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I've published a paper on local hidden variables with surprising consequences for Bells Theorem. It is available on https://goo.gl/K1vjCy

To the background of Bell's argument, the following comments: Since Bell published his theorem for the proof of distant action more than 50 years ago, no one has yet provided a proof of how this remote effect actually takes place. 

What's wrong with Bell's argument?

Bell had argued that if nature allowed only local effects, the results of polarization measurements would only depend on polarizer position and a possible hidden parameter. He then concluded that the expectation values of different measurements must be in a certain context, namely, that they followed Bell's inequality. If, as often measured, nature violates Bell's inequality, then, according to Bell, it can not be based on local effects. 

Bell has argued imprecisely. His theorem is valid only if the dependency of the polarization measurement results on polarizer position and hidden parameter is the only one possible. If other models are possible, which correctly predict the measured expectation values with entangled photon pairs, his theorem loses its generality. Bell has thus failed to prove the universality. A counter-example suffices to refute his theorem. I presented such a counterexample. The measurement results also depend on the polarization of the incoming photons.

Comments are welcome.

Hi Eugen, welcome to the forum.

You have fallen into the same ridiculous mathematical quagmire that countless others have; probably without even realizing it very much. After your eq.(19) you say, "...it also violates Bell's [4] inequality." It is mathematically impossible for anything to violate any of the Bell inequalities. What has happened is that you have "shifted" to a different inequality with a higher bound that is not at all violated. You should read more of some of the content about that on this forum. So, there is nothing wrong the Bell inequalities but that is what is wrong with Bell's theory. It doesn't really prove anything. All the Bell test experiments are just verifying that the predictions of QM are true. Nothing more; nothing less. They have nothing at all to say about hidden variables nor about realism.

I haven't studied your model much yet, but it seems like I have seen it somewhere else before.
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My recent twit on the subject: https://twitter.com/joy_jjc/status/957187530700582913.

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FrediFizzx wrote:
It is mathematically impossible for anything to violate any of the Bell inequalities.

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This is not true. How do you come to the conviction nothing can violate the Bell inequality? Read my paper. Then you see the model in section 3 reproduces the predictions of QM and thus violates the Bell inequality.

I didn’t say the mathematics of Bells inequality were wrong. In my contribution to this forum I talked about the Bell theorem postulated by him 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.” This was refuted by presenting a counter example.

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Esail, Welcome to the forum.

Fred is right and you --- and anyone else who thinks that a mathematical inequality can be violated by ANYTHING --- are clearly talking nonsense.

Moreover, your model presented in the above paper is non-local and thus does not refute Bell's argument. Your model respects parameter independence, but violates outcome independence and thus it is as non-local as quantum mechanics.

Here is a truly local model, of ALL quantum correlations, respecting both parameter and outcome independence: http://philsci-archive.pitt.edu/14305/.

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Joy Christian wrote:***

Your model respects parameter independence, but violates outcome independence and thus it is as non-local as quantum mechanics.

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This is not true. See page 895 of my paper:
"The rule that determines which polarizer exit a photon will take is the same for both sides. Dependencies between the photons on either side originate from the shared parameter lambda and not from a nonlocal influence of photon 1 upon photon 2."

Esail wrote:

Joy Christian wrote:***

Your model respects parameter independence, but violates outcome independence and thus it is as non-local as quantum mechanics.

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This is not true. See page 895 of my paper:
"The rule that determines which polarizer exit a photon will take is the same for both sides. Dependencies between the photons on either side originate from the shared parameter lambda and not from a nonlocal influence of photon 1 upon photon 2."

Sorry to disappoint you, but you have not refuted Bell's argument. His argument -- which in my opinion is simply wrong -- is very simple to understand. None of what is discussed in your paper has much to do with Bell's argument. His claim is quite simple. It does not involve any physics at all. He claimed that for local functions A(a, h) = +/-1 and B(b, h) = +/-1, where h is a shared randomness between Alice and Bob and a and b are freely chosen experimental settings, it is mathematically impossible to reproduce the averages < AB > = -a.b, < A > = 0, and < B > = 0 predicted by quantum mechanics for the singlet state. Anyone like you who wants to claim otherwise must explicitly write down local functions A(a, h) and B(b, h) exhibiting the above three averages. To do so, you are free to choose whatever physics and mathematics you like --- even completely wrong physics if you like. If you succeed, then you have refuted Bell. But in your paper I do not see the averages < AB > = -a.b, < A > = 0, and < B > = 0 for a pair of local functions A(a, h) = +/-1 and B(b, h) = +/-1. Until you demonstrate these averages, your paper has nothing much to do with Bell's claim.

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Joy Christian wrote:But in your paper I do not see the averages < AB > = -a.b, < A > = 0, and < B > = 0 for a pair of local functions A(a, h) = +/-1 and B(b, h) = +/-1. Until you demonstrate these averages, your paper has nothing much to do with Bell's claim.

With entangled photons <AB>= cos(2(beta-alpha)).
From equation 17 we obtain the expectation value correctly as
<AB> =E(alpha,beta)= cos(2(beta-alpha)).
<B> =0 can be obtained from
<B>= E(alpha,beta)+E(alpha+pi/2,beta) =cos(2(beta-alpha))+cos(2(beta-alpha)-pi))=0
<A> =0 vice versa.

I wrote:
Bell has argued imprecisely. His theorem is valid only if the dependency of the polarization measurement results on polarizer position and hidden parameter is the only one possible. If other models are possible, which correctly predict the measured expectation values with entangled photon pairs, his theorem loses its generality. Bell has thus failed to prove the universality. A counter-example suffices to refute his theorem. I presented such a counterexample. The measurement results also depend on the polarization of the incoming photons.

So A(alpha,lambda) is not an unambiguous function of alpha in my model.

Esail wrote:Bell has argued imprecisely. His theorem is valid only if the dependency of the polarization measurement results on polarizer position and hidden parameter is the only one possible. [In my model, the] measurement results also depend on the polarization of the incoming photons.

This makes your model non-local, even if the mathematics in it is all correct. It is not easy to refute Bell's argument without falling into many traps of non-locality.

Bell has argued correctly that the only way a model can be local is if A(a, h) depends only on a and h, and not on b or B, and likewise, B(b, h) depends only on b and h, and not on a or A. Your model does not satisfy these conditions and therefore it has fallen into one of the many traps of non-locality.

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Joy Christian wrote:This makes your model non-local, even if the mathematics in it is all correct. It is not easy to refute Bell's argument without falling into many traps of non-locality.

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I recommend you better read my paper and reply to the arguments in it. There is a proof of locality after equation 11.

Esail wrote:

Joy Christian wrote:This makes your model non-local, even if the mathematics in it is all correct. It is not easy to refute Bell's argument without falling into many traps of non-locality.

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I recommend you better read my paper and reply to the arguments in it. There is a proof of locality after equation 11.

I recommend that you first try to understand Bell's actual argument before trying to criticize it.

Your model is non-local, as I have pointed out in my previous posts.

But there are other people in this forum who may come to your aid.

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Esail,

On page 895 you write "the polarization of the incoming photon at side 2 depends on the setting of the polarizer at side 1 although there is no nonlocal action."

But this is the very definition of non-local. What kind of mechanism do you propose for the setting of the polarizer at side 1 to influence the polarization of the photon at side 2?

Heinera wrote:Esail,

On page 895 you write "the polarization of the incoming photon at side 2 depends on the setting of the polarizer at side 1 although there is no nonlocal action."

But this is the very definition of non-local. What kind of mechanism do you propose for the setting of the polarizer at side 1 to influence the polarization of the photon at side 2?

In fact, I think his model is similar to a non-local model that you did some time ago. Now where is that...

Heinera wrote:Esail,

On page 895 you write "the polarization of the incoming photon at side 2 depends on the setting of the polarizer at side 1 although there is no nonlocal action."

But this is the very definition of non-local. What kind of mechanism do you propose for the setting of the polarizer at side 1 to influence the polarization of the photon at side 2?

P1 is set to alpha. Then the polarizer at side 1 selects all photons with p-state alpha from the incoming photons having polarization 0° or 90°.
Those photons have peer photons at side 2 (polarization 90° or 0°) with p-state alpha+90°from the time of their creation in the source. This is clearly local.
According to model assumption M3 the polarization of the selected ensemble of photon 2 is then equal to the p-state alpha+90°. This is also local reasoning as it only refers to what is already present at side 2.

Esail wrote:

Heinera wrote:Esail,

On page 895 you write "the polarization of the incoming photon at side 2 depends on the setting of the polarizer at side 1 although there is no nonlocal action."

But this is the very definition of non-local. What kind of mechanism do you propose for the setting of the polarizer at side 1 to influence the polarization of the photon at side 2?

P1 is set to alpha. Then the polarizer at side 1 selects all photons with p-state alpha from the incoming photons having polarization 0° or 90°.
Those photons have peer photons at side 2 (polarization 90° or 0°) with p-state alpha+90°from the time of their creation in the source. This is clearly local.
According to model assumption M3 the polarization of the selected ensemble of photon 2 is then equal to the p-state alpha+90°. This is also local reasoning as it only refers to what is already present at side 2.

And what happens if the experimenter changes P1 from alpha to something else a split second before a photon arrives? What happens then to the polarization of the photon at side 2?

Heinera wrote:

Esail wrote:

Heinera wrote:Esail,

And what happens if the experimenter changes P1 from alpha to something else a split second before a photon arrives? What happens then to the polarization of the photon at side 2?

The ensemble for the measurement is selected by P1. If you change alpha no matter at what time you get a different ensemble at side 1 as well as at side 2, of course with a different polarization.

Esail wrote:
The ensemble for the measurement is selected by P1. If you change alpha no matter at what time you get a different ensemble at side 1 as well as at side 2, of course with a different polarization.

Then it sounds like you are exploiting the detection loophole (also known as the fair sampling loophole). See

https://en.wikipedia.org/wiki/Loopholes ... r_sampling

Heinera wrote:
Then it sounds like you are exploiting the detection loophole (also known as the fair sampling loophole).

Can you explain why you think I'm exploiting a loophole?

Esail wrote:

Heinera wrote:
Then it sounds like you are exploiting the detection loophole (also known as the fair sampling loophole).

Can you explain why you think I'm exploiting a loophole?

If you by changing the polarization of P1 can can cause a statistically different ensemble of photons to be detected at station 2, this violates the fair sampling assumption. Remember that the angle at P1 can be changed after the ensemble has been emitted by the source, if the distance between source and detector stations is sufficiently large.

Heinera wrote:If you by changing the polarization of P1 can can cause a statistically different ensemble of photons to be detected at station 2, this violates the fair sampling assumption.

I have to correct myself. Changing the angle of P1 does not change the ensemble detected by P2. Only the fraction of photon 2 whose peer was detected at P1 changes.