The Mistakes by Bell and von Neumann are Identical

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Expand view Topic review: The Mistakes by Bell and von Neumann are Identical

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Sat Nov 28, 2020 6:14 am

gill1109 wrote:
Joy Christian wrote:
Your comments on PubPeer are not worth responding to.

I made those same comments here, because I am looking forward to your response, here.


No response from me is necessary. If anyone is interested in my view and my arguments in support of my view, then they can read my paper: https://arxiv.org/pdf/1704.02876.pdf.
.

Re: The Mistakes by Bell and von Neumann are Identical

Post by gill1109 » Sat Nov 28, 2020 2:57 am

Joy Christian wrote:Your comments on PubPeer are not worth responding to.
.

I made those same comments here, because I am looking forward to your response, here.

As far as I can see the new version of your paper continues to make the same mistake.

I do think that you have discovered a neat, new proof of the Kochen-Specker theorem (at least, when the Hilbert space has dimension at least 4).

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Fri Nov 27, 2020 12:26 am

gill1109 wrote:
Is this "dishonest"? Of course, it could be mistaken, but that is something else.

The world does not revolve around you. I was not referring to you. I was referring to a couple of reviewers of a first-rate journal. Your comments on PubPeer are not worth responding to.
.

Re: The Mistakes by Bell and von Neumann are Identical

Post by gill1109 » Fri Nov 27, 2020 12:17 am

Joy Christian wrote:
Joy Christian wrote:.
I have revised this paper once again in response to some dishonest reviewer comments: https://arxiv.org/pdf/1704.02876.pdf.

The revised abstract reads:

Image

Hopefully, the revised version of the paper will appear online after 1:00 GMT tomorrow morning.

My paper has now appeared online: https://arxiv.org/pdf/1704.02876.pdf. The mistake in Bell's theorem is breathtakingly obvious. As discussed in my paper, it was identified by Einstein some 30 years before Bell made it. Unfortunately, the followers of Bell continue to make the same mistake today.
.

On PubPeer some time ago I wrote https://pubpeer.com/publications/66C8CA ... 45C4DE44F0 :

Suppose A and B are two self-adjoint operators which do not commute, e.g. spin in different directions of a spin half system. Their mean values when measured in (separate experiments) on systems in the same state rho are given by < A > = trace rho A, < B > = trace rho B. Now, C = A + B is another self-adjoint operator, so in principle, there could be an experiment in which it would be could be measured. It's expectation value would be < C > = trace rho C = trace rho A + trace rho B = < A > + < B >. A hidden variables theory which reproduces those predictions exactly would postulate the existence of a single probability space, and on it, random variables, corresponding to and A, B and C, say X, Y and Z, such that E X = < A >, E Y = < B >, and E Z = < C >. (X, Y and Z are functions of a variable lambda and these functions exist mathematically, independently of what a physicist can and cannot observe). Necessarily it follows that E X + E Y = E(X + Y) = EZ, because < A > + < B > = < C >. Additivity of expectation values in the hidden variable theory follows from the assumption that the hidden variable theory reproduces exactly the predictions of quantum mechanics.

In short: the claim of the author that additivity of expectation values is an extra, unphysical, assumption, is nonsense. It is a necessary consequence of the existence of a hidden variables theory.

Now, the hidden variable theory would also imply that the eigenvalues of A + B are sums of the eigenvalues of A with those of B. After all, quantum theory also predicts that we observe eigenvalues of the operators, when we measure "observables". Thus the present paper is actually giving a new proof of the Kochen-Specker theorem (for dimension 4 upwards). Bell did not make any oversight.


Is this "dishonest"? Of course, it could be mistaken, but that is something else.

Maybe I shouldn't have used the emotive word "nonsense". Please just replace it with the neutral word "wrong".

In Christian's paper, the author writes "for non-commuting observables, the equivalence of any sum of expectation values and the expectation value of the sum, although respected within quantum mechanics, need not hold within hidden variable theories, regardless of specific characteristics such as locality or realism they may be required to respect." He makes this assertion ("needs not hold") without any justification. I disagree with the second sentence and have just given the mathematical argument why it is easily seen to be wrong.

If you don't like density matrix formulas, take the state to be pure, rho = |psi><psi|, so that trace rho A = <psi | A | psi>

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Thu Nov 26, 2020 3:53 am

Joy Christian wrote:.
I have revised this paper once again in response to some dishonest reviewer comments: https://arxiv.org/pdf/1704.02876.pdf.

The revised abstract reads:

Image

Hopefully, the revised version of the paper will appear online after 1:00 GMT tomorrow morning.

My paper has now appeared online: https://arxiv.org/pdf/1704.02876.pdf. The mistake in Bell's theorem is breathtakingly obvious. As discussed in my paper, it was identified by Einstein some 30 years before Bell made it. Unfortunately, the followers of Bell continue to make the same mistake today.
.

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Wed Nov 25, 2020 10:10 am

.
I have revised this paper once again in response to some dishonest reviewer comments: https://arxiv.org/pdf/1704.02876.pdf.

The revised abstract reads:

Image

Hopefully, the revised version of the paper will appear online after 1:00 GMT tomorrow morning.
.

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Thu Oct 08, 2020 9:54 pm

gill1109 wrote:
Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Jeffrey Bub
Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the 'beables' of the theory, to use Bell's term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm's theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.
https://arxiv.org/abs/1006.0499

Jeff Bub is mistaken in his analysis. His analysis has been refuted by Mermin and Schack. I have a long discussion about it in my paper: https://arxiv.org/abs/1704.02876.

Joy Christian wrote:
Incidentally, in the past decade Bub and Dieks have attempted to revive von Neumann’s theorem despite the fact that the existence since 1952 of Bohm’s non-local hidden variable theory provides a constructive refutation of the theorem, independently of its formal defect discussed above. As Mermin and Schack in their refutation of the argument by Bub and
Dieks point out, the claim made by the latter authors amounts to insisting that von Neumann’s assumption (9) is “analytic” and therefore perfectly valid. But that misses the point of the objection to the theorem raised by Einstein, Bell, and others, which has to do with physics, not mathematics...

I will not quote my entire discussion on Bub's paper here because my paper is under peer-review by a prestigious journal and thus it is copyright protected by that journal.

***

Re: The Mistakes by Bell and von Neumann are Identical

Post by gill1109 » Thu Oct 08, 2020 9:14 pm

Joy Christian wrote:
gill1109 wrote:I guess that with half a brain you can see that S (the CHSH combination of four correlations) can’t exceed 4, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 4. Obviously, Nature is local. We don’t need to study physics to know that. There is nothing to explain. End of discussion.

You still don't get it. Let me rephrase the above comment to make it correct: "...S (the CHSH combination of four correlations) can’t exceed 2, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 2\sqrt{2} (which are the correct local-realistic bounds on S, as demonstrated in my paper). Obviously, Nature is local. We don’t need to study "Bell's so-called theorem" to know that. There is nothing to explain. End of discussion."

Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Jeffrey Bub
Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the 'beables' of the theory, to use Bell's term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm's theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.
https://arxiv.org/abs/1006.0499
Incidentally, Woerdman observed a value of S larger than 3 a few years ago.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.217901
How to Observe High-Dimensional Two-Photon Entanglement with Only Two Detectors
S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman
Phys. Rev. Lett. 92, 217901 – Published 24 May 2004
We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a 2x2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict that the Clauser-Horne-Shimony-Holt-Bell parameter S is larger than achievable for two qubits (S=2√2), namely, S=3 1/5.

Re: The Mistakes by Bell and von Neumann are Identical, unde

Post by gill1109 » Sat Sep 26, 2020 1:15 am

FrediFizzx wrote:
gill1109 wrote: ...
It’s not “my” theorem.

Who's theorem is it then? It's not Bell's junk physics theory. The only paper reference I have ever seen to the concept of modelling Nature and the experiments with an event by event simulation is from you. If not yours, then who did you get it from? Until then, it is your "theorem". Which BTW has nothing to do with Bell's. Bell's is about comparing local theories with quantum mechanics and that is completely shot down to pieces. In Gill's theorem, quantum mechanics can't do it either so no comparison at all.
:mrgreen:

It has been formulated by many eminent mathematicians as a purely *mathematical* theorem. I already several times, Fred, gave you references. Here I will just mention the name of one, very illustrious, author-mathematician: Boris Tsirelson. He also wrote survey papers and tutorials.

I am not talking about a physics theory. One could call it: metaphysics. Mathematical theories about the mathematical structures commonly employed in mathematical physics. Bell-type experiments are part of what is now known as “experimental metaphysics”.

Abner Shimony worked in this field. That’s Joy Christian’s PhD supervisor. Joy Christian works in this field. He has proposed an experiment intended to experimentally *disprove* Bell’s theorem. He also claims to have mathematical counter-examples to Bell’s theorem, and has has published in a prominent pure mathematics journal. Tsirelson wrote several beautiful pedagogical internet encyclopedia articles on quantum entanglement. Here is one, preserved on a website at the Radboud University, Nijmegen:
http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Entanglement_(physics).html

Re: The Mistakes by Bell and von Neumann are Identical, unde

Post by FrediFizzx » Thu Sep 24, 2020 10:25 pm

gill1109 wrote: ...
It’s not “my” theorem.

Who's theorem is it then? It's not Bell's junk physics theory. The only paper reference I have ever seen to the concept of modelling Nature and the experiments with an event by event simulation is from you. If not yours, then who did you get it from? Until then, it is your "theorem". Which BTW has nothing to do with Bell's. Bell's is about comparing local theories with quantum mechanics and that is completely shot down to pieces. In Gill's theorem, quantum mechanics can't do it either so no comparison at all.
:mrgreen:

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Thu Sep 24, 2020 9:32 pm

gill1109 wrote:
I guess that with half a brain you can see that S (the CHSH combination of four correlations) can’t exceed 4, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 4. Obviously, Nature is local. We don’t need to study physics to know that. There is nothing to explain. End of discussion.

You still don't get it. Let me rephrase the above comment to make it correct: "...S (the CHSH combination of four correlations) can’t exceed 2, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 2\sqrt{2} (which are the correct local-realistic bounds on S, as demonstrated in my paper). Obviously, Nature is local. We don’t need to study "Bell's so-called theorem" to know that. There is nothing to explain. End of discussion."

***

Re: The Mistakes by Bell and von Neumann are Identical

Post by gill1109 » Thu Sep 24, 2020 9:03 pm

I guess that with half a brain you can see that S (the CHSH combination of four correlations) can’t exceed 4, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 4. Obviously, Nature is local. We don’t need to study physics to know that. There is nothing to explain. End of discussion.

Re: The Mistakes by Bell and von Neumann are Identical, unde

Post by gill1109 » Thu Sep 24, 2020 8:51 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote: ...
viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

Dear Fred, you keep saying this, and I keep saying that I don’t agree (or I just don’t understand you). Experiments don’t “use an inequality”. Experiments observe four correlations. There is a mathematical theory which says that one minus the sum of the other three can’t exceed 2, under certain conditions; moreover, equality is possible. There is a different theory which says it can’t exceed 2 sqrt 2 under the same conditions, moreover, equality is possible. There is a third theory which says that under the same conditions it can’t exceed the natural bound, 4, which by definition of the correlation between binary outcomes, can’t exceed 4. And it could in principle attain the bound of 4. This is all mathematics. You can write it out as formally and rigorously as you like. Theory 1 is what Einstein had in mind. Theory 2 is called QM. Theory 3 is called “Rohrlich-Popescu” but nobody takes that theory seriously, it isn’t worked out in any detail at all. Do you need more references? Are you aware of Boris Tsirelson’s really impressive and deep mathematical work?

It’s all maths. It’s there. Physicists can do with it what they like. In 2015 physicists did very difficult experiments under very rigorous experimental conditions and observed 2.4 (Delft), 2.6 (Munich), 2.00001 (NIST, Vienna). One can have quite a few criticisms on the quality of those results. Since then, the experiments have been repeated and improved.

The experiments don’t “use an inequality”. They observe four correlations.

Richard

It is quite amazing that you don't understand the simple fact that NOTHING can exceed the Bell inequalities. Why are you going on about "...experiments don't use an inequality" when the experimenters claim they have exceeded the Bell inequalities? I didn't figure you would have a good answer because there is NO answer. The Bell inequalities are meaningless. Very simple.

However, there might be some meaning to your "theorem" that a local theory can't simulate Nature and the experiments. But I doubt it. Nature does it and we now know that even quantum mechanics is local for the EPR-Bohm scenario so Nature is most likely local in that scenario. Thus it should be possible to model Nature locally.
.

It’s not “my” theorem. Anyway, a local, realist, non-conspiratorial theory can’t simulate results like those of the 2015 experiments. Nature did it. Quantum mechanics predicts those results very well. Physicists disagree whether one has to ditch “local”, “realist”, or “non-conspiratorial”. Note that the word “realist”, in this context, is a technical word, having a precise mathematical meaning. However there is no doubt that Albert Einstein hoped, all his life, for a local realist theory to be found *behind* QM. Niels Bohr didn’t.

Everyone can think what they like. I believe it was von Neumann who said that if anyone ever found a theory “behind QM”, ie such that QM is just an emergent phenomenon following from deeper mathematical structures, thenthat underlying theory would be weirder still than QM. Personally, I think that by our way of thinking, one cannot “understand” quantum mechanics. One can only become familiar with the mathematics and one can develop mathematical intuition.

Re: The Mistakes by Bell and von Neumann are Identical

Post by FrediFizzx » Thu Sep 24, 2020 5:32 pm

Joy Christian wrote:
FrediFizzx wrote:
Joy Christian wrote: ...
Anyone with half a brain can understand that what you are saying is the simplest and most logical explanation of why the Bell inequalities seem to be exceeding in the experiments. But the trouble is that one does have to have half a brain to understand this.

***

Then it could be that one does not like to admit that they have been tricked for so long.

That is even worse. That would mean that they are being dishonest on purpose.

***

Well, it certainly is a head scratcher as to why so many people for so long have been fooled by something that is oh so simple.
:mrgreen:

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Thu Sep 24, 2020 3:36 pm

FrediFizzx wrote:
Joy Christian wrote:
FrediFizzx wrote:
It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.

Anyone with half a brain can understand that what you are saying is the simplest and most logical explanation of why the Bell inequalities seem to be exceeding in the experiments. But the trouble is that one does have to have half a brain to understand this.

***

Then it could be that one does not like to admit that they have been tricked for so long.

That is even worse. That would mean that they are being dishonest on purpose.

***

Re: The Mistakes by Bell and von Neumann are Identical

Post by FrediFizzx » Thu Sep 24, 2020 2:35 pm

Joy Christian wrote:
FrediFizzx wrote:
It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.

Anyone with half a brain can understand that what you are saying is the simplest and most logical explanation of why the Bell inequalities seem to be exceeding in the experiments. But the trouble is that one does have to have half a brain to understand this.

***

Then it could be that one does not like to admit that they have been tricked for so long.
.

Re: The Mistakes by Bell and von Neumann are Identical

Post by Joy Christian » Thu Sep 24, 2020 12:57 pm

FrediFizzx wrote:
It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.

Anyone with half a brain can understand that what you are saying is the simplest and most logical explanation of why the Bell inequalities seem to be exceeding in the experiments. But the trouble is that one does have to have half a brain to understand this.

***

Re: The Mistakes by Bell and von Neumann are Identical, unde

Post by FrediFizzx » Thu Sep 24, 2020 10:35 am

gill1109 wrote:
FrediFizzx wrote: ...
viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

Dear Fred, you keep saying this, and I keep saying that I don’t agree (or I just don’t understand you). Experiments don’t “use an inequality”. Experiments observe four correlations. There is a mathematical theory which says that one minus the sum of the other three can’t exceed 2, under certain conditions; moreover, equality is possible. There is a different theory which says it can’t exceed 2 sqrt 2 under the same conditions, moreover, equality is possible. There is a third theory which says that under the same conditions it can’t exceed the natural bound, 4, which by definition of the correlation between binary outcomes, can’t exceed 4. And it could in principle attain the bound of 4. This is all mathematics. You can write it out as formally and rigorously as you like. Theory 1 is what Einstein had in mind. Theory 2 is called QM. Theory 3 is called “Rohrlich-Popescu” but nobody takes that theory seriously, it isn’t worked out in any detail at all. Do you need more references? Are you aware of Boris Tsirelson’s really impressive and deep mathematical work?

It’s all maths. It’s there. Physicists can do with it what they like. In 2015 physicists did very difficult experiments under very rigorous experimental conditions and observed 2.4 (Delft), 2.6 (Munich), 2.00001 (NIST, Vienna). One can have quite a few criticisms on the quality of those results. Since then, the experiments have been repeated and improved.

The experiments don’t “use an inequality”. They observe four correlations.

Richard

It is quite amazing that you don't understand the simple fact that NOTHING can exceed the Bell inequalities. Why are you going on about "...experiments don't use an inequality" when the experimenters claim they have exceeded the Bell inequalities? I didn't figure you would have a good answer because there is NO answer. The Bell inequalities are meaningless. Very simple.

However, there might be some meaning to your "theorem" that a local theory can't simulate Nature and the experiments. But I doubt it. Nature does it and we now know that even quantum mechanics is local for the EPR-Bohm scenario so Nature is most likely local in that scenario. Thus it should be possible to model Nature locally.
.

Re: The Mistakes by Bell and von Neumann are Identical, unde

Post by gill1109 » Thu Sep 24, 2020 9:26 am

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:...
Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".
.

Fred, can you enlighten me as to what you mean by a “word theorem”? Pythagoras theorem is a word theorem. Euclid wrote words, not formulas. I’ve given you references to several present day top mathematicians who have expressed Bell’s theorem as a formal mathematical theorem. No retractions yet. You may have heard of the name “Tsirelson”. (Boris. RIP). Klaas Landsman is another. The list could go on and on. I don’t think some British-Dutch statistician by the name of Gill had anything to do with all that, anything at all.

viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

Dear Fred, you keep saying this, and I keep saying that I don’t agree (or I just don’t understand you). Experiments don’t “use an inequality”. Experiments observe four correlations. There is a mathematical theory which says that one minus the sum of the other three can’t exceed 2, under certain conditions; moreover, equality is possible. There is a different theory which says it can’t exceed 2 sqrt 2 under the same conditions, moreover, equality is possible. There is a third theory which says that under the same conditions it can’t exceed the natural bound, 4, which by definition of the correlation between binary outcomes, can’t exceed 4. And it could in principle attain the bound of 4. This is all mathematics. You can write it out as formally and rigorously as you like. Theory 1 is what Einstein had in mind. Theory 2 is called QM. Theory 3 is called “Rohrlich-Popescu” but nobody takes that theory seriously, it isn’t worked out in any detail at all. Do you need more references? Are you aware of Boris Tsirelson’s really impressive and deep mathematical work?

It’s all maths. It’s there. Physicists can do with it what they like. In 2015 physicists did very difficult experiments under very rigorous experimental conditions and observed 2.4 (Delft), 2.6 (Munich), 2.00001 (NIST, Vienna). One can have quite a few criticisms on the quality of those results. Since then, the experiments have been repeated and improved.

The experiments don’t “use an inequality”. They observe four correlations.

Richard

Re: The Mistakes by Bell and von Neumann are Identical

Post by FrediFizzx » Thu Sep 24, 2020 7:15 am

Gordon Watson wrote: ...
Thanks Richard, but Joy's comments do not match your explanation:

Joy writes: "The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:

Image

Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician."

By my reading of the defective "questioned-equality" such comments make no sense.

Gordon

Oh, jeez. Ya just had to muck up this thread with stuff that doesn't matter at all! Stay off this thread until Gill responds to my last post.
.

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