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What tells to us quantum physics on the World

The quantum physics is presented here by the introduction of 2 fundamental notions: the notion of system, that is of a set of not separable particles and the notion of measure that is of affectation of a value in a proposition on the system.

One of the paradoxical aspects of the model of the quantum physics is the impossibility to cut absolutely on the certainty of a proposition (tangled states). This leads to exceed the classic logic appropriate for the relativity of cause and effect and to envisage the paradoxical results of crossed effects on distant particles (EPR experiences) as a causal but active effect of a way crossed on all the constituents of an indivisible system.

The description will insist on the revolution that the notion of a granularity represents for the vision of the World which far from being constant depends on the considered system and thus the conditions of its genesis, what has important consequences on the link between the macroscopic universe and all the tiny systems.

The notion of non-existent fate in quantum physics also appears as a consequence of an effect of dissynchronization between different systems.

Finally propositions of experiences will be expressed as of new tracks of reflections.
 
 

1 Measure, particle and granularity *

2 Principle of the quantum physics *

2.1 The impossibility of the certainty of the truth *

2.2 Mathematical representation of a system in quantum physics *

3 Applications *

3.1 Photons with linear polarization *

3.2 Experience EPR *

4 The problem of the chaos *

Annex Questions and proposition of experiences *
 

1 Measure, particle and granularity

The quantum mechanics well report the stability of the matter, for example phenomena of spreading of loads on the electronic orbits of molecules, because it describes definable states globally for a not distinguishable and correlated system of particles. We speak about tangled states because the system of particle is described before the measure as a network of potentialities where all the combinations of states are possible. But the card is not
the territory; it is about a description, not about a concrete reality; there is no network of superimposed states which propagate.
Also, particles with their unambiguous properties do not exist except the act of measure on the system (or of interaction with a system influenced by the state of the system).

The system is described as a linear superimposing of correlated, tangled states. The act of measure allocates a value to a proposition on the state of the system. The measure is an interaction where becomes a reality collectively the properties of the system object and of the instrument; there is no distinction between the particle object and the particle instrument, quite two objects of the interaction implied by the measure. The measure does not create the particle outside of the act of measure or does not select it from a potential list. The particle is the influence, the interaction of the system object on the instrument. The particle does not propagate, it reveals a state. There is thus no reduction of a package of waves as the term is often used or realization of a potential. The particle is a particular, local organization. In certain models we allocate it an entropy because it is an information.

What propagates it is a system, that is a capacity to become a reality, we speak about wave of probability of presence.
Between two interactions there is distribution of the excitement of an environment empty of particles. The paradox is that to reveal this excitement it is necessary to operate a measure. The influence of the environment on the instrument creates particles.

The space, that is the minimum state of energy, is incited by the distribution of these systems. The environment is a field, it means a space to which we can allocate completely a level of excitement, linear reminder of excitements, every excitement is connected with a system which propagates; we speak about superimposing of fields and there is no fundamental distinction between fields connected with particles of matter and fields connected with vector particles of forces of interaction.
The disturbances bound to the particles of matter are coupled with disturbances bound to the particles of forces. The interaction between two disturbances absorbs or emits a disturbance: The field of electromagnetic force can lead disturbances, " waves of matter " (which will show themselves as the emission of two particles of matter and anti-matter and the disturbances of two particles of matter can lead particles of
forces (2 electrons exchange photons), also fields of force can be charged themselves that is sensitive to the disturbances of the fields of force (as gluons uniting the quarks of the nucleus which occur and are exchanged some the others strengthening the force with the distance and assuring the confinement of quarks).

Now in the system, the information is global and not divisible. Measure, it is to interact, to concretize a particle with an unambiguous state but it is not possible to allocate a value to a proposition to a state of the system and thus to allocate the property to a particle, without that the properties of the whole system are globally affected: any measure on the system aiming at revealing its properties in another place is irreparably and at once affected by the first measure. The distance between the correlated particles has no reality; particles are not individualisables. There is a distance only between these particles that with regard to referential one external. For example a measure which allocates a value to an event (for example the spin of an electron) affects globally the system; we speak of not separability.

The system of measurement can be macroscopic and described thus by the classic physics but in the general case, it is the interaction of 2 microscopic systems which leads the properties of 2 systems under a shape interpreted as corpuscles.

It is necessary to agree to have no appropriate image. What shocks us fundamentally it is that we try to affect a level of granularity constant in any experience. Let us consider the case where a function of wave describes a
system which in an experience becomes a reality as a single electron, free of any link with an atom; the unity
reached by the measure appears to be the electron. But in another experience we cannot come down under the level of a system which appears as a set of not separable electrons.

Why have we unitarian systems appearing as localized particles and other not divisible systems?

What says to us the quantum physics on the World, it is that the level of granularité, that is the level where we can affect values
defined in a proposition on a state, depends on conditions of genesis of the studied system. If the system is constituted by particles correlated at the time of their genesis, they  will exist until the destruction of the system
by its absorption. The conversion of an energy in a system of coupled particles is the equivalent of a mini Big-Bang: we have a microuniverse which during the measure becomes a reality as a system in n not separable particles. The measure constitutes a determination of the system by the affectation of a value in a proposition on the state of the system but between two measures it is not possible to affect a value.

When the system is that is absorbed reconverted to energy, the correlation is lost.

For that reason the initial particles stemming from the Big-Bang were largely absorbed (in what proportion?) and lost their correlation. The universe macrocosm is a succession of microcosm. The limitation of the rate of the information would characterize states not correlated between 2 microcosms because the distance would exist only for 2 different systems.

Let us consider the following model. Particles are created from the state incited by the space. A zone of dimension R planck (minimal dimension of 10-35 m imposed by the relation of indetermination of Heisenberg where the dispersal of speeds is maximal because equal in c), this sphere enters intrinsically expanding. Its properties depend on the state of excitement. When the zone reaches a critical length said about Compton, characteristic of the mass of particles, these are produced. The energy is connected with the distance through the relations of indetermination.

By considering the relativist equation connecting the energy with the impulse and with the mass, we deduct a celerity equal to c. We deduct that from it a zone of size R~10-35 m is going to infer a propagation extending at the speed of light; for that reason this speed does not vary; the electromagnetic law is deductible from the expansion of occluded space.

Within a microcosm, there is no exchange of information because the values of probability do not allow to privilege two states different from the system.

Between 2 microcosms, it required of re synchronization there of times so that is made the exchange of information. Can we say that there is not a distance within the microcosm? All the particles of the same microcosm would thus possess all the same specific time.

Noted: the quantum mechanics constitute a system between 2 measures as a network of potentialities; there are thus many more states than in the classic mechanics; the system can contain a much more high symmetry.
So a spherical symmetry in classic physics requires the immobility. In quantum mechanics it always
remains a state of movement but the system seen as the meeting of all the potential states preserves its spherical symmetry.
 
 

2 Principle of the quantum physics

2.1 The impossibility of the certainty of the truth

The quantum physics specifies systems which are the objects of the physics.

To this system is associated by the contingent variables of types continuum (the position), discrete (the energy) or boolean (the truth of a proposition or an eventuality, for example the centre of gravity is included in a region determined).

In classic physics, the specification of a system is independent from the other systems. What gives a value
true / false to an eventuality.

In quantum physics the truth and the false are not separable: the eventualities are objectively defined.

We call a pure state the maximal specification of a system. Other cases will call mixed states.

If the S state where the eventuality is indefinite is subjected to a procedure P in the term of which an eventuality is defined, the result is not determined by the state S nor by that of the other states of the other systems occurring in the procedure: the result depends on an objective fate. It is not about ignorance as in statistical mechanics.

There is a probability to find the eventuality E true or false, probability which depends of E and of S.

The results of the measures of E on systems in the state S aim towards the calculated probability.

The value of E is not characterized by frequencies outside the measure because S would not be a maximal specification.

To attribute a value defined in an eventuality is usually called " to update a potential ".

A quantum state is a field of potentialities characterized by the probability of all its eventualities, probability which we verify by
the realization of its potentialities.

In classic physics, the eventualities 1 and 2 are separable.

In quantum physics, 1 and 2 separately can be indefinite and {1+2} defined because in the system {1+2}
the potentialities of 1 and 2 are thus it exist correlated  couples of eventualities E1 on 1 and E2 on 2 who are collectively updated.
 
 

2.2 Mathematical representation of a system in quantum physics

- Every state is représentable by a unitarian vector of a space vectoriel complex

     For the defined eventualities, the eventuality is true in a state S of the system, the system being represented by a vector of the corresponding vectorial space. If the system is represented by a vector of the orthogonal space vectoriel, the eventuality is false.

     V being a representing vector of S, the vectoriel space E representing the eventuality e then Probability = (projection V on E) ².

As a consequence, there is a principle of superimposing according to which there is an infinity of vector u = c1u1 + c2u2 with u1 and u2 orthogonal and c1 ² + c2 ² =1

U representing an intermediate state between u1, state where the eventuality is true, and u2, state where it is false.

C1 ² = probability (true eventuality after realization)

C2 ² = probability (false eventuality after realization)

To the system 1 is associated the vectoriel space U1

To the system 2 is associated the vectoriel space U2

{1+2} is associated to the vectorial space U1*U2 constituted by  y =SiS j ci,j ui*uj

Being u1, u2 include in U1

Being v1, v2 include in U2

u1*v1 the state characterized by the system 1 in u1 and the system 2 in v1

u2*v2 the state characterized by the system 1 in u2 and the system 2 in v2

Let us suppose that u1, u2 of length unity and orthogonal between them

Let us suppose that v1, v2 of length unity and orthogonal between them

Then there  y =1/Ö2 * (u1*v1+u2*v2) has a length unity

Neither 1, nor 2 are defined if {1+2} is in the state ?

States are said tangled because:

E1 Eventuality of 1 true in u1

E2 Eventuality of 2 true in v1

If e1 and e2 updated then probability (e1=true e2=true) = ½ and prob (e1=false e2=false) = ½

Probability (e1=true e2=false) = probability (e1=false e2=true) 0

Corollary 1 and 2 are  separated  thus the correlated realization  of the potentialities of 1 and 2 is not a local process

In a system in an environment not affected by the system, u is a state t=0 then it exist V ( t ) a linear operator such as V ( t ) ( u) is the state of the system u there t

|| V ( t ) ( u ) || = || u ||

Consequence if in first estimation, the environment does not react to {1+2} then the last principle can be applied to follow the evolution of 1.

So that a measure is made, the environment has to react differently if the realization produces e1 really or if e1 is false.

But the system 1 and the measuring device 2 can form a not reagent environment. The principle is then applied to {1+2}. It is the formalization of the problem of the coupling of the object and the measure

The principle is applied to the minimal compound system in the environment which does not depend on the realization of the system.

Noted: it is about a not causal sphere.
 
 

3 Applications

3.1 Photons with linear polarization

The vectoriel space associated to the polarization of a photon is a space in 2 dimensions V which we can express as a combination c1Ux +c2Uy with orthogonal Ux and Uy.

If a bundle of photons propagates according to an axis z is prepared in a state of polarization according to an axis x and crosses a polarisateur the optical axis of which is x ' which forms an angle A with x then the photons which appear are in a state ux ' and their probability equal to cos²A. This probability of passage corresponds to an act of measure and must be thus treated as a realization of an eventuality of passage. This probability is given by the square of the length of the projection of ux onto the sub-space Ex ' corresponding to the eventuality ex ' of passage.

Let us consider then 2 experiences.

In the first one 2 successive sheets have for axis of polarization x and y

Photons are going all to cross the first sheet and anybody are going to cross the second one.

In the second experience the sheet of axis x ' is interposed

Photons are thus going to spend the first one with a probability equal to cos²A and it will be left by it a probability equal to  cos²A sin²A  after the  second one.

The quantum formalism allows to restore the result of this experience. In determinist physics which claims that the passage or the absence of passage through the filter is knowable by a specification of the photon more complete than in quantum mechanics requires to think that the passage of the photon already crossed by the filter x guess the particular state of the new filter x ' and what this information modifies its state to cross through x '. It is about theory which claims to be more spread than the quantum mechanics, the theory with hidden variables.
But the experience EPR seems demonstrated that there are no theories with acceptable hidden variables which
maintain the notion of village of a phenomenon.
 
 

3.2 Experience EPR

Fundamental theorem (corollary of a theorem of A.Gleason found in a simpler way by J.Bell, S.Kochen and E.Specker):

If the dimension of a vectoriel space V is superior to 2 there is no function m assigning to any sub-space E of V a
number 0 or 1 such as m (V)= 1 and m (E) = M (E1) +m (E2) with orthogonal E1 and E2 and E the smallest sub-space containing them both.

In other words in a space in three dimensions disjunction of two exclusive mutual eventualities is not strictly possible.

We thus see that the formal structure of the quantum mechanics is inseparable of the notion where in every state certain eventualities are defined.

J.Bell demonstrated that the theories with hidden variables implied a disparity.

We have an experience with 2 well separated parts 1 and 2.

The test on 1 concerns the parameter X, the test on 2 concerns the parameter Y.

If  x and x ' are 2 possible values of the parameter X and if y and y' are 2 possible values of the parameter Y.

The theory of the hidden variables supposes the séparabilité of 1 and 2 where from p (x, y) =p (x) p (y)

Where from a general disparity -1 < = p (x ', y') +p (x ', y) +p (x, y')-p (x, y)-p (x)-p (y) =< 0

Then the disparity is violated in certain experiences.

For example the emission of a pair of photons emitted in waterfall and having a total angular moment
equal to zero.

The state of polarization is given by

 y =1/Ö2 * (ux (1) *ux (2) + uy (1) *uy (2)).

If the axes of polarisateurs in 1 and 2 are aligned , two possibilities: either 2 photons cross the polarizers , either none of them  cross the polarizers.

The almost determining experience was that of Aspect, Dalibard and Roger (Orsay 1982); the choice of the values of  X and of Y is independently realized one of the other one there 1 and 2 by electronic devices during the time of distribution of photons towards detectors.

The term is almost determining is useful because the efficiency of photomultipliers is very weak and alone a part of the events is enregistrable.

For (x,y, x ',y ') = (45 °, 0 °, 22,5 °, 67,5 °), the result of the disparity is 0,207 in perfect agreement of the predictions of the quantum mechanics and in violation with the theories supposing the separability. There is no more independence.

Now Einstein, Podolsky, Rosen asserted that the physics had to be such as there is an operation allowing to determine a value of the truth of an eventuality on 1 without perturbing the eventuality on 2.

The results of the experiences contradict this presupposition.

In fact the realization of the potentiality on a photon which determines in a unambiguous way the realization of the potentiality on the photon 2 is a causal process but of another order than that envisaged by the restricted relativity. It there mutual influence but according to the referential we shall indicate that the one is the cause of the other one and conversely.

There is no analogy in classic logic because the notion of potentiality actualisable widened the notion of events.

In any case these phenomena not violent not the principle of not transmission of the information more quickly than the rate of the light because the result of the measure is statistically not predictable. If the choice of the experimenter to direct the analyzer is x instead of x ', the observer in 2 not knowing which is the choice but knowing 2 possible choices then in half of the cases the choice selected Ux ( 1 ) *Ux (2) and in the other half Uy ( 1 ) *Uy (2). If the observer in 2 chooses to test Ex ( 2 ) (passage of the photon 2 through the polarizer directed according to x), it will find that Ex (2) is true in half of the cases. The situation is symmetric if the experimenter in 1 selects the polarizer x '.

In conclusion, the quantum probability are perfectly to adapt to prevent from betting on the not local phenomenas to send messages without delay of propagation.

The quantum mechanics and the restricted relativity, although conceptually not compatible, are it in their effects and forecasts.

But the general relativity seems the good abstract frame, the restricted relativity appearing as a borderline case but nobody defined a compatible frame for the quantum mechanics and the general relativity.
 
 

Annexe A The problem of the chaos

The equations of the quantum physics do not seem to bring in the fate and thus to introduce the chaos. How can the chaos appear in classic physics if this one is the application of the quantum physics in the case of the big
numbers?

The answer could be in the necessity of synchronizing clocks to exchange of the information. N systems are not synchronized; a system cannot thus remain in the same state and the fate intervenes as a factorial function of the number of the systems, aiming towards the exponential for the big numbers.

Annex B Questions and proposition of experiences

Question: is the system protected after the measure or is it destroyed? We can imagine that a particle is made by
anti-matter and be destroyed by colliding a particle of matter. How to describe a system partially reconverted to energy? Does it become again a network of partial potential?

Question: is there experiences allowing to measure a particle in the absorbent, the other particles staying
free? Can a coupled system be partially uncoupled?

Question: if there is no distance between 2 correlated particles, they are subjected to the same constraints of evolutions in the timespace. In other words the differences of drainages of time are valid only for 2 not correlated particles?

The measure of a particle affects all the system That is that an experimenter is going to receive information about all the particles of the system. The measure affects all the particles collectively.

Experience

Phase 1

Measure A and time= ta of the particle 1 Measure B and tb of the particle 2
 Confrontation of the results when t=t " in A and when t=t " b in B results: there is correlation.

Phase 2

Measure A and t=ta of the particle 1 Measure B and tb of the particle 2.

Measure A and t=t'a  of the particle 1 Measure B and t' b of the particle 2

Confrontation of the results when t= t "a in A and when t=t"b in B: is the measure when t=t'a et when t=t'b influence  the result found when t=t " and t= t "b?.

Can the double measure A affect the information which returns of B?
 
 

Sources

The big debate of the quantum physics

The geometrical model of the physics

The new physics