generates the dynamic viewpoint dividing the entities in the scale of energy (mass) and thus time. Further, the part of micro-energies in that scale is studied by quantum mechanic, and that of macro-energies by special and general relativity. Back to the kinematic viewpoint of (quantum) information both mean one and the same

The structure of the paper itself instead of conclusions

• Section 1 introduces the concept of complex (negative in particular) probability and its possible physical interpretation as both ‘force’ and ‘information’ • The prehistory and background (Section 2) include the generalization and utilization of ‘negative and complex probabilities’ in quantum mechanics and probability theory • The narrow purpose of the paper is to be introduced negative and complex probability relevant to special and general relativity and thus to events in our usual perceptive world rather than to microscopic or micro-energetic events studied by quantum mechanics (Section 3) • Section 4 compares their use in quantum mechanics and information, signal theory, probability theory, and in special and general relativity • Section 3 & 4 almost coincide with this presentation

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