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The Paper “On a contextual model refuting Bell’s theorem” has now been published by the journal EPL (Europhysics Letters) and is available under
https://iopscience.iop.org/article/10.1209/0295-5075/134/10004

In this paper a contextual realistic model is presented which correctly predicts measurement results with entangled photons or spin ½ particles. Contextual models can have properties which are correlated with the setting of the measurement instruments. The reason for this is the indistinguishability of entangled particles.
Bell's theorem was refuted because he ignored contextual models in his reasoning. This also applies to any other theorem that claims that no local realistic model for quantum effects is possible, if they fail to rule out contextual models. These include, for example, the theorems of CHSH, GHZ and Hardy.
For over 55 years John Bell has misled the physicists community and made us believe that nature does show superluminal non-local interactions. This could have been proven experimentally, since the correlations of quantum physics violate Bell's inequality. But so far nobody has found the slightest hint of how those non-local interaction work. Now we know that the assumption of spooky action at a distance as Einstein called it, is unfounded. The correlations can be explained locally.

This also makes it clear that particles cannot be in different incompatible spin states at the same time. If that were the case, non-local interactions would have to occur with entangled particles because the measurement of the spin on one particle means that the opposite spin is measured on the other particle, regardless of the distance. As a consequence, the concept of a quantum computer also comes into question, as it relies upon the assumption that a quantum system bears simultaneous information about two mutually exclusive outcomes. As this assumption is no longer tenable, the diversity of the solution of a quantum computer is considerably restricted.

Congratulations! I hope to come back later with questions about your model.

I do not understand the following:
You initially have two photons with or H/V polarisations. The Horizontal polarized photon goes to Alice and sets her polarizer at . You say the photon selection is changed to . What does changing the photon selection mean? You have only one photon at Alice's location with either H or V polarization, how can you select a different polarization?

Juso, I don't understand what you mean, maybe you cite the passage in the paper you are talking about

Esail wrote:Juso, I don't understand what you mean, maybe you cite the passage in the paper you are talking about
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"Predicting measurement results for an arbitrary context
We now calculate probabilities for an arbitrary setting of the polarizers; that is, having polarizer PA set to α and polarizer PB set to β. This means changing the selections of the photons. In the initial context (0°/90°), the generated photons with 0° polarization and 90° polarization comprised the selection. Now, the selection is changed and, so, the polarization of the photons —which is defined by model assumption MA3—is also changed.

If PA is set to α, all selected photons 1 which take PA exit α have peer photons 2 which would take a polarizer PB' exit , as we have seen above."

It seems that you initially have, for instance, a Horizontal(or Vertical) polarization going to Alice. But then if Alice puts her setting to the selection is changed from 0(or 90) to . What does changing the selection means? How a photon that is Horizontally( or Vertitally) polarized change to ?

Justo wrote:
It seems that you initially have, for instance, a Horizontal(or Vertical) polarization going to Alice. But then if Alice puts her setting to the selection is changed from 0(or 90) to . What does changing the selection means? How a photon that is Horizontally( or Vertitally) polarized change to ?

See
Model assumption MA3: Selected photons from each wing of the singlet state which would take a polarizer exit α have polarization phi= alpha . With a selection other than the initial context, all information about the origin from the initial context is lost.

A selection comprises all photons which take the same polarizer exit. Photons with polarization α and α+pi/2 come in equal shares, due to symmetry. MA3 accounts for the fact that the polarization of photons from the singlet state is undefined (due to indistinguishability) but changed and redefined by entanglement. Thus, the photons of a selection cannot be distinguished by their polarization. For a selection of the initial states 0° or 90°, the polarization is not changed as it is already equal to the selected state.

Esail wrote:

Justo wrote:
It seems that you initially have, for instance, a Horizontal(or Vertical) polarization going to Alice. But then if Alice puts her setting to the selection is changed from 0(or 90) to . What does changing the selection means? How a photon that is Horizontally( or Vertitally) polarized change to ?

See
Model assumption MA3: Selected photons from each wing of the singlet state which would take a polarizer exit α have polarization phi= alpha . With a selection other than the initial context, all information about the origin from the initial context is lost.

A selection comprises all photons which take the same polarizer exit. Photons with polarization α and α+pi/2 come in equal shares, due to symmetry. MA3 accounts for the fact that the polarization of photons from the singlet state is undefined (due to indistinguishability) but changed and redefined by entanglement. Thus, the photons of a selection cannot be distinguished by their polarization. For a selection of the initial states 0° or 90°, the polarization is not changed as it is already equal to the selected state.

I still do not know if I understand correctly but it seems that what you say makes sense only if we consider an isotropic population of entangled photons from which the polarizer "select" an entangled pair. I that correct?

Maybe Fred Diether would like to program this model. A working computer simulation which could run on a computer network with only forwards connections from a source computer to two measurement station computers would certainly make this paper, and the computer programmer, world famous. That’s because a number of famous mathematical theorems say it is impossible. It’s always exciting to find a contradiction. It gives an opportunity to make some progress.
https://arxiv.org/abs/2012.00719

Justo wrote:
I still do not know if I understand correctly but it seems that what you say makes sense only if we consider an isotropic population of entangled photons from which the polarizer "select" an entangled pair. I that correct?

I don't know what you mean with isotropic. The initial context comprises of beams of 0° and 90° polarized photons in equal shares, each with lambda values statistically distributed in the range 0-1.

gill1109 wrote:Maybe Fred Diether would like to program this model.

You can make a computer program calculating the model results. But you need to implement the contextual properties of the model though. Otherwise you have a non-contextual model which after KS cannot meet the results of QM.

Esail wrote:

gill1109 wrote:Maybe Fred Diether would like to program this model.

You can make a computer program calculating the model results. But you need to implement the contextual properties of the model though. Otherwise you have a non-contextual model which after KS cannot meet the results of QM.

We have been discussing your model in some FaceBook threads. Your model allows statistical dependence between measurement settings and hidden variables driving the physics in source and detectors. If you would try to implement this model in a distributed computer simulation you would be forced either to prevent the experimenter from freely choosing the settings, or to allow communication between the detection systems (possibly via the source). That means: non-local; or retrocausal.

Local contextuality is no issue. This has been known for ages. But you need global contextuality (or conspiracy or superdeterminism...)

gill1109 wrote:

Esail wrote:
You can make a computer program calculating the model results. But you need to implement the contextual properties of the model though. Otherwise you have a non-contextual model which after KS cannot meet the results of QM.

We have been discussing your model in some FaceBook threads. Your model allows statistical dependence between measurement settings and hidden variables driving the physics in source and detectors. If you would try to implement this model in a distributed computer simulation you would be forced either to prevent the experimenter from freely choosing the settings, or to allow communication between the detection systems (possibly via the source). That means: non-local; or retrocausal.

It is a property of photon pairs from the singlet state that if photon 1 hits a polarizer PA set to alpha photon 2 definitely hits a polarizer PB set to alpha+pi/2. This doesn't require any communication between the two photons but comes 1. from the initial context with the polarization of the photons orthogonal to each other plus 2. the common parameter lambda.
This property was proved in the paper and has to be implemented in the computer program.
The contextual behaviour (MA3) that photons selected by a polarizer have the polarization given by the polarizer's setting has also to be implemented in the computer program. Together you get the required results.

Esail wrote:

gill1109 wrote:

Esail wrote:
You can make a computer program calculating the model results. But you need to implement the contextual properties of the model though. Otherwise you have a non-contextual model which after KS cannot meet the results of QM.

We have been discussing your model in some FaceBook threads. Your model allows statistical dependence between measurement settings and hidden variables driving the physics in source and detectors. If you would try to implement this model in a distributed computer simulation you would be forced either to prevent the experimenter from freely choosing the settings, or to allow communication between the detection systems (possibly via the source). That means: non-local; or retrocausal.

It is a property of photon pairs from the singlet state that if photon 1 hits a polarizer PA set to alpha photon 2 definitely hits a polarizer PB set to alpha+pi/2. This doesn't require any communication between the two photons but comes 1. from the initial context with the polarization of the photons orthogonal to each other plus 2. the common parameter lambda.
This property was proved in the paper and has to be implemented in the computer program.
The contextual behaviour (MA3) that photons selected by a polarizer have the polarization given by the polarizer's setting has also to be implemented in the computer program. Together you get the required results.

Please implement this in your computer programs! Note: plural! Source, Detector 1, Detector 2. User1 may freely submit settings to Detector1 and User2 to Detector2. Measurement outcomes come out of Detector1 and Detector2.

Of course, you may write just one program. As long as it has a minimal set of essential features (User supplies settings, Program generates outcomes, RNG "set.seed" facility for 100% reproducibility) I can test it to check that it could in principle be "modularised". However, when you sit down and think about that programming task (you can for instance write down specifications which you could give to a programmer) you will discover that it can't be done. ie your maths can't be implemented in that way.

gill1109 wrote:

Esail wrote:
It is a property of photon pairs from the singlet state that if photon 1 hits a polarizer PA set to alpha photon 2 definitely hits a polarizer PB set to alpha+pi/2. This doesn't require any communication between the two photons but comes 1. from the initial context with the polarization of the photons orthogonal to each other plus 2. the common parameter lambda.
This property was proved in the paper and has to be implemented in the computer program.
The contextual behaviour (MA3) that photons selected by a polarizer have the polarization given by the polarizer's setting has also to be implemented in the computer program. Together you get the required results.

However, when you sit down and think about that programming task (you can for instance write down specifications which you could give to a programmer) you will discover that it can't be done. ie your maths can't be implemented in that way.

I've explained the procedure clearly above and in the paper. In order to refute my model you've got to show any contradiction. This is how scientific discussions work.

Esail wrote:I've explained the procedure clearly above and in the paper. In order to refute my model you've got to show any contradiction. This is how scientific discussions work.

Actually, there is nothing to refute. The model is obviously nonlocal hence cannot be a refutation of the Bell theorem.

Justo wrote:

Esail wrote:I've explained the procedure clearly above and in the paper. In order to refute my model you've got to show any contradiction. This is how scientific discussions work.

Actually, there is nothing to refute. The model is obviously nonlocal hence cannot be a refutation of the Bell theorem.

This was pointed out to Esail by several people in an earlier thread. Here is one of my posts in that thread: viewtopic.php?f=6&t=444&start=40#p11249

The discussion is futile. The model, as you say, is manifestly nonlocal (or remotely contextual). Moreover, it is based on a misunderstanding of Bell's argument regarding contextuality.
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Joy Christian wrote:This was pointed out to Esail by several people in an earlier thread. Here is one of my posts in that thread: viewtopic.php?f=6&t=444&start=40#p11249

The discussion is futile. The model, as you say, is manifestly nonlocal (or remotely contextual). Moreover, it is based on a misunderstanding of Bell's argument regarding contextuality.
.

The situation is very weird indeed. I found this discussion on ResearchGate where Karl Hess and colleagues also explain this to Esail two years ago. It seems that everybody noticed the nonlocal character of the model except the reviewers of EPL https://www.researchgate.net/project/To ... ickThrough

I have posted my paper in Physics Forums -Quantum Physics. But I have deleted my account there because of inappropriate behavior (censorship) of a moderator.

There were though two remarks open which I do repeat here and answer as they may be of general interest.

First remark: Someone wrote the model were inconsistent with QM and presented the following example:

Let's measure the polarization at the same angle α=β=π/3 (φ1=0,φ2=π/2). Now δ1=π/3,δ2=−π/6 and hence we have A=1 when λ<=1/4 and B=−1 when λ<=3/4 so that the A,B measurement results matching or not is not guaranteed, but varies with λ which is inconsistent with QM.

Answer: The model was not correctly applied for the case δ2=−π/6.

From the paper we obtain that δ is defined in the value range 0≤δ<π/2.
“The case π/2≤δ<π, is covered referring to the other exit of the polarizer. δ<0 is covered by reversing the polarizer direction by 180°. Thus, −π≤δ<−π/2 is equivalent to 0≤δ<π/2 and −π/2≤δ<0 is equivalent to π/2≤δ<π.”

In the example above we have δ2=−π/6. So we have to reverse the direction and get δ2’=−π/6+ π = 5π/6. As 5π/6 > π/2 we have to refer to the other exit and change the sign of B.
Thus we get B=-1 for λ<=1/4 and B=+1 for λ>1/4 and thus no match for α=β=π/3.
So the model is consistent with QM!

Second remark: someone else wrote:
I think the model is in fact nonlocal, so it has a potential to be consistent with QM. This is seen in the paragraph around Eq. (9). In particular, before (9) it says that it uses
δ=α+π/2−β
It's not clear to me how exactly did he get this formula, but this formula is nonlocal. It is nonlocal because α is a property of one apparatus, while β is a property of the other apparatus. Or if the author still claims that this formula has a local origin, it would help if he could better explain how did he obtain this formula, because to me it's not clear from the paper.

Answer: The paper reads:
“If PA is set to α, all selected photons 1 which take PA exit α have peer photons 2 which would take a polarizer PB' exit α+π/2, as we have seen above.
The polarizer PB set to β selects all photons 2 which would take PB exit β. By MA3, the polarization of the selected photons 2 is equal to the polarizer setting β. In order to identify matching events with PA at α and PB at β we need to find all photons 2 with polarization β which would pass an assumed polarizer PB' at side B set to α+π/2. Those photons 2 have a peer photon 1 which would take PA exit α as we have shown above. The probability that photons 2 with polarization β would pass PB' at α + π/2 can be obtained by eqs. (4), (4a), using δ=α+π/2−β, “

Local means that the measurement results do not depend on superluminal communication between the two sides. (Einstein locality condition)
So imagine Bob with his polarizer PB is on the earth and Alice with her polarizer PA is on the moon, 1 light second apart from the earth. Bob measures a photon 2 having the parameter lambda0. He then calculates a list of possible outcomes at A for any possible setting angle α of Alice’s polarizer. He then stores this list in a safe 0.1 second after he obtained the result. 0.5 seconds after the peer photon 1 has left the earth Alice sets her polarizer to α0 and sends this information to Bob via a classical channel.
After Bob gets this information he opens the safe and picks the outcome from the list for the submitted value of α0. A match occurs if this outcome is +1.

So the outcome for A is determined (at the time of storing the list in Bob’s safe) even before Alice has obtained her measurement results. And the outcome for B is defined before Alice has set her polarizer.

This is clearly local as the measurement results do not depend on superluminal communication between the two sides!

Esail wrote:
Local means that the measurement results do not depend on superluminal communication between the two sides. (Einstein locality condition)

No. That is not what local means in the context of Bell's theorem. The nonlocality Bell was concerned about has little to do with superluminal communication. The nonlocality that is of concern in Bell's theorem is called no-signaling nonlocality, or, more precisely, "outcome dependence." Thus, I am afraid, you are barking on the wrong tree.

Esail wrote:

So the outcome for A is determined (at the time of storing the list in Bob’s safe) even before Alice has obtained her measurement results. And the outcome for B is defined before Alice has set her polarizer.

This is clearly local as the measurement results do not depend on superluminal communication between the two sides!

See my previous comment. "No superluminal communication" is a necessary but not sufficient condition for establishing Bell locality. Your model is manifestly nonlocal in Bell's sense.
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Joy Christian wrote:Your model is manifestly nonlocal in Bell's sense.
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Can you show explicitely where my model is nonlocal in Bell's sense?