The non-local debate: week one

[Bryan Sanctuary]

Hi all

I give my assessment of the week since I posted my first paper,

Spin with hyperhelicity.

The comments are on my Blog

http://blog.mchmultimedia.com/2022/04/29/the-non-local-debate-hyperhelicity-and-quantum-weirdness/

Bryan

[Richard Gill]

Dear Bryan

You start your report by claiming no-one saw errors in your maths. That is not true. You claimed to have a counter-example to Bell’s theorem but you don’t. 

Bell’s theorem states that no local hidden variables model, by which he means a deterministic model in which any randomness in measurement outcomes is attributed to statistical variation in initial values of unmeasured variables, can reproduce certain statistical QM predictions, or even approximately reproduce them. You did not refute Bell’s claim.

You seem to imagine that Chantal or Pierre will be able to do that for you. This shows that you do not understand Bell’s maths, which shows that a computer network with nodes and links mimicking a Bell type experiment cannot reproduce quantum correlations. Bell’s theorem is a no-go theorem in theoretical computer science, subfield distributed computation, as well as a no-go theorem in physics, subfield foundations of quantum mechanics.

You seem to have your own notions of “local” and “realistic” though you fail to make them explicit. This means that you don’t even have any clear mathematical claim concerning your helicity ideas.

These are all major mathematical errors. Much more serious than any mistakes in computations within your chosen framework. Because of these serious errors, I, for one, have little motivation in checking those computations. 

You have till New Year to gain support for your work from a majority of our peers. I don’t see much chance that you will succeed.

Richard

Sent from my iPad

On 1 May 2022, at 15:59, Bryan Sanctuary <bryancs...@gmail.com> wrote:

Hi all

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[Alexandre de Castro]

Dear Bryan, Richard, friends
I think we should use a Wigner-d'Espagnat-like model to point out gaps in Bell's theorem because Inequality 9  in "Bertlmann's socks and the nature of reality" is a local model of probability distribution , undoubtedly. I chose a similar circumstance to Inequation 9, in a recent review for a Richard's paper in RSOS:

Report of reviewer 4:  pp. 3, 13, 22, 27, 30 and Appendix B  [ https://royalsocietypublishing.org/action/downloadSupplement?doi=10.1098/rsos.201909&file=rsos201909_review_history.pdf ]. If the Born rule is compatible with Inequality 9, then there is a loophole in Bell's theorem.

Alexandre

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[Richard Gill]

Dear Alexandre

I disagree with your conclusions and I never succeeded in making sense of your proposal in that referee report you wrote on my paper. I have the impression that the other reviewers did not understand your comments either. Have you got this work published anywhere yet? In fact, some of the referees suggested I removed any comments on the question of the possible inconsistency of ZFC. However, the editor instructed me to respond *in the paper* to all comments of all referees, so my response to your comments is published in the final version too.

I don't see any problem with inequality (9) in "Bertlmann’s socks”, https://hal.archives-ouvertes.fr/jpa-00220688/document. Bell has defined what he means by local realism very precisely, and this inequality is a trivial consequence thereof, as he says himself.

Richard

[Bryan Sanctuary]

I'll comment on Richard's email.

You start your report by claiming no-one saw errors in your maths. That is not true. You claimed to have a counter-example to Bell’s theorem but you don’t. 

PLEASE POINT OUT MY MATH ERRORS

Bell’s theorem states that no local hidden variables model, by which he means a deterministic model in which any randomness in measurement outcomes is attributed to statistical variation in initial values of unmeasured variables, can reproduce certain statistical QM predictions, or even approximately reproduce them. You did not refute Bell’s claim.

You seem to imagine that Chantal or Pierre will be able to do that for you. This shows that you do not understand Bell’s maths, which shows that a computer network with nodes and links mimicking a Bell type experiment cannot reproduce quantum correlations. Bell’s theorem is a no-go theorem in theoretical computer science, subfield distributed computation, as well as a no-go theorem in physics, subfield foundations of quantum mechanics.

I HAVE NO ISSUES WITH BELL'S PROOF, ITS CORRECT. SURE IT IS A CLASSICAL NO-GO THEOREM FOR CLASSICAL COMPUTERS. SPIN IS NOT A CLASSICAL COMPUTER.

You seem to have your own notions of “local” and “realistic” though you fail to make them explicit. This means that you don’t even have any clear mathematical claim concerning your helicity ideas.

NO I DO NOT, I HAVE CLEAR DEFINITIONS, BUT I HAVE TO DEAL WITH YOUR OBFUSCATATIONS.  THEY ARE CONSISTENT WITH EPR AND BELL'S DEFINITIONS. 

BESIDES LOCALITY IS TRIVIAL,  THE UNIVERSE IS NOT ONE BIG WAVEFUNCTION. ITS NOT AN "UNDIVIDED WHOLE" ITS A BUNCH OF FIELDS WITH INVERSE POWER FORCES. BELL DEFINES IT HIS WAY.

These are all major mathematical errors. Much more serious than any mistakes in computations within your chosen framework. Because of these serious errors, I, for one, have little motivation in checking those computations. 

WOW! MATH NOT WORTH CHECKING! FROM RICHARD! 

You have till New Year to gain support for your work from a majority of our peers. I don’t see much chance that you will succeed.

SHOULD BE ENOUGH TIME .

YOU RAISE  CONSTANT MUDDLES ABOUT DEFINITIONS OF LOCALITIES, THAT YOU EXPRESS WITH OTHERS TO DISCREDIT WHEN YOU ARE TRAPPED.

I SUGGEST THAT WE GO BACK TO 1964 AND CONFIRM DEFINITIONS WHEN YOU CLAIM "NOT THIS BUT THAT". YOU CONSTANTLY NIT PICK AND  THROW IN WRENCHES TO ANY CHALLENGE TO YOUR BELLIST OBSESSION.

I PREDICT THAT QUANTUM INFO WILL DROP TELEPORTATION THIS YEAR AND RESTRUCTURE. HOWEVER, I'M AN OPTIMIST.

BUT PERSISTED ENTANGLEMENT IT TOAST.

Bryan

[Jan-Åke Larsson]

On mån, 2022-05-02 at 06:22 -0400, Bryan Sanctuary wrote:

I'll comment on Richard's email.

You start your report by claiming no-one saw errors in your maths. That is not true. You claimed to have a counter-example to Bell’s theorem but you don’t. 

PLEASE POINT OUT MY MATH ERRORS

Don't shout.

Your model is less descriptive than quantum mechanics, since it provides no mechanism for a click-by-click simulation.

This is a severe deficiency and actually, there is no basis for your claim that this is a model that describes the experiment.

You can calculate the correlation, nothing else. 

Also, you do not write what you mean with "local realist". since for certain it cannot be Bell's notion. Because of this, it is unclear to me how your "local realist quantum" description is "local realist quantum" and standard quantum mechanics is not "local realist quantum" in your sense.

Your paper is not a counterexample.

/JÅ

-- 

Jan-Åke Larsson
Professor, Head of Department

Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:482 Please visit us at www.liu.se

[Bryan Sanctuary]

Hi Jan-Åke

I was not shouting, I was just distinguishing with caps from Richard.  I will use something different if it upsets you.

I agree a statistical model would seal my case and that is now underway, but a local counter example dooms Bell's or anyone's theorem.  That you reject my couterexample  because a non-proven mechanism is laughable:  I simply have to point to the "mechanism"for "quantum weirdness" that you embrace.  If you do not like my counter example, then please explain the mechanism that you rely on, namely quantum weirdness.  

In English we say you are a "pot calling the kettle black."

Here is local realism;

These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.

Any problems with this?

But, I do have a mechanism that I sent you:  what is wrong with that?

https://www.dropbox.com/s/fn1d2endryrrn2t/weirdness.pdf?dl=0

If I know the starting point at separation, and the spin spins to the filter, it carries correlation. Please show my mechanism does not provide a local realistic and deterministic account of EPR correlation.

Also Spin Helicity paper just introduces helicity.  There is a lot more.

Thanks for your comments.  But I would give up teleportation (hey what is the mechanism?) and move  on to reality.

Bryan

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[Alexandre de Castro]

Dear Richard,
Editors and reviewer were fairly critical of your initial approach. Already at first reading, I realized that your paper would fail. However, I recommended your paper from the beginning.. Look on the bright side!

Because of my job, I am involved in a government project on cryptography and information security applied to agricultural production in Brazil: https://www.cnnbrasil.com.br/business/setor-agro-adere-ao-blockchain-para-registrar-processo-de-producao-de-graos/ . This work is taking up my time. I will write a paper on Ineq. 9 soon.

But, here, you infer: "I have the impression that the other reviewers did not understand your comments either."

Why do you say that? I haven't read anything about it.

You also write, here: "In fact, some of the referees suggested I removed any comments on the question of the possible inconsistency of ZFC."

Where is this written in the report?

You say “I don't see any problem with inequality (9) in "Bertlmann’s socks”, https://hal.archives-ouvertes.fr/jpa-00220688/document. Bell has defined what he means by local realism very precisely, and this inequality is a trivial consequence thereof, as he says himself.”

I totally agree with Bell.
I totally agree with you as well.

In this connection, Inequality 9 wiil be the substrate for my future work.

Alexandre

[Jan-Åke Larsson]

On mån, 2022-05-02 at 07:15 -0400, Bryan Sanctuary wrote:

Hi Jan-Åke

I was not shouting, I was just distinguishing with caps from Richard.  I will use something different if it upsets you.

I agree a statistical model would seal my case and that is now underway, but a local counter example dooms Bell's or anyone's theorem.  That you reject my couterexample  because a non-proven mechanism is laughable:  I simply have to point to the "mechanism"for "quantum weirdness" that you embrace.  If you do not like my counter example, then please explain the mechanism that you rely on, namely quantum weirdness.  

You do not have a mechanism. That formula of yours does not describe (statistics for, or predict) individual outcomes.

In English we say you are a "pot calling the kettle black."

You use "quantum wierdness", I do not.

Here is local realism;

These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.

Any problems with this?

The problem is that there is no "additional variables" that "restore to the theory causality or locality" in your mathematical description.

I must conclude you mean something other than Bell, but you have not told us what /you/ mean. Your paper is not a counterexample.

But, I do have a mechanism that I sent you:  what is wrong with that?

https://www.dropbox.com/s/fn1d2endryrrn2t/weirdness.pdf?dl=0

That paper contains no mechanism. It contains a correlation calculation.

If I know the starting point at separation, and the spin spins to the filter, it carries correlation. Please show my mechanism does not provide a local realistic and deterministic account of EPR correlation.

Also Spin Helicity paper just introduces helicity.  There is a lot more.

Thanks for your comments.  But I would give up teleportation (hey what is the mechanism?) and move  on to reality.

I *am* moving on. See https://arxiv.org/abs/2202.05081 . Also not a counterexample.

Also, "quantum teleportation" is the wrong name. This is well understood among experts, not so well understood in popsci.

None of what you wrote changes the following:

Your model is less descriptive than quantum mechanics, since it provides no mechanism for a click-by-click simulation.

This is a severe deficiency and actually, there is no basis for your claim that this is a model that describes the experiment.

You can calculate the correlation, nothing else. 

Also, you do not write what you mean with "local realist", since for certain it cannot be Bell's notion. Because of this, it is unclear to me how your "local realist quantum" description is "local realist quantum" and standard quantum mechanics is not "local realist quantum" in your sense.

[Richard Gill]

Bryan

Writing in block capitals is generally thought of as “shouting” by civilized denizens of the web.

I checked out your “weirdness” note. I see no mechanism there. Just a fantasy. Give Chantal or Pierre instructions for getting the *separate* outcomes in Alice  and Bob’s devices, from your sigma and i sigma. Then we can talk further.

Richard

Sent from my iPad

On 2 May 2022, at 13:15, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:482 Please visit us at www.liu.se

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[Bryan Sanctuary]

Hi Richard

Like I said, I was distinguishing not shouting.  There is little malice in me, but look at you guys, like Jan-Åke and you too, who question my understanding of stuff, my ideas, background and my language "Also, "quantum teleportation" is the wrong name. This is well understood among experts, not so well understood in popsci."  I suggest you go to Google Scholar and google "teleportation" to see how many use the term.  Go and look at the title of Bennet et al, and read their first paragraph which, I recall, justifies non-local entanglement swapping.  The reason you want to change the vernacular is because "teleportation" is a weird concept.  You guys, in my view, are rationalizing the absurd. (google quantum weirdness".)

Now I have presented my first paper. Ok, you don't accept my counterexample, but not to do so leaves non-locality is the only alternative.

I do not want or like personal attacks, discrediting others or me, etc but it is water off my duck's back, although  Richard said something about lies, and I react quite negatively to any suggestion that  I am dishonest. I would rather now let the matter rest as I get ready to release my second paper.

We disagree, I did not think it would be otherwise

Bryan

[Алексей Никулов]

Dear Richard, 
Alexandre drew attention to a problem with inequality (9) in "Bertlmann’s socks” [1]. I draw your attention once again that the equality (4) in the Bell article [1] cannot be correct 
according to the orthodox quantum mechanics since results of observations of two particles cannot be different if operators acting on different particles commute. It is surprising to me 
that it is necessary to convince a mathematician that the result of the actions of operators cannot depend on the order of their actions if these operators commute. 
Bell deduced the equality (4) in [1] since he followed Bohm’s quantum mechanics, according to which operators acting on different particles do not commute, rather than the orthodox 
quantum mechanics, according to which operators acting on different particles commute. Only Bohm’s quantum mechanics can contradict locality and predicts the EPR correlation and 
violation of Bell’s inequalities whereas the orthodox quantum mechanics cannot make this because of its principle that operators acting on different particles commute.  
It is necessary to know and understand this at least in order not to repeat the mistakes of the authors [2,3] of the GHZ theorem who followed orthodox quantum mechanics, in
 order to prove that quantum mechanics contradicts locality. It is necessary also to understand that Bohm postulated the contradiction with locality with the help of an absurdity. 
According to the equality (4) in the Bell article [1] the results of Alice's measurements depend on who will be the first to measure the spin projections of their particles, she or Bob. 
Alice will see spin up with the probability 1/2 at measurements of the spin projections of her particles in any direction if she will measure first. But this probability sin^{2}(a-b)/2 will 
depend, according to (4) in [1], not only from the direction “a” of measurement of the spin projection of her particles, but also from the direction “b” of measurement of the Bob 
particles, if Bob will measure first. Are you not confused by this absurdity necessary to predict the violation of Bell's inequalities?

[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).

[2] D.M. Greenberger, M.A. Home and A. Zeilinger, Bell’s Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Dordrecht: Kluwer Academic), pp. 73-76 (1989).
[3] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

With best wishes,

Alexey

пн, 2 мая 2022 г. в 18:06, Bryan Sanctuary <bryancs...@gmail.com>:

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YzGCFKq8HAuDrwXcDp-rqzn4ZRyChxz1SgRLfwF1cR8dA%40mail.gmail.com.

[Richard Gill]

Alexey, you said “results of observations of two particles cannot be different if operators acting on different particles commute. It is surprising to me that it is necessary to convince a mathematician that the result of the actions of operators cannot depend on the order of their actions if these operators commute. “

I know that very well, already

Richard

Sent from my iP

On 2 May 2022, at 19:19, Алексе<nikulo...@gmail.com> wrote:



[Алексей Никулов]

Dear Richard, 
You also wrote to me that you know that operators acting on different particles commute according to the orthodox quantum mechanics. Then why don't you understand that the orthodox 
quantum mechanics cannot predict the violation of Bell's inequalities and that Bell's theorem contradicts the orthodox quantum mechanics?  

With best wishes,

Alexey

пн, 2 мая 2022 г. в 21:30, Richard Gill <gill...@gmail.com>:

[Richard Gill]

Alexei

I just do not understand you. The quantum state of two separated particles is by definition a non-local thing. Bell’s theorem can be formulated as a mathematical theorem which states that two mathematical structures make different predictions. QM allows strictly more joint probability distributions of measurement outcomes given settings than LR. Read my survey paper https://arxiv.org/abs/1207.5103 and tell me where you see mathematical errors.

I’m getting very tired of talking to people who keep saying I’m wrong but don’t bother to look at my own work.

While you’re at it, look at my paper on Gull’s theorem. https://arxiv.org/abs/2012.00719 . What’s wrong with it? It’s relevant to Bryan Sanctuary’s aims but he doesn’t bother to read it either.

Richard

Sent from my iPhone

On 2 May 2022, at 21:47, Алексей Никулов <nikulo...@gmail.com> wrote:



[Алексей Никулов]

Dear Richard, 
You do not understand logic rather than my statement. You know: 1) operators acting on different particles commute according to the orthodox quantum mechanics; 
2) results of observations of two particles cannot be different if operators acting on different particles commute. From this knowledge of yours, it logically 
follows that the results of observations of two particles cannot be different according to the orthodox quantum mechanics. But the results of observations of the first and second particles of the EPR pair are fundamentally different according to the equality (4) in the Bell article [1]. Consequently the equality (4), which provides the prediction of violation of Bell’s inequality, cannot be correct according to  the orthodox quantum mechanics.

You wrote: “The quantum state of two separated particles is by definition a non-local thing”. Earlier, May 1 you wrote in the discussion about “Bell's Blunder”: “I would like to see 
Alexei’s definition of “locality", and his definition of "quantum state ``''. I provided my definitions of “locality" and "quantum state” May 1. I wrote: “The mass delusion about quantum 
mechanics was provoked, first of all, by the fact that the quantum state has two different definitions: subjective and objective. According to the subjective definition, proposed by Born, 
the quantum state describes the observer's knowledge of the probability of the result of an upcoming observation. For example, the EPR state describes the knowledge that the first 
measurement of spin projection in any direction of one of the two particles will give spin up with probability 1/2. According to the objective definition spin states of non-entangled 
particles exist really in the real three-dimensional space”.  

When you write that “The quantum state of two separated particles is by definition a non-local thing” you use the objective definition. But the objective definition cannot be applied to 
the entangled spin states according mathematics, since entangled spin states, such as the EPR state and the GHSZ state, cannot be eigenstates and the operators of finite rotations of 
coordinate system are not applicable to them, see my manuscript “Physical thinking and the GHZ theorem”. The entangled spin states can describe only the observer's knowledge of 
the probability of the result of an upcoming observation. Schrodinger defined in 1935 the EPR correlation as entanglement of our knowledge. This definition is the only one possible 
according to mathematics. Bohm considered in 1951 the EPR state as a non-local thing, contrary to logic and mathematics. Bohm misled not only most physicists, but even Bell. 
Bohm and Bell were wrong rather than you.

[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).

With best wishes,

Alexey

пн, 2 мая 2022 г. в 23:32, Richard Gill <gill...@gmail.com>:

[Richard Gill]

Alexei

Equation (4) in “Bertlmann’s socks” does not say that the results of the first and second particles are different. It is easy to compute. The easiest way is to compute the expectations of the two spin observables (zero), and the expectations of their squares (plus one) and of their product ( - cos (a-b) ). From those five numbers, and knowing the particles can be measured together, we can deduce the probabilities in Bell’s Equation (4). Would you like me to do this calculation for you?

I do not use what you call the “objective definition” of the quantum state. Why do you think that? I use what you call the “subjective definition”.

I would call it an interpretation, not a definition.

Richard

Sent from my iPad

[Алексей Никулов]

Dear Richard, 
You surprised me! You claim that 1/2 is not different from sin^{2}(a-b)/2! I draw your attention that quantum mechanics predicts the same result for two measurements of single 
particles which Bell predicted in equation (4) in “Bertlmann’s socks” [1] for two particles of the EPR pair. The first measurement of single particles along a direction with an angle “a” 
relative to the given direction should give spin up with the probability 1/2 when particles are in random states. But the probability to observe spin down at the second measurements 
will depend both the angles of the first “a” and second “b” measurements due to the Dirac jump which postulates ”that a measurement always causes the system to jump into an 
eigenstate of the dynamical variable that is being measured” [2].  All particles jump into the same eigenstate in the direction with the angle “a” after the first measurement. The 
probability to observe spin down at the second measurement in the direction with the angle “b” is calculated uniquely using the operators of finite rotations of the coordinate system, 
see [3]. Therefore, quantum mechanics predicts for two measurements of single particles the probability 0.5sin^{2}(a-b)/2 predicted by equation (4) in “Bertlmann’s socks” [1]. 
I draw your attention that this prediction could be impossible without the Dirac jump, the operators of finite rotations of coordinate system and if the operators of measurements of spin 
projections of the same particles in different directions “a” and  “b” commute.  According to the orthodox quantum mechanics the operators fail to commute when they act on the 
same particle. Therefore the orthodox quantum mechanics predicts the violation of the trivial inequality (4) in section 4. THE ASSUMPTION USED AT THE DEDUCTION OF 
THE GHZ THEOREM MAKES IMPOSSIBLE THE PREDICTION OF VIOLATION OF BELL’S INEQUALITIES of my manuscript “Physical thinking and the GHZ theorem”, 
which you do not want to read. 
But the orthodox quantum mechanics cannot predicts violation of Bell’s inequality (equation (8) in my manuscript) because of two reasons: 1) operators acting on different particles 
commute according to the orthodox quantum mechanics; 2) Dirac postulated that only measured particle jumps into an eigenstate of the dynamical variable that is being measured, and 
therefore the spin state of other particles cannot change. The particles of the EPR pair (1) jump in the state (2) in my manuscript according to the Dirac jump. No correlation can be in this 
case between results of measurements of the first and second particles. The EPR correlation can be only if the both particles jump in the state (3) in my manuscript when one of the 
particles is measured. This jump, postulated by Bohm in 1951, not only contradicts the orthodox quantum mechanics, but also logically leads to the absurd, see section 6. THE 
REJECTION OF REALISM RESULTS TO THE ABSURD in my manuscript. 
Bell wrote for physicists. Therefore, he did not explain in sufficient detail from which principles of quantum mechanics equation (4) in “Bertlmann’s socks” [1] is derived. Apparently 
this has misled you. But, even many physicists do not understand the necessity of the Dirac jump and its sense.   

[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).

[2] A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, 1958).

[3] L. D. Landau, E. M. Lifshitz, Quantum Mechanics: NonRelativistic Theory (Volume 3, Third Edition, Elsevier Science, Oxford, 1977).

With best wishes,

Alexey

вт, 3 мая 2022 г. в 07:05, Richard Gill <gill...@gmail.com>:

[Richard Gill]

Alexei, I did not claim that. You are confusing marginal and conditional probability.

Sent from my iPhone

[Алексей Никулов]

Dear Richard, 
I think that you are confusing quantum mechanics and theory of probability. Bell deduced equation (4) in “Bertlmann’s socks” from quantum mechanics rather than theory of 
probability. I am not sure that Bell was knowing about marginal and conditional probability. But Bell was understanding that according to the expression for the EPR state 
(1/2)^{1/2}|+-> - (1/2)^{1/2}|-+> the measurement of the first particle will give spin up (+) with the probability 1/2 = (1/2)^{1/2}^{2}. Consequently sin^{2}(a-b)/2 in equation (4) in 
“Bertlmann’s socks” is the probability to observe spin up of the second particle. What does the marginal and conditional probability have to do with it? Can you deduce sin^{2}(a-b)/2 
from the marginal or conditional probability? But do you know how Bell derived the probability sin^{2}(a-b)/2 to observe spin up of the second particle from Bohm's quantum 
mechanics?

With best wishes,

Alexey

вт, 3 мая 2022 г. в 14:38, Richard Gill <gill...@gmail.com>:

[Richard Gill]

Quantum mechanics and probability theory are compatible. Consider spin observables on two particles. Denote them by a and b. They commute. Moreover, a, a^2, b, b^2 and ab all commute. They can therefore be measured simultaneously or separately and the probability distributions are compatible with one another. Thus we can define random variables A, A^2, B, B^2, AB, with the joint probability distribution of a joint measurement of all five and they satisfy the same functional relations as the observables. For the singlet state, we find E(A) = E(B) = 0, A^2 = B^2 = 1 with probability 1, E(AB) = - cos(alpha - beta). From this we deduce that the pair (A, B) takes on the four values (+/-1, +/-1) with the probabilities given by Bell.

This is all very well known. The computations are a standard exercise in a first course in modern quantum information theory.

Sent from my iPad

[Алексей Никулов]

Dear Richard, 
I think you don't understand at all why Bohm's quantum mechanics predicts the violation of Bell's inequalities. What you wrote, you probably read from authors like M. A. Nielsen and 
I. L. Chuang, who does not understand quantum mechanics. The expectation value E(AB) = - cos(alpha — beta), which you wrote, is deduced from equation (4) in “Bertlmann’s socks”.
 But where do the values of 1/2 and sin^{2}(a-b)/2 in equation (4) come from? You do not take into account that even when the joint probability is determined the spin projection of 
each particle is measured and the result depends on whether the measurement of one particle affects the state of other particles. Such an effect cannot be if the operators (rather than 
observables) acting on different particles commute. The value sin^{2}(a-b)/2 cannot be in principle in equation (4) in “Bertlmann’s socks” since the probability to observe spin up of 
the second particle in a direction “b” cannot depend on the direction “a”, in which the first particle was measured, if the measurement of the first particle does not the state of the second 
particle. 

You don't seem to understand very well that Bell's inequality was provoked by the quantum dispute between Einstein and Bohr about the EPR paradox. Einstein argued that measuring one particle cannot change the state of another particle, and Bohr disputed this. If most physicists understood quantum mechanics, they would have to understand that Einstein is right, since measuring one particle cannot change the state of another particle according to the principle of quantum mechanics that operators acting on different particles commute. But most physicists rather believe than understand quantum mechanics. Therefore they concluded that Bohr rather than Einstein was right. Only this blind faith can have provoked this comedy with EPR correlation and Bell inequalities.

With best wishes,

Alexey

вт, 3 мая 2022 г. в 21:03, Richard Gill <gill...@gmail.com>:

[Richard Gill]

Alexei. 

I told you how to do the computations. 

What you said about a - b is nonsense. The probability to observe both particles up given the two settings can obviously depend on both settings.

Sent from my iPhone

[Алексей Никулов]

Dear Richard,

The probability to observe one of the two particles of the EPR pair can depend on both settings only if the observation of one particle can change the state of another particle. You keep forgetting that the only point of Bell's inequalities is to determine whether the measurement of one particle affects the state of another particle. You state that such an effect should always be, according to your mathematics. But in this case, Bell's inequalities lose any sense. You don't want to understand that Bell's inequalities have nothing to do with probability theory and mathematics in general, since they are mathematically trivial. Bell's inequality is deduced under one condition: the turn of her analyzer by Alice cannot influence the result of the measurement by Bohm of his particle.

Mathematicians, for example you and Frank Lad (Department of Mathematics and Statistics, University of Canterbury, New Zealand) argue about Bell's inequalities only because they can't believe that quantum mechanics, which almost all physicists believe in, is absurd. Frank Lad submitted three manuscripts to the Special Issue "Violation of Bell’s Inequalities and the Idea of a Quantum Computer" https://www.mdpi.com/journal/entropy/special_issues/Bell_Inequalities : “Quantum violations of Bell's inequality: a misunderstanding based on a mathematical error of neglect”, “The GHSZ argument: a gedankenexperiment requiring more denken” and “Resurrecting the principle of Local Realism and the prospect of supplementary variables”. I was Guest Editor of this Special Issue. I managed with great difficulty to publish only one article of Frank Lad [1], since most believe in Bell's inequalities. Frank Lad was expressing his indignation at Bell's inequalities quite emotionally. As a mathematician, he did not understand that one should be outraged not by Bell's inequalities, but by quantum mechanics.

You, like most people, do not want to admit that quantum mechanics is absurd, although it is obvious. I will try to explain the absurdity of quantum mechanics to you using the example of the EPR pair. According to the expression

EPR = (1/2)^{1/2}|A+B-> - (1/2)^{1/2}|A-B+> (1)

the first measurement will give spin up (+) with the probability 1/2. For this reason 1/2 is in equation (4) in “Bertlmann’s socks”. I draw your attention that the amplitude in the expression (1) for the EPR pair cannot differ from (1/2)^{1/2} since we cannot know which particle A or B will be measured first.

Thus, the first measurement of spin projection in any direction of one of the particles will give spin up (+) with probability 1/2. This mathematical fact means that the particles A and B in the EPR state (1) cannot have eigenstates in any direction since the measurement in eigenstate should give spin up (+) with probability 1. Eigenstates of both particles will appear only after the first observation. Eigenstates will appear according to both the orthodox quantum mechanics and Bohm's quantum mechanics. But the eigenstates of the particle, which is not measured, will depend on which quantum mechanics is used.

The orthodox quantum mechanics postulated in 1930 the Dirac jump according to which only measured particle jumps ”into an eigenstate of the dynamical variable that is being measured” [2]. The particles A and B will jump to the states

Dirac = |A+z1>[ (1/2)^{1/2}|B-> - (1/2)^{1/2}|B+>] (2)

according to the Dirac jump when Alice will see that her particle deflects up along the direction z1 in which she measures spin projection. The expression (2) predicts no correlation between results of observations of the A and B particles. Quantum mechanics can predict the EPR correlation only if not only a measured particle but also another particle which is not measured will jump ”into an eigenstate of the dynamical variable that is being measured”. Bohm postulated such a jump only in 1951 under the influence of Bohr's claim that measurement of one particle can change the state of another particle. Therefore I call this jump as the Bohr jump in the manuscript "Physical thinking and the GHZ theorem". The particles A and B will jump to the states

Bohr = |A+z1>|B-z1> (3)

according to the Bohr jump when Alice will see that her particle deflects up along the direction z1. The expression (3) provides the EPR correlation: spin projections of the A and B particles in the z1 direction are opposite with probability 1. This expression provides the probability sin^{2}(a-b)/2 for the second particle in equation (4) in “Bertlmann’s socks” together with the operators of finite rotation of the coordinate axes which can be applied to non-entangled states such as (2) and (3), but not to entangled states (1).

Quantum mechanics, both orthodox and Bohm's, is absurd since it postulates that the mind of the observer creates eigenstates (2) or (3) at observation.

[1] Lad, F. The GHSZ Argument: A Gedankenexperiment Requiring More Denken. Entropy 2020, 22, 759. https://doi.org/10.3390/e22070759 ; https://www.mdpi.com/1099-4300/22/7/759

[2] A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, 1958).

With best wishes,

Alexey

ср, 4 мая 2022 г. в 07:19, Richard Gill <gill...@gmail.com>:

[Alexandre de Castro]

Dear Alexey,
you raised a very important issue.

1/2 and sin^{2}(a-b)/2 [Eq (4) in “Bertlmann’s socks”] can be inferred from the Born rule, and Bell showed that Eq (4) is not compatible with Inequality (9).

However, it's possible to prove, arithmetically, that one can derive directly Eq (4) from Inequality (9).

Because of that, I believe that it's not possible to obtain a [conclusive] proof for Bell's theorem.

I think Bell's theorem is, indeed, an undecidable hypothesis.

Alexandre

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAKiL4iJ6n93HKEEUJR_sG%2B8bJLKDWR3kkv%3DVRcCcgLjZV6WQzg%40mail.gmail.com.

[Алексей Никулов]

Dear Richard,
Indeed, "The probability to observe one particle “up” or “down” does
not depend on the setting with which the other is measured" according
to the orthodox quantum mechanics. Therefore, orthodox quantum
mechanics cannot predict the EPR correlation and violation of Bell’
inequalities. The probability sin^{2}(a-b)/2 to observe “spin up” of
the second particle in equation (4) in “Bertlmann’s socks” depends on
the setting “a” with which the first particle is measured since Bell
followed Bohm's quantum mechanics rather than the orthodox quantum
mechanics.
Bohm postulated the EPR correlation with the help of an absurdity.
Most physicists believed in this absurdity because of the degradation
of physical thinking. This degradation is the result of the rejection
by the creators of quantum mechanics of realism, which is the
presupposition of every kind of physical thinking, as Einstein
understood. The creators rejected realism because of the impossibility
to realistically describe some quantum phenomena. They did not take
into account that the inability of our reason to describe
realistically some quantum phenomena reveals only the inability of our
reason, and not the absence of reality. Physicists must admit that the
possibilities of our reason may be limited even in the realm of our
experience in order physical thinking could be possible.

With best wishes,

Alexey


ср, 4 мая 2022 г. в 17:11, Alexandre de Castro <alx...@gmail.com>:

[Richard Gill]

If particle 2 has been measured and one knows the setting and the outcome, this changes the probability of the two outcomes when particle 1 is measured in any given direction. This holds under QM and it holds under LR. In itself, it is not surprising. It is a post-selection of a sun-population.

Sent from my iPhone

[Алексей Никулов]

Dear Alexandre,

I think that Bell's theorem appeared because of blind faith of most
physicists in quantum mechanics. Most physicists, in contrast to
Einstein, Schrodinger and few others, did not understand that Born’s
proposal to consider the Schrodinger wave function as a description of
the amplitude of the observation probability is a trick that is
misleading. Einstein as far back as 1927 during the discussion at the
Fifth Solvay Conference rightly noted that Born’s proposal ”leads to a
contradiction with the postulate of relativity”. This contradiction is
a consequence of two different definitions of the quantum state:
subjective and objective. I wrote about these two definitions on May
1.

According to the subjective definition, proposed by Born, the quantum

state describes the observer's knowledge about the probability of the

result of an upcoming observation. For example, the EPR state
describes the knowledge that the first measurement of spin projection
in any direction of one of the two particles will give spin up with

probability 1/2. On other hand, according to the objective definition
the quantum state exists really, i.e. regardless of the observer's
knowledge, between observations. For example, spin states of

non-entangled particles exist really in the real three-dimensional

space. Einstein drew attention back in 1927 that the quantum state
must change by jumping together with the observer's knowledge during
observation, in order quantum mechanics does not predict the absurd.
The needed jump was postulated first by Dirac in 1930 [1]. Dirac
postulated ”that a measurement always causes the system to jump into
an eigenstate of the dynamical variable that is being measured” [1].
Quantum mechanics could predict the possibility of observing a single
particle in several places in space, i.e. absurdity, without the Dirac
jump.

Dirac, like other creators of quantum mechanics, falsely substituted
"observation" for "measurement". Dirac postulated the Dirac jump on
the basis of the assumption that ”after the first measurement has been
made, there is no indeterminacy in the result of the second” [1]. It
is extremely surprising that neither Dirac nor numerous believers in
quantum mechanics could understand that no first measurement can
provide determinacy of the result of the second measurement. But we
know from our experience that after the first observation has been
made, there is no indeterminacy in the result of the second
observation since our knowledge changes at the first observation.
Thus, Dirac postulated the jump of the quantum state of the observed
system under the influence of the jump in the observer's knowledge.

But most physicists could not or did not want to understand this. They
preferred to believe that Dirac postulated the jump in the system
because of measurement rather than because of observation. The EPR
paradox and Bell's inequalities could only have appeared because of
the unwillingness of most physicists to think logically. Even Bohr
didn't want to think logically. He argued in his response to the EPR
that measurement can change the state of even the particle which is
not measured, and at any distance. Most physicists believed Bohr, not
Einstein, because they preferred to believe blindly rather than think
logically. Therefore Bohm postulated the Dirac jump for the particle
which is not measured. Thus, blind faith instead of logical thinking
provoked Bell's theorem.

[1] A.M. Dirac, The Principles of Quantum Mechanics (Oxford University
Press, 1958).

With best wishes,

Alexey

ср, 4 мая 2022 г. в 19:40, Richard Gill <gill...@gmail.com>: