"Bell's theorem refuted" now published by EPL

[Joy Christian]

Joy, what do you mean by this: "Bell's mathematical formulation of what local means."

I mean the following (the image is taken from one of my recent papers: https://arxiv.org/pdf/1704.02876.pdf):



This is Bell's formulation of local causality. It simply crystallizes Einstein's conception of local causality, found in his writings on the subject, from the EPR paper onwards, until his death.
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[gill1109]

At last, thanks to you, Bell believers(like Richard and me) and Bell deniers(like Joy and Karl) agree on something. Congratulations!.

Just for the record, Justo, serious researchers like Karl and I have never challenged Bell's mathematical formulation of what local means. His formulation is simply a mathematically precise version of Einstein's conception of locality in the present context. You will find that several other Bell-challengers in this forum also agree with Bell what local means. Our disagreement lies elsewhere, as both Karl, I, and others have explained in our respective publications many times before. But you are right that all parties agree that the model published in EPL is not local.
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Joy, what do you mean by this: "Bell's mathematical formulation of what local means."

In my view, Bell-local is not the same as Einstein-local.
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So now we have heard what "Bell-local" means according to people on all sides of the great Bell divide. Now we need to know, Gordon, what you understand by "Einstein-local".

I would like to point out that conceptions of "local" and "realism" are often somewhat entangled. For instance, things that are not "real" obviously don't have to be localized. QM believers (in the sense of those who have no need of local realism at all since they see everything through the eyes of QM) believe that quantum theory is local, and they can even formulate this in a mathematically precise way. I think, however, that this is going too far. I think that using the words "local" and "real" means you are making a connection to concepts in our minds and in our cultures which existed long before physicists or mathematicians existed.

[Esail]

For a polarizer setting beta on side B we obtain delta = alpha+pi/2 - beta. Here B depends on the value of lambda.

Yes, it depends on the value of lambda but it also depends on the value of alpha and beta. A local function for Bob can only depend on beta and lambda. If it depends on alpha(Alice setting) it cannot be a local function.
That is what everybody here and also in ResearchGate is trying to tell you.

With a contextual model the polarization is not fixed but depends on the setting of a polarizer.
From the initial context we obtain that if the polarizer is set to alpha on side A the polarization of the thus selected peer photons 2 on side B is alpha+pi/2. This is immediately the case without communication between A and B.

We have shown in the paper that if photons 1 from the initial state (0° or 90° polarization) hit a polarizer set to alpha on side A then the peer photons 2 (90° or 0° polarization) definitely hit a polarizer on side B set to alpha + pi/2. Looking from the polarizer point of view we have photons 1 selected by polarizer set to alpha with peer photons 2 selected by polarizer set to alpha+pi/2. Due to MA3 the polarization of the those selected photons 1 and photon 2 are alpha and alpha+pi/2 respectively for any angle alpha.

So if we are looking at side B we have peer photons 2 with polarizaton alpha+pi/2 moving towards a polarizer set to beta. This is a completely local situation with no communication involved between the distant sides.

These are the same predictions which we already know from QM but QM doesn't tell us why.

[Justo]

With a contextual model the polarization is not fixed but depends on the setting of a polarizer.
From the initial context we obtain that if the polarizer is set to alpha on side A the polarization of the thus selected peer photons 2 on side B is alpha+pi/2. This is immediately the case without communication between A and B.

We have shown in the paper that if photons 1 from the initial state (0° or 90° polarization) hit a polarizer set to alpha on side A then the peer photons 2 (90° or 0° polarization) definitely hit a polarizer on side B set to alpha + pi/2. Looking from the polarizer point of view we have photons 1 selected by polarizer set to alpha with peer photons 2 selected by polarizer set to alpha+pi/2. Due to MA3 the polarization of the those selected photons 1 and photon 2 are alpha and alpha+pi/2 respectively for any angle alpha.

So if we are looking at side B we have peer photons 2 with polarizaton alpha+pi/2 moving towards a polarizer set to beta. This is a completely local situation with no communication involved between the distant sides.

These are the same predictions which we already know from QM but QM doesn't tell us why.

Dear Esail
No matter how you explain it. The mathematical expression of Bob's result after Alice's has made her measurement determines the nonlocal property of your model. Unless you propose a new definition of what should be "local", which you do not present in your paper, your model is unanimously considered, in this forum and elsewhere, nonlocal (except perhaps by referees of your paper).

[Gordon Watson]

At last, thanks to you, Bell believers(like Richard and me) and Bell deniers(like Joy and Karl) agree on something. Congratulations!.

Just for the record, Justo, serious researchers like Karl and I have never challenged Bell's mathematical formulation of what local means. His formulation is simply a mathematically precise version of Einstein's conception of locality in the present context. You will find that several other Bell-challengers in this forum also agree with Bell what local means. Our disagreement lies elsewhere, as both Karl, I, and others have explained in our respective publications many times before. But you are right that all parties agree that the model published in EPL is not local.
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Joy, what do you mean by this: "Bell's mathematical formulation of what local means."

In my view, Bell-local is not the same as Einstein-local.
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So now we have heard what "Bell-local" means according to people on all sides of the great Bell divide. Now we need to know, Gordon, what you understand by "Einstein-local".

I would like to point out that conceptions of "local" and "realism" are often somewhat entangled. For instance, things that are not "real" obviously don't have to be localized. QM believers (in the sense of those who have no need of local realism at all since they see everything through the eyes of QM) believe that quantum theory is local, and they can even formulate this in a mathematically precise way. I think, however, that this is going too far. I think that using the words "local" and "real" means you are making a connection to concepts in our minds and in our cultures which existed long before physicists or mathematicians existed.

Richard,

With E = Expectation and P = Probability:

1. Einstein-locality: See Bell (1964), eqn (1), A(a,λ) = ±1, B(b,λ) = ±1, ***

with E(a,b) = -a.b via my analysis, with experimental and QT confirmation.

2. Bell-locality: See Bell (2004), p.243, eqn (10), with P(AB|a,b,λ) = P(A|a,λ)P(B|b,λ),

but E(a,b) ≠ -a.b via Bell's analysis, with experimental and QT repudiation.

*** NB: Bell will later claim (2004), p.65, that such functions are impossible. Once more, against my analysis with its experimental and QT confirmation.

QED.
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[Esail]

With a contextual model the polarization is not fixed but depends on the setting of a polarizer.
From the initial context we obtain that if the polarizer is set to alpha on side A the polarization of the thus selected peer photons 2 on side B is alpha+pi/2. This is immediately the case without communication between A and B.

We have shown in the paper that if photons 1 from the initial state (0° or 90° polarization) hit a polarizer set to alpha on side A then the peer photons 2 (90° or 0° polarization) definitely hit a polarizer on side B set to alpha + pi/2. Looking from the polarizer point of view we have photons 1 selected by polarizer set to alpha with peer photons 2 selected by polarizer set to alpha+pi/2. Due to MA3 the polarization of the those selected photons 1 and photon 2 are alpha and alpha+pi/2 respectively for any angle alpha.

So if we are looking at side B we have peer photons 2 with polarizaton alpha+pi/2 moving towards a polarizer set to beta. This is a completely local situation with no communication involved between the distant sides.

These are the same predictions which we already know from QM but QM doesn't tell us why.

Dear Esail
No matter how you explain it. The mathematical expression of Bob's result after Alice's has made her measurement determines the nonlocal property of your model. Unless you propose a new definition of what should be "local", which you do not present in your paper, your model is unanimously considered, in this forum and elsewhere, nonlocal (except perhaps by referees of your paper).

Dear Justo,
It is unsatisfactory if you argue without responding to my arguments. I have proven what you think is impossible. Don't forget that in the explanation above the results for B are obtained under the condition that the result for A =1. So it is no wonder that under this condition the results for B depend on A as this condition means the polarization of the peer photons 2 is alpha+pi/2 without communication between side A and side B.

[FrediFizzx]

Maybe Fred Diether would like to program this model. ...

I tried to program his model. Can't be done without making it non-local.
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[Joy Christian]

I have proven what you think is impossible.

You have proven nothing until you are able to write down two local-realistic functions that comply with their definitions spelt out in the image below, together with a demonstration that those functions satisfy the following three averages: << A(a, h) >> = 0, << B(b, h) >> = 0, and << A(a, h)B(b, h) >> = -cos(a, b). Until you can do that, all you are doing is demonstrating to us that you have not understood what the actual problem Bell had identified. I suggest that you first try to understand the problem Bell had identified before claiming that you have solved it.


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[Austin Fearnley]

I seem to be the only person who thinks that you might have a local model. OTOH I may not understand your model fully.
Will you check a few numbers/probabilities to see if I am getting it right, please.

Set alpha = 0 degrees and beta = 22 degrees.
If the initial approach of a particle pair has polarisation angle at 10 degrees.
Then 97 % of such particles would have A = +1.
And 29% of such particles would have B = +1.
Is that correct?

This is using equations 4 and 4a for A values.
And using equations 4 and 4a with beta replacing alpha for B values.
(Surely the order of calculation of A and B can have no bearing on the outcomes.)

[Esail]

I have proven what you think is impossible.

You have proven nothing until you are able to write down two local-realistic functions that comply with their definitions spelt out in the image below, together with a demonstration that those functions satisfy the following three averages: << A(a, h) >> = 0, << B(b, h) >> = 0, and << A(a, h)B(b, h) >> = -cos(a, b). Until you can do that, all you are doing is demonstrating to us that you have not understood what the actual problem Bell had identified. I suggest that you first try to understand the problem Bell had identified before claiming that you have solved it.


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Correct were << A(a, h) >> = 0, << B(b, h) >> = 0, and << A(a, h)B(b, h) >> = -cos(a- b)
My model says for any chosen direction phi defining the initial context
A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).
With this we get in deed << A(a, h) >> = 0, and << B(b, h) >> = 0. see eq. (12) of the paper.
Also << A(a, h)B(b, h) >> = -cos(a- b) for spin 1/2 particles as shown in the paper eq. (14) and
<< A(a, h)B(b, h) >> = -cos(2(a- b)) for spin 1 particles as shown in the paper eq. (13). Could you happen not having read the paper?

[Joy Christian]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

These functions are manifestly nonlocal. You have not refuted anything.
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[Esail]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

These functions are manifestly nonlocal. You have not refuted anything.
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That's enough for me now, I had clearly explained

With a contextual model the polarization is not fixed but depends on the setting of a polarizer.
From the initial context we obtain that if the polarizer is set to alpha on side A the polarization of the thus selected peer photons 2 on side B is alpha+pi/2. This is immediately the case without communication between A and B.

We have shown in the paper that if photons 1 from the initial state (0° or 90° polarization) hit a polarizer set to alpha on side A then the peer photons 2 (90° or 0° polarization) definitely hit a polarizer on side B set to alpha + pi/2. Looking from the polarizer point of view we have photons 1 selected by polarizer set to alpha with peer photons 2 selected by polarizer set to alpha+pi/2. Due to MA3 the polarization of the those selected photons 1 and photon 2 are alpha and alpha+pi/2 respectively for any angle alpha.

So if we are looking at side B we have peer photons 2 with polarizaton alpha+pi/2 moving towards a polarizer set to beta. This is a completely local situation with no communication involved between the distant sides.

These are the same predictions which we already know from QM but QM doesn't tell us why.

One must at least deal with the arguments of the other side, otherwise the discussion is fruitless. What am I supposed to make of your arguments if you haven't even read the paper?

[Joy Christian]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

The discussion is indeed futile. You are unable to appreciate that the above functions are nonlocal.

The choice of the settings "a = a-phi" and "b = b-phi-pi/2" are not free and independent of each other.
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[Justo]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

The discussion is indeed futile. You are unable to appreciate that the above functions are nonlocal.

The choice of the settings "a = a-phi" and "b = b-phi-pi/2" are not free and independent of each other.
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I'm sorry Esail, Joy is correct. Your arguments are irrelevant because your equations are explicitly nonlocal. That is why Richard cannot program them.

[minkwe]

I'm a bit surprised that the key behind Esail's model is not obvious to everyone. It's not non-local, it's what is done in every Bell-test experiment to date, including the so-called "loophole-free" ones. They used to call it post-selection. These days they use the fancy term "heralding".

[Gordon Watson]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

The discussion is indeed futile. You are unable to appreciate that the above functions are nonlocal.

The choice of the settings "a = a-phi" and "b = b-phi-pi/2" are not free and independent of each other.
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Joy,

If Esail writes A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

Then this is wholly local: for A does not depend on b and B does not depend on a.

EDIT: See minkwe's post above!
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[Joy Christian]

I'm a bit surprised that the key behind Esail's model is not obvious to everyone. It's not non-local, it's what is done in every Bell-test experiment to date, including the so-called "loophole-free" ones. They used to call it post-selection. These days they use the fancy term "heralding".

I have not paid much attention to what they do in Bell-test experiments. I take your word for it. It is quite possible that experimentalists are cheating.

But theoretically, the two measurement functions Esail has written down are manifestly nonlocal:

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

They tell us that the settings on two sides are "a = a - phi" and "b = b - phi - pi/2". I am not bothered by pi/2 in b. But both settings depend on phi, which is not a hidden variable h. I don't care whether phi is chosen initially or at a later stage. If it is lumped with the hidden variable h, then the model is either superdeterministic or retrocausal because it influences the two settings either backward or forward in time. That is allowed, but it does not refute Bell's theorem. If phi is part of the settings, as it appears to be from what is written down by Esail, then a change in phi at Alice's end can induce a change in the setting b at Bob's end and vice versa. I don't care what verbal justification is given for such a change. It is evidently nonlocal action, happening at a spacelike distance. Thus the model violates the locality conditions of both Einstein and Bell.
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[Esail]

A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

The discussion is indeed futile. You are unable to appreciate that the above functions are nonlocal.

The choice of the settings "a = a-phi" and "b = b-phi-pi/2" are not free and independent of each other.
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Joy,

If Esail writes A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

Then this is wholly local: for A does not depend on b and B does not depend on a.

EDIT: See minkwe's post above!
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phi and phi+pi/2 are the initial context with phi=0° or phi =90°. As the problem is rotationally symmetric (phi, phi+pi/2) can be any pair of angles without changing the results for the statistical outcomes.

[Austin Fearnley]

Aha. (I seem to be talking to myself on this site ... ?)

Up to now I had assumed that the 'predicting' paragraphs of Esail's paper were merely post-experiment calculations but now I realise they are not.

As Esail's paper is a forwards-in-time model then photon 2 gets a very spooky (normal QM spookiness?) alteration of its polarisation setting after photon 1 is measured but before photon 2 is itself measured. That is why alpha (or alpha - pi/2 appears in the calculation of B (rather than beta) for photon 2. This of course means that the B measurement (at setting beta) is always carried out on a particle polarised along or against alpha. This will give the required Bell correlation of 0.7070 for alpha-beta =22.5 degrees. But this method uses spooky (QM type of spooky) action at a distance. Using the Malus Law variable of cos^2 (delta) ensures the 0.707 correlation as Alice is acting like the first polarisation filter in a Malus experiment while Bob is acting like the second filter in a Malus exeriment. The cos^2 probability ensures 85% of photons pass the second filter at 22.5 degrees, which is always equivalent to a correlation of 0.707.

I was at this stage in my Aug 2019 paper but I carried on by trying to remove the QM spookiness. I resolved the spookiness in my June 2020 paper. Most people would say that my retrocausal method is even spookier than QM spookiness, but I like the retrocausal method.

I wrote here about my retrocausal method to Richard:
viewtopic.php?f=6&t=460&start=60#p12795

There I wrote: "Alice's detector detects an electron arriving with a polarisation vector (that is, the electron's polarisation vector) aligned with Bob's detector angle because the measurement by Bob's detector changed the positron's polarisation vector (that is, the positron's polarisation vector) to align with or against Bob's detector's polarisation angle. That is the correct way around. The detectors change the particles' polarisation vectors. That is not spooky. The particles do not change the detector setting angles. Now if that were to happen it would be very spooky."

Esail's method has photon 2 change its polarisation vector before its measurement by Bob via spooky QM action-at-a-distance. My retrocausal method has photon 2 given an initial polarisation vector along or against alpha which does not change during its time of flight before it is measured by Bob. So there is no spooky action-at-a distance in my retrocausal method.

Esail's method has different outcomes depending on the order of measurement. A then B would be different physically from B then A. In my retrocausal method, the antiparticle is measured first (with respect to the antiparticle's point of view).

So I like the way Esail's paper has formulae clarifying the QM spookiness. I see it as very similar to my retrocausal paper except that I eliminate the QM spookiness and replace it with a more generalised approach to space/times of particles and antiparticles (See my Jan 2021 paper).

This brings me to the question of the QM spookiness which I circumvented using a retrocausal model. In my June 2020 paper I devised physical, classical models for electron and photon spin. With these models I obtained Malus's Law using normal forwards-in-time classical physics. Nothing spooky there. To obtain the Bell QM correlation I added retrocausality to my classical Malus's Law model. Nothing spooky here apart from retrocausality.

In the last month I have looked at QM formulae for deriving the Bell QM correlation and have not found a completely general derivation. Susskind's online course on entanglement uses projection operators on a singlet pair of electrons. The calculations are fine up to a point but they are only really covering the Malus Law context. In a sense this is what Esail's calculations are doing and ditto for my June 2020 retrocausal paper. So can anyone point to a QM derivation using a non-Malus context? I do not think such a calculation is possible. Esail's paper is useful to me as it shows that my quest for a generalised calculation is not possible even in QM. Esail is clearly showing that QM uses a Malus-like solution only. Susskind's formulae use a projection operator projecting on to the |up> direction. And it operates on a singlet mixing up and down: |u,d> - |d,u>. To me that is very much like a Malus context. Alpha is zero degrees and the singlet is polarised either at zero or against zero degrees. I suspect QM cannot work with a generalised pointer m where the 'm' singlet is not pointing at |u,d> - |d,u>, where neither Alice nor Bob measure along |up>.

A long time ago when Oh No (?) was a moderator of the old version of s.p.foundations, he maintained that there would be no gain in using GA rather than QM. My Jan 2021 paper uses an idea by Chappell, using GA, that time is a quality dependent on the curvature of the space of the environment. If he is correct, then does QM have in it a similar idea still buried? What I suspect is that QM spookiness is really equivalent to retrocausal spookiness where the equivalence is not yet recognised. Well, not yet believed as anything but tricks or temporary conveniences such as the 'wrong' direction of time used for antiparticles in a Feynmann diagram.

[Joy Christian]

If Esail writes A(a, h)= A(a-phi, h) and B(b, h) = B(b-phi -pi/2, h).

Then this is wholly local: for A does not depend on b and B does not depend on a.

But A does depend on b and B does depend on a.

Notice that b' = b - phi - pi/2 implies phi = b - b' - pi/2. Now substitute this in the expression for A, which becomes A(a - b + b' + pi/2, h). And similarly, we can write B in terms of a.
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