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I’ve posted an update of my preprint “On a contextual model refuting Bell's Theorem”
on ResearchGate https://www.researchgate.net/deref/http ... qJdKwYZAJQ

In the preprint, a local model is presented, which precisely makes the quantum mechanical predictions for measurement results on entangled photons or spin 1/2 particles. In the previous version, some readers had difficulty understanding that the model presented is really local. These problems have been addressed in this version through clearer explanations of the individual assumptions and their consequences.

My interest in the discussion is in two things:
1. The assessment of contextuality based on the indistinguishability of the particles
2. The discussion of the consequences of a local hidden variable model for our understanding of the quantum world

Esail wrote:I’ve posted an update of my preprint “On a contextual model refuting Bell's Theorem”
on ResearchGate DOI: 10.13140/RG.2.2.28737.38242

In the preprint, a local model is presented, which precisely makes the quantum mechanical predictions for measurement results on entangled photons or spin 1/2 particles. In the previous version, some readers had difficulty understanding that the model presented is really local. These problems have been addressed in this version through clearer explanations of the individual assumptions and their consequences.

My interest in the discussion is in two things:
1. The assessment of contextuality based on the indistinguishability of the particles
2. The discussion of the consequences of a local hidden variable model for our understanding of the quantum world

I couldn’t find the preprint using the DOI. But I found your name from earlier postings, and from there found your ResearchGate pages, and from there your latest paper.
https://www.researchgate.net/publicatio ... 7s_Theorem

The link to RG is now active,
Thanks

I'm afraid this model is not "local". The description of what happens to the particles going to detector 2 just before equation (20) depends on delta = beta - alpha - pi.

Bell did not have a problem with contextuality. A local context (at each measurement station) is not an issue. His problem was the conjunction of locality and realism.

gill1109 wrote:
I'm afraid this model is not "local". The description of what happens to the particles going to detector 2 just before equation (20) depends on delta = beta - alpha - pi.

Bell did not have a problem with contextuality. A local context (at each measurement station) is not an issue. His problem was the conjunction of locality and realism.

These points have been pointed out to Esail many times before but, for some incomprehensible reasons, he does not accept that his model is manifestly nonlocal.
.

gill1109 wrote:I'm afraid this model is not "local". The description of what happens to the particles going to detector 2 just before equation (20) depends on delta = beta - alpha - pi.

I have clearly and precisely described my assumptions and derivations in my manuscript. Only this can be the basis for a scientific discussion. There is no point in picking out a term and drawing further conclusions from it. You have to look at the whole derivation and apply your arguments to it. When developing a model, every single formulation counts.

Esail wrote:

gill1109 wrote:I'm afraid this model is not "local". The description of what happens to the particles going to detector 2 just before equation (20) depends on delta = beta - alpha - pi.

I have clearly and precisely described my assumptions and derivations in my manuscript. Only this can be the basis for a scientific discussion. There is no point in picking out a term and drawing further conclusions from it. You have to look at the whole derivation and apply your arguments to it. When developing a model, every single formulation counts.

I disagree. I don’t draw my conclusion just from one equation.

But we don’t have to have a discussion.

I suggest you implement your model as a computer program. I will then be able to check whether or not it is local. If it is local you can apply for a prize of 64 000 Euro from me. https://www.math.leidenuniv.nl/~gill/gull.pdf

Your paper contradicts very well known and generally accepted mathematical theorems. You don’t explain what is wrong with the proofs of those theorems. I make the point I make, in order to help you find out what you are doing wrong, in case you are worried that you might have made a mistake somewhere. And in case other people on this forum are interested in figuring that out.

I hope you can get your paper published in a good journal.

gill1109 wrote:Your paper contradicts very well known and generally accepted mathematical theorems. You don’t explain what is wrong with the proofs of those theorems.

It is completely clear that the parameters alpha and beta must appear in a model, simply because these are freely selectable boundary conditions. One cannot conclude from this that the model is not local or wrong. In order to refute the model, one must deal with the course and the details of the derivation.

Bell's theorem is not a mathematical proof (his inequality is mathematically correct) but the claim that there can be no local model. He overlooked contextual models. This is also stated in the paper. This is not about mathematical questions, but about the physical question of what effects the indistinguishability of particles has.
Physical discussions can be decided without a computer program. Computer programs are not proof and only cover up the essence that matters.

Esail wrote:

gill1109 wrote:Your paper contradicts very well known and generally accepted mathematical theorems. You don’t explain what is wrong with the proofs of those theorems.

It is completely clear that the parameters alpha and beta must appear in a model, simply because these are freely selectable boundary conditions. One cannot conclude from this that the model is not local or wrong. In order to refute the model, one must deal with the course and the details of the derivation.

Bell's theorem is not a mathematical proof (his inequality is mathematically correct) but the claim that there can be no local model. He overlooked contextual models. This is also stated in the paper. This is not about mathematical questions, but about the physical question of what effects the indistinguishability of particles has.
Physical discussions can be decided without a computer program. Computer programs are not proof and only cover up the essence that matters.

Bell did *not* overlook contextual models. I am not talking about his inequality. I'm talking about his claim that QM and local realism are incompatible. That's also a mathematical theorem.

I don't have to refute your model because I have mathematical proof that your model is not local, and I believe that my proof is correct. You don't believe or don't understand my proof. You do not point out where it is wrong, either.

I don't need to convince you, or anyone else. Go ahead and submit your paper to a journal and try to convince someone else.

I just point out that you will easily convince the whole world, including me, and moreover get the Nobel prize, if you can implement your model in computer code. Otherwise, I'm afraid that I, and many others, are justified in believing you just have words, no proof of anything.

I am interested to know why you don't go ahead and do that.

gill1109 wrote:
I don't have to refute your model because I have mathematical proof that your model is not local, and I believe that my proof is correct. You don't believe or don't understand my proof. You do not point out where it is wrong, either.

Why don't you show us your proof that my model is not local?

Esail1 wrote:

gill1109 wrote:
I don't have to refute your model because I have mathematical proof that your model is not local, and I believe that my proof is correct. You don't believe or don't understand my proof. You do not point out where it is wrong, either.

Why don't you show us your proof that my model is not local?

My proof that your model is not local is Bell’s theorem.
Why don’t you show me the errors in my paper Gull’s Theorem Revisited https://arxiv.org/abs/2012.00719?

Why don’t you write computer code for your model which I can run and test? I don’t want to study some else’s computer code. I’ve done it before many times, done it enough. I don’t want to work through somebody else’s maths to find the mistake which I know must be there. It’s pointless, since you will not be convinced by my arguments.

I have developed methodology whereby I can test if an “EPR-B” app satisfies locality, and after that I can test if it reproduces the singlet correlations. Your EPR-B app can be used and tested by lots of people. Establishment conspiracy cannot stop it spreading round the world. You’ll get famous. You’ll get the Nobel prize.

gill1109 wrote:My proof that your model is not local is Bell’s theorem.

You say that a proof that Bell's theorem is wrong cannot be right because Bell's theorem is right. That's pretty absurd and illogical.

Esail wrote:

gill1109 wrote:My proof that your model is not local is Bell’s theorem.

You say that a proof that Bell's theorem is wrong cannot be right because Bell's theorem is right. That's pretty absurd and illogical.

What I said is very logical. If Bell’s theorem is right (because there is a correct proof of it) then there cannot be a correct proof that it is wrong. If someone alleges to have a disproof, their disproof is wrong.

Or are you suggesting that mathematics as we know it leads to self-contradiction, hence must be abandoned?

gill1109 wrote:If Bell’s theorem is right (because there is a correct proof of it) then there cannot be a correct proof that it is wrong. If someone alleges to have a disproof, their disproof is wrong.

Bell stated this theorem in his 1964 paper: “In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.”

There is no correct proof that Bell's theorem is right. Presenting a contextual local model would refute his theorem. This was done with my paper without you having refuted it.

Esail wrote:

gill1109 wrote:If Bell’s theorem is right (because there is a correct proof of it) then there cannot be a correct proof that it is wrong. If someone alleges to have a disproof, their disproof is wrong.

Bell stated this theorem in his 1964 paper: “In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.”

There is no correct proof that Bell's theorem is right. Presenting a contextual local model would refute his theorem. This was done with my paper without you having refuted it.

Dear “Esail”, I think there are correct proofs of Bell’s theorem. I am not going to look for errors in your paper. Maybe someone else feels like trying. But in my experience, once people think they have “found the error in Bell”, they will never ever change their mind. It becomes something like a religious conviction.

Now, I would be very interested if you could show me an error in my own work!

Alternatively, if you are right with your “counterexample” to Bell, you can write an app which shows you are right, without anyone having to check formulas or code. Go for it!

(Or get someone to do it for you. Several people in this forum are good programmers).

And good luck with getting your paper published, and then getting people to pay attention to it! Maybe you can find a programmer that way.

gill1109 wrote:I think there are correct proofs of Bell’s theorem.

Bell did not prove that his theorem was correct, only that a non-contextual model obeyed his (Bell's) inequality.

In a local contextual model, there are no definite properties of the particles because they are indistinguishable. Therefore, the measurement results depend on the selection of the particles by the measuring instrument (polarizer or Stern Gerlach apparatus). However, Bell did not consider these types of models.
This is why his claim that only non-local models can map the measurement results in the singlet state is simply wrong.

Esail wrote:

gill1109 wrote:I think there are correct proofs of Bell’s theorem.

Bell did not prove that his theorem was correct, only that a non-contextual model obeyed his (Bell's) inequality.

In a local contextual model, there are no definite properties of the particles because they are indistinguishable. Therefore, the measurement results depend on the selection of the particles by the measuring instrument (polarizer or Stern Gerlach apparatus). However, Bell did not consider these types of models.
This is why his claim that only non-local models can map the measurement results in the singlet state is simply wrong.

You are wrong, “Esail”. Please study Bell’s own “reply to critics”, http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423. His formulation does allow contextuality. Your criticism was made 50 years ago, and indeed, was made and is still repeated by prominent physicists, but is easily countered.

Get someone to program your model in an app which can run over internet or on any ordinary PC. Make sure that it satisfies the criteria I have laid out here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=460. Then no more discussion will be needed. Let me know if you consider the rules I laid out to be unfair.

gill1109 wrote: His (Bell’s () formulation does allow contextuality. .

This is not true. In a contextual model, measurement values do not exist unambiguously independent of the selected context. But in Bell's model from 1964 they do. Thus, his derivation in the 1964 paper cannot include contextual models. In Bell's response to the critic you mentioned, he did not dispel this objection either.

Esail wrote:

gill1109 wrote: His (Bell’s () formulation does allow contextuality. .

This is not true. In a contextual model, measurement values do not exist unambiguously independent of the selected context. But in Bell's model from 1964 they do. Thus, his derivation in the 1964 paper cannot include contextual models. In Bell's response to the critic you mentioned, he did not dispel this objection either.

It is true. Bell’s A(a, lambda) is an arbitrary function of the initial state of everything relevant in all of the physical systems involved - detectors, source, transmission lines - and of the setting “a”, which is later introduced into Alice’s detector, from outside. A dial on an apparatus is set to point at “a”. “lambda” is the context!

Do you claim your model can be programmed? Do you accept my rules - a proposed procedure to test that it correctly implements locality? Would it pass the tests which I’ve outlined?

gill1109 wrote:Bell’s A(a, lambda) is an arbitrary function of the initial state of everything relevant in all of the physical systems involved - detectors, source, transmission lines - and of the setting “a”, which is later introduced into Alice’s detector, from outside. A dial on an apparatus is set to point at “a”. “lambda” is the context!

Do you claim your model can be programmed? Do you accept my rules - a proposed procedure to test that it correctly implements locality? Would it pass the tests which I’ve outlined?

"lambda" in Bell's 1964 paper does not depend on the setting of either polarizer. The context on the other hand is given by the selection by the opposite polarizer. Thus, "lambda" cannot be the context.

By the way, my model can be programmed. But I refuse to do so. I'm a physicist and discuss arguments instead of computer programs. So do other physicists including Bell.