Dear Sofia,

your question arises from the fact that you refer to the classical quantum mechanics, (QM), to interpret the meaning of measurement. In fact the incompleteness of this theory produces problems as you emphasize in your question. Really in QM a quantum system is identified with a vector of some Hilbert space, namely with a state. But a quantum system is not simply a vector of some Hilbert space ! In this way one cannot seriously say whether your statement 1) is right or wrong. Furthermore, in such a situation it is also impossible to understand whether your statement 2) is correct. In other words, QM is incomplete ! Its incompleteness is related to the absence of a suitable geometric structure that it is enough to encode a quantum system.

These problems are solved in my quantum gravity theory, where there exists a well defined geometric noncommutative structure encoding a quantum system (quantum PDE). With respect to this structure one can define observed quantum PDE and also quantum states. In other words a quantum system is not confused with a state, and with respect to different frames one can know with relation there is with respect different observers. In particular it is possible to know with relation there exists between quantum measurement and proper-time of some observer.

The so-called 'quantum indeterminism' has nothing to do with the statements 1) and 2), but it is connected with the non-commutative logic of the quantum world.

No-substructure can eliminate this 'quantum indeterminism' ...  that arises in the process of representation of the quantum world at the macroscopic level and that produce Heisenberg uncertainty relations.

My best regards,

Agostino

There is no shield to the broglian noise that swathes and beats every particle (atom for instance) from the others. The panoptic fantasy in microphysics remains a fantasy, and the cruel theorem of necessary variety from W.R. Ashby ruins all our ambitions to "know all the initial conditions".

The question of "free will" is quite outside of the microphysics, but belongs to the neurosciences. Someones militate for a universal entanglement (Bernard d'Espagnat, for instance) ==> Mektoub ! All is written !

However between any successful transactions, the broglian noise reshuffles the cards constantly and thermalizations occur quickly. So the universal entanglement is another fantasy.

Only the transfer itself of a photon, an electron, a neutrino and so on are deterministic, but which transaction will be effective is not.

Jacques,

Do you really intend to be understood? People are busy, don't have time for metaphors. So, please, stay with the physics when you want to say something. I sincerely tell you that I understood nothing from what you said.

About the question that I asked, I proved a theorem which seems to me broader than the free will theorem. But, the best test, is to see whether there can be a counter-example. I don't see a possible counter example, but from a whole community as RG, maybe somebody would come with a counter-example.

By the way, the free will seems to me unquestionable. The decision made by an experimenter cannot be known anywhere in the universe, and by no frame of coordinates. Assuming otherwise, the meaning is that we are robots, components of a huge machine a priori programmed. And who is the Great Universal Programmer? What would you say? . . . Well, if we deal with science, let's stay with the axioms of the science and nothing else.

Now, I repeat, if you have something to say, please be kind and put it clearly, without poetry.

Best regards,

Sofia

Dear Agostino,

(Hello! Good to "see" you! We didn't talk for a long time. Soon, a new year will begin. I hope that everything is well in your life.)

Now to physics:

I didn't say that I deal with non-relativistic QM.

You also say,

"Really in QM a quantum system is identified with a vector of some Hilbert space, namely with a state. But a quantum system is not simply a vector of some Hilbert space ! In this way one cannot seriously say whether your statement 1) is right or wrong."

You know that you can't define an object by saying what it is not. A quantum system is not many things.

Now, the relativity theory admits no preferred frame, s.t. a quantum system has to evolve in such a way that in whatever frame of coordinates, the wave-function according to that frame, be obeyed. We learnt the Dirac equation and it can provide a wave-function transforming correctly at a change of frame of coordinates. (By the way, the de Broglie - Bohm interpretation of QM is unable to satisfy this requirement, that interpretation definitely needs a preferred frame.)

My best regards and wishes,

Sofia

Dear Sofia,

thanks for your kind words that I reciprocate.

About your question:

 You claim:

'I didn't say that I deal with non-relativistic QM.'

and

'We learnt the Dirac equation and it can provide a wave-function transforming correctly at a change of frame of coordinates.'

Well ! But in your question you talk only of 'the wave-function of quantum systems.' Thus I cannot understand to which QM you refer ...

You know that classical field theory (Klein-Gordon PDEs, Dirac PDEs, Maxwell PDEs, Yang-Mills PDEs, Einstein PDEs and their interactions ...) cannot encode a quantum system ! On the other hand their quantization cannot encode quantum systems at high energy levels. Therefore, I cannot understand of which wave-function you are talking ... Whether you refer to quantum field theory, then my remark on the incompleteness of this theory cannot be contradicted !

Therefore ...

All the best,

Agostino

Dear Agostino,

I don't understand what you say. Why Dirac's equation from the relativistic QM "cannot encode a quantum system"? As to high energy levels, what is the problem with them? Can you be some clearer?

What I have in mind are entangled particles, i.e. entangled by spin, or by path variables, or e.m. polarization. Though from the point of view of the space-behavior these are free particles, no external fields act on them, except that they pass through beam-splitters (or polarization beam-splitters, Stern-Gerlach apparatuses, etc. as the case requires). So, the equation describing their evolution in space is simple, be it Dirac or other. All the issue is that in one frame of coordinates the particles pass simultaneously through splitters, and in another frame one or another particle from the entanglement is the first to pass. This fact imposes different forms and a different evolution of the wave-function of the system of particles.

I don't see at all that we need to write an equation for such a simple evolution, we can write directly how the wave-function evolves. 

You also say "incompleteness of theory ..." These are vague words, can you give a specific example which would contradict my claim?

With thanks in advance and best regards,

Sofia

Dear Sofia,

you ask:

'Why Dirac's equation from the relativistic QM "cannot encode a quantum system"? '

 In the classical Dirac equation, say (D), the wave function is a Clifford field or a spinor field. These are classic fields. In order (D) could encode a quantum system, one must quantize it. Usually in particle physics one quantizes (D) by means of the so-called covariant quantization. But this is equivalent to linearize (D) along a fixed classical solution. Since (D) is just a linear equation, one formally regains the same equation, but now the wave function represents a perturbation of the original classical solution (wave function) of (D). These linearized solutions satisfy to a non-commutative algebra. This approach works well at low energy levels. But cannot be accepted at high energy levels, since the quantum world cannot be considered in general a simple quantum fluctuation of the classical system.

Furthermore, whether one considers interactions between more particles, as it happens in entanglement phenomena, then the classical equation is not more linear. Therefore in such cases the linearized equation can be neither confused with the classical one ... 

The incompleteness of this theory is therefore related to the fact that it starts from a classical equation ! ...

My best regards,

Agostino

@Agostino Prástaro. What is your definition of "classical" ?

@Jacques Lavau

I refer to equations on fiber bundles whose sections are locally R-functions or C-functions, where R (resp. C) ia the algebra of real numbers (resp. complex numbers).

Dear Agostino,

May thanks for your wise advice, your warnings about theoretical difficulties are most well-come.

Therefore, for avoiding those difficulties, a proof on a simple case is desirable, and so I do. Especially (according to your warnings), no high energies and for rest-mass particles no velocities close to c.

So, let's admit that the entanglement is produced locally, as for instance the pair of down-conversion photons, or an electron & proton obtained from breaking a hydrogen atom. Afterwards the particles propagate in the free space - no fields, only beam-splitters (of types suitable to the particles).

 We have to do with (almost) plane waves, and the relativity enters into play in the variables of the phases (k, r, ω, t) and in the distances and time-order of the events (passing through beam-splitters and detections). Why do we need equations here?

Let me tell you more. I think that I have in hand a proof of my claim. It is simpler than the Conway and Kochen - by the way, examining very rigorously their proof I found some questionable points. The worth of such a proof is big, it tells us that at the quantum level, the nature is truly non-deterministic. That means, no type of hidden variables are allowed, local or nonlocal, governed by Bell-type probabilities (Kolmogorov), or working through amplitudes of probabilities as I showed in my article.

My thanks and kindest regards,

Sofia

Dear Sofia,

you ask:

'Why do we need equations here?'

When, one talks about a quantum system one cannot forget that this system never is truly free, but it is always constrained by some quantum dynamical equation that encodes such a system.

In the phenomenological scattering theory, adopted for many decades in High Energy Physics, one has usually considered that before and after the scattering, in the remote past, and in the remote future respectively, particles are free. (See the theory of scattering by means of S -matrix as introduced by Wheeler ...) This phenomenological approach has had many important successes in high energy physics in a long period where it was impossible have a suitable mathematics for noncommutative differential equations. (Let me add that the gold age of this Physics has been in 60's, when I was student in theoretical physics at the University of Torino. There was present an advanced research team in high energy physics (Regge, Fubini, Veneziano, ... )

However, nowadays thanks to my algebraic topology of quantum (super) PDEs, and my formulation of quantum gravity theory, it is not more necessary to adopt the 'free-particle' hypothesis in a scattering process. In other words when one says that a particle is free is some quantum system, encoded by an observed quantum differential equation, it means that this particle is described by a steady-state solution.

About:

'...it tells us that at the quantum level, the nature is truly non-deterministic. ...'

let me add that the quantum PDE encoding an observed quantum system, the so-called quantum indeterminism does not directly work. In fact at this level you can justify quantum entanglement by means of algebraic topologic properties of nonlinear quantum propagators. (In some other your question I have given to you an example of such a phenomena by means of nonlinear quantum propagators ...) Therefore, quantum entanglement is not related to the quantum-indeterminism !

Quantum indeterminism arises when one aims to represent some quantum-observable  (e.g. energy)  in some quantum state.

By conclusion the so-called 'quantum indeterminism' does not mean that God plays dice ..., but that when we observe a quantum system we necessarily get a statistical information on it. Of course this is related to the noncommutative geometric structure of the quantum world.

In other words, quantum nature is noncommutative !

Our interaction with the quantum nature is necessarily of statistical type !

Regards,

Agostino

Dear Agostino,

I still don't see why is there need for those non-commutative differential equations and super-PDEs. But, probably the fact that you don't know my proof leads you to think, for rigor, of the above equations. I have to stay and write down my proof.

By the way, all the proofs that I know and are based on entanglements, e.g. the Conway and Kochen, or Hardy's paradox, or the GHZ experiment, and different others, don't go to such equations. People write the wave-functions which describe the entanglements, and then follow the evolution of these wave-functions through beam-splitters.

(Anyway I am thankful for what I learn from you. I wonder whether in those 60's you were taught quantum field theory, or whether you learnt it later. I was a student a decade later, and we weren't taught QFT. It's a big gap in my knowledge, and I have no time now to complete the missing.  . . . I am impressed by your words "the gold age". Yes, there were in those time "giants" of the Physics, I also remember some, and the "electrifying" lectures in the over-crowded auditorium.)

You also say

"Therefore, quantum entanglement is not related to the quantum-indeterminism !"

I agree with you that entanglement and the quantum non-determinism are two different issues, but the rest of things that you say don't seem to me so clear

"when we observe a quantum system we necessarily get a statistical information ".

Let's leave the "we observe" aside, the question is whether the non-determinism is an objective property, not a technologic weakness of our macroscopic apparatuses.

My kindest regards, and a deep sigh in the memory of those beautiful years,

Sofia

Dear Sofia,

Yes I started to study quantum field theory just in 60's ... But at that times geometry of noncommutative PDEs was not yet born ! ...

You state:

'I still don't see why is there need for those non-commutative differential equations and super-PDEs.'

and

'... People write the wave-functions which describe the entanglements, and then follow the evolution of these wave-functions through beam-splitters.'

This is the problem ! People do not know of what they are talking ...

About my statement:

"when we observe a quantum system we necessarily get a statistical information ".

let me only add that the so-called 'quantum-indeterminism' is strictly related to the so-called quantum-measurement, namely the representation of the observed non-commutative system by means of so-called 'quantum-states'. It is just in this particular type of measurement that arises the statistical description of the quantum world. Therefore quantum-indeterminism is not an objective property of the quantum world, but it is uniquely related to the a methodology of measurement that is intrinsically probabilistic.

My best regards,

Agostino

Dear Agostino,

Do you want to say that Hardy's paradox, the GHZ experiment, the Kochen and Conway proof, all these are wrong because they didn't write equations? What writing equations would have given, other than what was proved without writing equations? Why write non-commutative differential equations and super-PDEs for plane waves?

When passing from an inertial frame to another inertial frame, in relative movement, a plane wave remains a plane wave, just though with other parameters, wave vector, frequency and time-space coordinates and order of events. What gives us to write non-commutative differential equations and super-PDEs for plane waves? A plane wave would transform into something else than a plane wave?

Kind regards,

Sofia

No Sofia !

You talk of plane wave ... but in Mathematical Physics a plane wave must be a solution of some equation ... You cannot simply refer to a plane wave by considering a quantum system ...

Sorry, I am surprised of your naivety !

Agostino

@Agostino Prástaro.

No way to find what you call "PDE".

https://en.wikipedia.org/wiki/PDE hm...

nor in your three enclosed papers.

However, did the Fermat's principle become obsolete just because the radiation is quantified ? Just because there is only one absorber, only one emitter, only one quantum h of action-per-cycle transferred and only one momentum h.\nu/c transferred to the absorber ?

All the interference experiments persist to prove that the Fermat's principle, Fresnel's optics and Maxwell equations are still valid for individual photons, individual electrons or individual neutrons. Radiocrystallography still works with electrons and neutrons, though it is still under Fresnel optical laws.

The wave fronts we handle in the Snellius-Descartes' law of refraction, and in the Bragg's law, are still valid at the individual scale, and still come under the macroscopical geometry. So why are you so discarding on them ?

Yes I do not deal at all about high energies. But on balance, I do not see you dealing with the intrinsic frequencies of particles with mass. Did you know that a team conducted by Michel Gouanère has experimentally proved the Dirac-Schrödinger frequency 2mc²/h ?

Agostino,

If you are surprised of me, then you are surprised of a whole quantum community that does not deal with non-commutative PDE when they may use plane waves. If you have to calculate 1+1, you first write non-commutative equations whose solutions are 1?

Do you know Hardy's article, the so-called paradox? He discussed an entanglement whose space evolution is plane waves. What is relevant there is results obtained behind beam-splitters. Was he naïve? Should he first have proved that the plane waves are, or not, solutions of non-commutative PDE?

Do you know the GHZ experiment? The entanglement that Zeilinger and his co-workers discussed, evolves, from beam-splitter to beam-splitter as plane waves, and again, what is relevant is results obtained after passing the beam-splitters. Should they have written non-commutative PDE?

Do you know the Aspect experiments with the polarization singlet? What is relevant here is polarization, the space evolution is simple plane waves. Should one first obtain these waves from non-commutative PDE?

In my country they say "for killing a mosquito one doesn't throw an atomic bomb, a kick with the hand is enough".

Who is the naïve here?

@Jacques Lavau

the acronym PDE means 'partial differential equations'. (It is often used in Mathematics ...)

I suppose that the meaning of your last post is related to the last Sofia's remarks ... I see that you quote 'Michel Gouanère experiment' ... This means that you refer to the Schroedinger PDE or to the Dirac PDE, namely you are talking of first quantization ...

Unfortunately I have seen in many questions and discussions on RG that users talk about quantum mechanics without consider that we are not at the beginning of the last century ...

By the way whether you have some specific question I will be glad to answer you.

Thanks,

Agostino

No Sofia,

we are talking of different things ! You refer to some experiments on quantum particles ... I refer to mathematical models of quantum particles ...

You work with experimental machines ... I work with mathematics...

By the way in order experiments should not a simple collection of data, it is necessary to refer to a mathematical theory.  Therefore in any case you must calculate ! You must know which solutions are your plane waves !

Let me add  that, after a century from the Schroedinger and Dirac times, one continues to talk of wave mechanics ...

In this long lapse the Science did not stop ...

About the following sentence

"for killing a mosquito one doesn't throw an atomic bomb, a kick with the hand is enough".

that you reported,  I must conclude that you are interested to mosquito only ...

I insist !

Your point of view is truly too naive !

Regards,

Agostino

Yes I do not look further than the first quantization : Dirac PDE.

If the yield of the scientific teaching is so low, maybe the content itself is questionable. And what is most questionable is not the mathematization of QM, but the semantics : the semantic postulates and the corresponding physical postulates. There remain lots of mine clearance to do.

Agostino,

What I am interested, is if somebody can show me a model of hidden variables of any type, local or not, which can reproduce the results of QM while respecting the relativity and without requiring that the future be known.

This was the question. There was no question whether to work or not with PDE. You can work the model, if you have one, with whatever tools you want including non-commutative PDE. But in order to provide an answer to MY question, the bottom line has to be a model as I asked.

Also, please STAY WITH PHYSICS. To call me naïve is OUTSIDE physics. I never gave you psychological characterizations, and please DON'T give me such.

The Dirac equation (1928) and its solutions (Schrödinger 1930 ...) respect the relativistic invariance BUT do not respect the macrophysical orthochronality-only postulate. Two of the four components are retrochrone.

Like or hate it...

Maybe, in some ranges, "knowing" is out of physics for us, macroscopical animals. Maybe the laws of nature are not designed and optimized for the purpose of our information. If most of neutrinos do not react in our laboratory, that is hurtful for our pride, indeed they have no obligations toward us. However I presume we have the obligation to tell the taxpayers that there are some predictions we cannot do. Forever.

Dear Sofia,

I just answered to your question ! ... please so kind to read my previous posts in this thread and also in some other your questions. The present your question does not substantially differs from other ones you previously posted. You really change the envelop of your questions, but the underling big problem is always the same. Probably you suspect that there is something not clear in the actual formulation of the quantum physics, but at the end you do not want to accept that the solution is more complex than your usual framework, where you are working.

Of course to seriously understand what I am posting it should be necessary to read my works ... It is not correct to pretend to understand the most advanced results in mathematical physics solving fundamental problems, simply reading some answers to your questions.

You really do not pretend to kill mosquitos, but blazing dragons !

About my terminology ... 'naive' . Please consider that this it not addressed to your person, (I am no so bad-mannered ...), but to your point of view that does not recognize the necessity to refer plane waves to some suitable PDE.

With this respect, let me add that also in the old scattering theory in high energy physics, namely the one encoded by the so-called S-matrix, (we are in the 60's), since it was not possible to characterize the quantum dynamics in the black-box of the reaction, theoretical physicists was forced to characterize only the initial and final 'free particles' as solutions of suitable PDEs.

Regards,

Agostino

Agostino,

I am in a conflict with the time. In my country there is a saying "to sit at once in two boats". This is my case. I work on a couple of things. I think that I'd better write down my proof and send you. But it takes time. To gain time, I made a trial to see if someone can contradict my claim, with an example, s.t. I posted this question. Probably my trial cannot work. I see your answers, but all the time I don't see a connection between them and my problem - I suppose that if I'll show you my proof, we'll understand better one another.

Just as some flavor of the problem, QM leads us, when considering moving frames, to the unbearable conclusion that the future is known (decisions of experimenters on which type of experiment to pick). Or, alternatively, we run into all sort of contradictions.

Of course my questions gravitate around this issue, because my work is in clarifying it, in a certain (indirect) way.

By the way, I have the feeling that if we accept that the quantum indeterminism is a true property of the nature, the contradictions (those known to me) are removed. This is what stands behind my questions. Believe me, it's a thorny ground all this issue. That's why I don't want any additional complication.

Well, I suppose that my country is in advance by 1 hour with respect to yours. So, we'll talk in the next days.

Good night and pleasant dreams!

 Dear Sofia,

you stated:

 'I have the feeling that if we accept that the quantum indeterminism is a true property of the nature, the contradictions (those known to me) are removed....'

 What I instead communicated to you is exactly the opposite !

 The quantum World follows a noncommutative logic ... not a chaotic logic ! This noncommutative logic can be exactly decrypted by us with a geometry of noncommutative PDEs.

When  we measure such noncommutative geometry with quantum states we get a statistical representation of the quantum world.

 Furthermore, quantum entanglement cannot change our future and neither our past. Who has a different opinion on this point shows that he did not understand the meaning of quantum entanglement ... He has really a naive concept of quantum entanglement !

 Of course I do not aspect that you believe me ... but whether you want seriously understand my posts you are forced to read my works ...

 Otherwise it is better to stop here our dialog.

'Ibi deficit orbis ...'

 Agostino

Agostino,

you can withdraw from this dialogue whenever you wish. Does somebody force you to continue?

Now, I find a logical mistake in what you say: you claim that

"The quantum World follows a noncommutative logic ... not a chaotic logic ! . . . When  we measure such noncommutative geometry with quantum states we get a statistical representation of the quantum world."

Bottom line, you present a mathematical model from which IS NOT what I ask for. Look at my question!!! The fact that you offer a model which DOESN'T fit what I ask for, is NO PROOF that a model AS I ASK FOR, cannot be found. Do you understand that? Suggesting a model that DOES NOT fit what I ask for, DOES NOT IMPLY that such a model as I ask for, does not exist. Do you understand the NON-implication?

People won't read theories just because you say so. The RG is full of requirements of "read my article". Do you realize that it is impossible to invest so much time? People read ONLY if they consider that the article gives an answer to what they look for. If you feel offended by that, you may withdraw from my question, does somebody force you to stay?

Sofia ,

you stated that there is 'a logical mistake' in my last post since my point of view does not agree with what you should pretend to find !

This your claim is truly illogical !

Furthermore, I did not asked you to read my work ! I invited you to do it since you often submitted me (also with private messages), some your physical problems that I suggested to solve with my quantum gravity theory.

It does not matter, whether you changed opinion ...

On the other hand my work is not for all, since it requires a strong mathematical background in PDE's Geometry and Algebraic Topology ...

I wish you to find other users in RG that could share your opinions ... I sincerely cannot do it !

I must confirm.

Your point of view is truly too naive !

Agostino

SOME CLARIFICATIONS,

The question whether hidden variable (HV) models can obtain the same results as QM was already and widely tackled. Everybody knows Bell's inequalities. Bohm also offered, in his mechanics so-called Bohmian, a model of non-local HVs. I suggested in my last article on RG, a model of HVs inherently non-local, based on full/empty waves and amplitudes of probabilities.

All these models suffer from limitations. Bell's model of local HVs governed by positive probabilities, does not reproduce the QM predictions - the Bell-type inequalities are violated. As Bohm's model showed, introducing non-locality is not enough for reproducing the QM predictions. Indeed, Bohm's mechanics clashes with the relativity, i.e. leads to the conclusion that the wave-function is correct only in a certain frame  - a preferred frame. The full/empty waves hypothesis also clashes with the relativity, from the same reasons as Bohm's mechanics, s.t. the model that I suggested suffers from the same limitation.

My question was just a challenge: can somebody suggest/know a better model?

There is a famous proof, due to Kochen and Conway, so-called "The free will theorem" (quant-ph/0604079v1) which proves the following:

Assuming that the result of a measurement is decided only by variables/events in the past of that measurement, leads to a clash with the assumption of free will. This assumption says that decisions of experimenters are taken freely, not imposed by some signals from past or future, and such decisions may eventually fall at the experiment time, not be known or taken in advance.

This is of course a proof against hidden variables, however, it suffers of a limitation - only parameters or events occurring in the absolute past of a measurement, are supposed to influence its result. This is a wider class of variables, hidden or not, than Bell's local HVs, but this is still a limitation to the proof.

My question was: can somebody suggest a less limited model? I acknowledge that the question is very, very difficult, but at least, it poses the widely discussed problem, if, at the microscopic level, the nature is indeed non-deterministic.

The fact that the various models of HVs proposed so far are limited, does not prove that such a model cannot be found. Also, the fact that the quantum formalism (mainly the uncertainty principle), or other formalisms, yield indeterminism, is not a proof that no substructure can exist that would remove the indeterminism.

Thanks for your 'clarifications'...

In particular I agree with your last statement:

'... the fact that the quantum formalism (mainly the uncertainty principle), or other formalisms, yield indeterminism, is not a proof that no substructure can exist that would remove the indeterminism.'

This is just what does my quantum gravity theory !

Agostino

A more dynamic and fertile approach would be a reformulation of the problem : to ask how much we are able to set the frontiers of the system we are thinking about and experimenting on.

The inventors of "free energy" devices always exhibit the symptom of never fermly knowing what is in and what is out their device ; their own frontiers are not firmly established.

In september 1923 (CRAS), and confirmed in his thesis in 1924, Louis de Broglie, by establishing his theorem of Harmony of phases, had demonstrated that the wave of a flying electron has a not negligible, finite and fuzzy bulk (width and length). So the phase velocity (c²/v), at this stade of theorization was infinite in the frame of the electron (v = 0 in its frame).

What de Broglie never thought is it implies, at least in condensed matter, that each quanton is in the lapping of the broglian waves of all the others, at least the neighbours others. This is the broglian noise.

In 1923, the "waves functions" of Born and Heisenberg were not invented, so we speak about physical waves.

With Dirac in 1928 we learned that this noise is with positive and negative phase velocities, towards the past and towards the future.

Anyway, no shielding to this broglian noise. With all this wave lapping, you will never be able to predict when and which emitter-medium-absorber transaction will occur. The effective frontiers are not at our will, they are fluctuating beyond our reach. The desexcitation of an atom or a nucleus escapes to our predictions, but statistically.

In the Sofia last post it is claimed:

'... the fact that the quantum formalism (mainly the uncertainty principle), or other formalisms, yield indeterminism, is not a proof that no substructure can exist that would remove the indeterminism.'

I answered my agreement with my last post.

In fact my quantum gravity theory is founded on the quantum super Yang-Mills PDEs (say (YM)). This geometric object can be identified with the substructure that removes the indeterminism according to what Sofia claims. In fact by using my geometric theory of quantum (super) PDEs we can integrate (YM) and to encode quantum reactions as a boundary value problem in (YM). Furthermore, by considering an observer, encoded by a time-like flow on a macroscopic space-time N, we can represent (YM) on N and to talk of observed (YM), say (YM)[i]. In such a way we get a non-commutative formulation of quantum world, observed by a specific frame. Of course by changing the observer, namely the time-like flow in N, we get another observed (YM)[i']. By taking into account the relation between two observers in N, we get also a relation between the two observed quantum PDEs, (YM)[i] and (YM)[i'].

Let us remarks that at this level the quantum world is encoded in a deterministic way, but in a noncommutative world.

Then we can represent quantum observables, e.g., quantum Hamiltonian of an observed nonlinear quantum propagator, encoding an observed quantum reaction, by means of quantum states. These are suitable functions on the fundamental quantum algebra A of the quantum system, that give a statistical measure on the quantum observables. For example we can obtain quantum statistical informations on the quantum Hamiltonian of some quantunm reaction.

In this way we can also obtain the Heisenberg uncertainty rellation between observed quantum energy and observed quantum time. (Warning. this last is not the proper time of the observer, but a noncommutative time characteristic of the observed nonlinear quantum propagator.)

By conclusion we can remove the indeterminism at the quantum level by using quantum PDEs to encode quantum systems, but by using measures with quantum states we get a statistical information on quantum systems that recovers the language of the classical QM, In this way one solves the problem of the incompleteness of QM.

Let us consider my quantum gravity theory with respect to the three points stressed by Sofia.

1. Relativity is respected. The relation between two observed frames it means that the 'Relativity' is respected.

2. Free will is respected. Since all my quantum gravity theory is founded on a geometric theory of observed quantum PDEs, it follows that we can state that causality is respected. With this respect, let us emphasize that since particles are considered extended objects, observed quantum reactions are encoded by means of compact solutions of (YM)[i], namely observed nonlinear quantum propagators. The algebraic topologic properties of such objects justify quantum entanglements. This phenomena does not contradict causality.

3. The QM predictions are reproduced. Measurement of quantum systems, as previously considered, by means of quantum states, reproduces the language of the QM.

CONCLUSION. Sofia's claim:

'... no substructure can exist, with local or non-local variables, hidden or accessible, which fulfills my 3 conditions:

1. relativity is respected,

2. free will is respected

3. the QM predictions are reproduced.'

Well ! I disproved Sofia's claim with my quantum gravity theory.

Agostino

"What I am interested, is if somebody can show me a model of hidden variables of any type, local or not, which can reproduce the results of QM while respecting the relativity and without requiring that the future be known."

Drop a coin from a height, the best you can, exactly from above the border of a glass. It will fall inside the glass or outside it.

So, it produces uncertainties and statistics exactly like QM.

There are hidden variables.

The properties in another frame at a distance according to relativity can be calculated.

It is not required that the future is known.

Dear Agostino,

I have a question. You say

"This geometric object can be identified with the substructure that removes the indeterminism according to what you claim.

. . . . . At this point we can represent quantum observables, e.g., quantum Hamiltonian of an observed nonlinear quantum propagator, . . ., by means of quantum states. These are suitable functions . . . . , that give a statistical measure on the quantum observables"

    Bottom line, is your theory able to predict, by means of those "suitable functions", the result of each trial and trial in an experiment?

For instance, given a beam of x-polarized electrons that we pass through a Stern-Gerlach apparatus with magnetic field in the direction z, do those functions predict in each trial and trial whether the electron will be found with spin-up, or will be found with spin-down?

I remind you what's written in the question:

"By subquantal structure I mean parameters of whatever type that might decide deterministically the results of measurements"

The substructure sought in the question is one which removes the indeterminism.

Best regards

Sofia

REMARK: 

For a wave-function in a 2D space, it is possible to construct a hidden variable model of substructure, which predicts deterministically the same results as the respective wave-function.

For wave-functions in a Hilbert space of dimension 3 or more, the possibility to construct a substructure which would reproduce deterministically the same results as the respective wave-function, is not sure. On certain wave-functions in 3D Hilbert space, contextual experiments can be built, which put under a big question mark the possibility of such a substructure.

It is proven that for hadrons, there is a substructure : quarks and gluons.

For leptons and photons : no substructure to find, only overhead and interties.

Problem : these interties, experimentally proven, contradict some surrepticious macrophysical postulates.

See above.

No, Jacques,

It's not the substructure of which my question asks. Look at the question! It's written there:

"By subquantal structure I mean parameters of whatever type that might decide deterministically the results of measurements, in particular of entangled particles."

That means, parameters that define uniquely the result of each trial and trial in an experiment. For instance, assume that we work with the polarization singlet. The power of prediction I expect from these parameters is not to predict a result R1 with probability P1, a result R2 with probability P2, etc., but to predict for the pair of particles in each given trial, exactly the result. And of course, considering all the trials, the statistics of the results should be the same as the QM statistics.

Best regards!

 I have proven just before, that your expectation will never been met, and explained why  : as strongly as you dream that your "system" is isolated and "prepared" it is not so.

Due to the frequencies involved in the Dirac-Broglie wave-lapping, no instrumentation gives you the hand on these fluctuations. You will never be able to predict which one of the possible and probable transactions will really occur, nor when.

No Jacques,

I don't dream of that substructure of which I asked. I challenge people to try to propose one.

You say "Due to the frequencies involved in the Dirac-Broglie wave-lapping, no instrumentation gives you the hand on these fluctuations. You will never be able to predict which one of the possible and probable transactions will really occur, nor when."

Which frequencies, which lapping and which instrumentation? I don't ask whether we can detect that substructure, I ask whether mathematically we can prove that such a substructure is possible.

 No change : mc²/h and 2mc²/h for each (rated in its own frame), for each, for each, for each, at all scales...

De Broglie 1923, Schrödinger 1930.

With frames that are flying at the speeds of the molecules of the gaz, or agitated at the speeds of the phonons in condensed matter...

The Dirac-Schrödinger clock frequency of the electrons has been measured at the ALS at Saclay :

Experimental observation compatible with the particle internal clock,

by M.Gouanère, M.Spighel, N.Cue, M.J.Gaillard, R.Genre, R.Kirsch, J.C.Poizat, J.Remillieux, P.Catillon, L.Roussel.

http://aflb.ensmp.fr/AFLB-331/aflb331m625.pdf

http://aflb.ensmp.fr/AFLB-301/aflb301m416.pdf

(What if we measure the time difference of electrons in the double slit experiment ? - ResearchGate. Available from: https://www.researchgate.net/post/What_if_we_measure_the_time_difference_of_electrons_in_the_double_slit_experiment/1 )

Of course, the experiment will never been conducted again before dozens of years, and Coluche has explained why :

"They cannot tell the truth at the TV, because too much people watch it !" :

http://www.agoravox.fr/culture-loisirs/culture/article/coluche-nous-avait-explique-154321

Dear Sofia,

I have seen another post addressed to me ... I cannot repeat what I have just posted in my last long post ...

By the way, whether it is useful to a better understanding:

YES THE QUANTUM SUPER YANG-MILLS PDEs IS THE STRUCTURE THAT GIVES AT QUANTUM LEVEL A COMPLETE DETERMINISM. THIS MEANS THAT ONE CAN KNOW THE TIME-EVOLUTION, WITH RESPECT TO AN OBSERVER, OF THE SPECTRAL CONTENT OF A QUANTUM REACTION !

Agostino

Dear Agostino,

I have no idea of which reaction you speak. I didn't ask about spectral content of reactions, but about results of measurements. For me is also TIRESOME to repeat endlessly what exactly is my question. 

I asked whether somebody can suggest a substructure of the QM, that predicts deterministically the result of the measurements (in particular of entangled particles) in each trial and trial of the experiment, and satisfying the 3 conditions that I mentioned. I don't ask about a spectrum, but about a precise result.

Answers to other things are not relevant to me, so, indeed I'd be glad that they BE NOT REPEATED.

Also, I'd appreciate if users would refrain from posting here general thoughts about QM. It's not a saloon talk here, but a precise question, so only specific answers to the question are relevant.

@ Sofia D. Wechsler : "Also, I'd appreciate if users would refrain from posting here general thoughts about QM. It's not a saloon talk here, but a precise question, so only specific answers to the question are relevant."

Business as usual : throwing margaritas ante porcos.

The advice "nolite mittere margaritas ante porcos" was given in public many centuries before SDW became mad on us, and insulted us, because we corrected her blunders. She did not understood any of the given corrections, behaving like a hen who had found a knife.

https://la.wikipedia.org/wiki/Margaritas_ante_porcos

*"Margaritas ante porcos* est pars proverbii in Evangelio secundum Matthaeum , capite 7, versu 6,"

NO SOFIA !

Now I am sure that you do not understand what you are asking !

You claim now:

'I asked whether somebody can suggest a substructure of the QM, that predicts deterministically the result of the measurements (in particular of entangled particles) in each trial and trial of the experiment, and satisfying the 3 conditions that I mentioned. I don't ask about a spectrum, but about a precise  result.'

This your new statement completely contradicts your previous interpretation of your question. In fact you sent me the following explication in a separated message:

'Do you claim that you have such a general proof as I ask about? I mean, a proof that no substructure can exist, with local or non-local variables, hidden or accessible, which fulfills my 3 conditions:

1. relativity is respected,

2. free will is respected

3. the QM predictions are reproduced.'

Well ! My quantum gravity theory disproves this last your statement.

Now you change, and pretend that such a substructure deterministically gives  measures in QM !

Of course this your last post is a NON-SENSE and contradicts your previously one !

Sorry but I find this your behaviour completely unprofessional ! ...

I cannot lose time with such your stupidities !

Agostino

Agostino,

Did I ask you to loose your PRECIOUS time with my question? Please NEVER loose your time with my NON-professionality and STUPIDITY. I would be very glad if you'd NEVER mix in my questions, if this is your type of LANGUAGE.

Until now you didn't understand that a particular model that doesn't accomplish the requirements of the substructure, is not a proof that the substructure is impossible. However, given your insults, our dialogue ENDS HERE.

You were repeatedly warned to control your style of talking with people, but you keep insulting. I DON'T WANT TO SEE YOU ANYMORE in my posts.

Jacques Lavau,

If you call the users PORCS, don't mix anymore with my posts. This is my last word to you.

NO SOFIA !

I end to write my posts when I decide to do it ! You surely have not the power to stop me on RG !

Your hysterical reaction to my scientific arguments is completely inappropriate and it does not agree with a correct behaviour between serious RG users.

In particular you should thank my patience to answer you giving useful suggestions to your RG questions (also submitted to me by your personal RG messages ... ).

Really your research it appears focused on old points of view ... you talk of first quantization only ... A century of science is passed in vain for you ...

Often it happens that you are not understanding what you are talking.

Let us recall the more recent examples in this thread:

1)  'I don't understand what you say. Why Dirac's equation from the relativistic QM "cannot encode a quantum system"? As to high energy levels, what is the problem with them? Can you be some clearer?'

It is clear that you do not know that after the first quantization there exists the second quantization just to consider quantum systems at high energy levels !

2) 'Until now you didn't understand that a particular model that doesn't accomplish the requirements of the substructure, is not a proof that the substructure is impossible.'

Evidently you do not know the meaning of a counterexample in  logic !

But you pretend also to be considered offended by my patience !

This is surely unacceptable !

All the best,

Agostino

Of course, Agostino,

You can write whatever you want, insult people as you please, give them degrees about their knowledge whenever something is inconvenient to you. All these you CAN do. But to force people to read your INSULTS and REVENGES, you CANNOT  do.

So, I have NO IDEA what you wrote, as I said, I stopped my dialogue with you. You CAN'T impose your opinions by INSULTS. So, write whatever you want, you can fill whole pages.

NO !

I have never tried to impose my opinions with insults to Sofia D. Wechsler and any other body !

Any RG's user can verify it by reading my posts in Sofia's  RG questions ...

It is too easy to exchange for insults serious scientific arguments that it is impossible to confute !

However Sofia does not worry ! I will not add more comments on her threads ... It is a useless effort ...

'Acta non verba ...'

YES!

I got insults from Agostino Prastaro. I quote:

"Sorry but I find this your behaviour completely unprofessional ! ...

I cannot lose time with such your stupidities !"

Also:

"Your hysterical reaction to my scientific arguments . . . Often it happens that you are not understanding what you are talking . . ."

Such a language should not be used!

Also he decided to give me grades in different domains while he is not entitled/invited to do so.

"It is clear that you do not know that . . . there exists the second quantization . . . Evidently you do not know the meaning of a counterexample in  logic !"

If a user disagrees with Prastaro, thst doesn't mean that the user doesn't understand in the given field, all the more when it's THE field in which the user has gained years of experience. Prastaro is NOT the SUPREME WISDOM, he may be correct or wrong as everyone, and he is supposed to support/defend his views ONLY BY SCIENTIFIC ARGUMENTS, not by giving grades to others.

Thanks for your summary that confirms that I never used offensive words !

What you report confirms that I used scientific arguments that you did not understand, but consider them as insults !

In this way you take grades by yourself !

You confirm that it is a useless effort to follow your questions ...

'Ab ovo usque ad mala ...'

Of course,

the words "your stupidities" is not an insult IN YOUR VOCABULARY.

As to "it is clear that you don't know", you are not supposed to say that at all, but to bring counter-arguments to my statements. My grades are NOT YOUR BUSSINESS.

To remind you, it's not only I who suffered from your insults, other people complained of insults from you too. I personally saw a couple of them. Now, please be so kind and LEAVE ME IN PEACE !!!

"errare humanum est, perseverare, diabolicum"

I am not here for you, please bestow you attention and grades giving to whom is willing to undergo such things. All this dispute that you impose on me I DISLIKE.

FULL STOP.

 A good thing is done : in her fall, Sofia D. Wechsler has dragged down with her the David Bohm's theory. Indeed, there was already a very good reason to discard it : il is essentially corpuscular.

Jacques Lavau's comment,

is a comment of HATRED: "in her fall, Sofia D. Wechsler has . . .". Which fall?. I require that the scientific line be respected, as this is a site of science and only of science.

Besides, J. Lavau has NO RIGHT to make declarations about my scientific views. I didn't fall, I am O.K., and I can explain my views. ONLY I have the right to do it. Thus, I make clear that am no supporter of Bohm's mechanics, neither am I against it. Only the experiment can decide between in favor or against it, and I claim that such an experiment should be done.

Next, Bohm's mechanics has nothing to do with my question, as this type of mechanics doesn't satisfy the relativity - see condition 1 in the question. I strongly recommend, before answering a question, the details of the question should be read.

'Errare humanum est, perseverare autem diabolicum ...'

Some considerations about the Conway and Kochen "Free Will" theorems.

One of the assumptions of "The Free Will Theorem", called FIN by the authors, is that whatever variables that may determine a measurement result, took values in the absolute past of that measurement. This assumption is equivalent with locality.

In "The Strong Free Will Theorem" the assumption FIN, is replaced by MIN, which is weaker than FIN. As the measurements of the two particles in the entanglement are space-like separated events, MIN assumes that the result produced by Alice's particle is independent of the type of experiment chosen by Bob, and vice versa. Thus, MIN is still an assumption of locality, however, it is exactly the requirement 2 in the present question. 

On the other side, "The Strong Free Will Theorem" neither confirms nor disconfirms the possibility of a substructure as the present question asks. The theorem only proves that the result of a measurement cannot be the exclusively and deterministically established by parameters that took values in the absolute past of that measurement.

For whomever this question is interesting,

a recent work of GianCarlo Ghirardi and Raffaele Romano

"Is a description deeper than the quantum one possible?"

arXiv:quant-ph/1501.04127v1, may be relevant.

Please read the paper, may be helpful for you.  A new approach to the correction of

Galilean transformation.