My Challenge to All Bell-Believers --- Meet it or Beat it:

[Joy Christian]

Let me note that for the 4-particle GHZS state the condition E(a, b, c, d) = << ABCD >> = +1 or -1 for some specific settings for all runs and thus even for a single run is similar to the familiar condition E(a, b) = << AB >> = +1 or -1 for the 2-particle EPRB state for some specific settings (i.e., for a = b and a = -b, respectively) for all runs and thus even for a single run. In the latter example, it is the condition of perfect correlation (or perfect anti-correlation), which is predicted by quantum mechanics.

For completeness, let me prove this here for the EPRB case, parallelling the proof below which I provided in response to the counterchallenge to me by Tim Maudlin:



For the EPRB case, let us follow the construction of my 3-sphere model presented in this paper: https://arxiv.org/abs/1405.2355. The proof goes through as follows:

What I want to show is AB = -1 for a = +b and AB = +1 for a = -b even for a single run. It would suffice to prove AB = +1 for a = -b since the case AB = -1 for a = +b follows quite similarly. We start with equations (54) and (55) of the above paper, which define the binary valued functions A = +/-1 and B = +/-1, subject to the conservation of the spin-0 defined in equations (65) and (66). The expectation value E(a, b) = < AB > = - a . b is then derived in equations (67) to (75) of the paper using these functions A and B. In fact, the expectation value (75) or (76) follows from the very construction of the functions A and B in the equations (54) and (55), as a geometrical identity within my 3-sphere model. Therefore we can use this geometrical identity to prove that AB = +1 for a = -b. In fact, for the chosen settings this identity reduces simply to E(a, b) = < AB > = +1. But E(a, b) = < AB > = +1 tells us that the average of the number AB is a constant, and it is equal to +1. This is mathematically possible only if AB = +1 for all runs, for a = -b. But if AB = +1 for all runs, then AB = +1 holds also for any given run. Therefore AB = +1 for any single run, for the chosen settings a = -b. QED.

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[Joy Christian]

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[Joy Christian]

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I rarely use my twitter account. But sometimes the opportunity to twit is just too sweet to let go:



https://arxiv.org/abs/1704.02876

http://philsci-archive.pitt.edu/14305/

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[Joy Christian]

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I posted my original challenge above more than two years ago: viewtopic.php?f=6&t=275#p6681.

To date no one has been able to meet this challenge. And yet, many continue to believe in the traditional interpretation of Bell's theorem: viewtopic.php?f=6&t=342&p=8222#p8221.

The traditional interpretation of Bell's theorem is based on the claim that in the actual experiments such as the above the Bell-CHSH inequality with the upper bound of 2 is "violated." If so, then the claimant(s) should be able to provide actual experimental data --- event-by-event --- that violates the Bell-CHSH inequality. In other words, they should be able to provide actual experimental data for which the absolute value of the following sum,

E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) ,

exceeds the bound of 2, where

E(a, b) = << A(a)B(b) >> ,

E(a, b' ) = << A(a)B(b' ) >> ,

E(a', b) = << A(a' )B(b) >> ,

and

E(a', b' ) = << A(a' )B(b' ) >> .

So this is my new (or perhaps not so new) challenge. Please do not try to insult my intelligence by obfuscating the issue with statistics or probabilities. Just face up the challenge!

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[FrediFizzx]

Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

[Joy Christian]

Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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[FrediFizzx]

Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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The actual data from the experiments do violate the bound of 2. You can probably get the data from Weihs, et al (1998) to confirm that.

But they don't violate the real bound of 4 or even the QM bound of 2*sqrt(2) for CHSH.

[Joy Christian]

Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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The actual data from the experiments do violate the bound of 2. You can probably get the data from Weihs, et al (1998) to confirm that.

But they don't violate the real bound of 4 or even the QM bound of 2*sqrt(2) for CHSH.

Indeed. We are both saying the same thing with different words. My point is that the actual data do not violate the absolute bound of 2 on the CHSH sum

E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) ,

where

E(a, b) = << A(a)B(b) >> ,

E(a, b' ) = << A(a)B(b' ) >> ,

E(a', b) = << A(a' )B(b) >> ,

and

E(a', b' ) = << A(a' )B(b' ) >> .

But the experimenters and people like Richard D. Gill are claiming that the latter violation is what is happening in experiments, which is of course false.

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[Joy Christian]

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I note that --- three years on --- no Bell-believer has been able to meet my challenge: viewtopic.php?f=6&t=275#p6681

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[gill1109]

Sorry Joy, I met it immediately, but you apparently could not understand my argument. It was a simple argument using Fourier analysis, from one of the founders of Geometric Algebra. I recommend you reformulate your challenge so that an independent jury of unbiased observers can objectively determine whether or not a challenge is succesful. That is a difficult job, I know! I gave the "reverse" challenge a lot of thought, and even as it is, I can see issues where an anti-Bellist could object to some of the rules

[FrediFizzx]

Sorry Joy, I met it immediately, but you apparently could not understand my argument. It was a simple argument using Fourier analysis, from one of the founders of Geometric Algebra. I recommend you reformulate your challenge so that an independent jury of unbiased observers can objectively determine whether or not a challenge is succesful. That is a difficult job, I know! I gave the "reverse" challenge a lot of thought, and even as it is, I can see issues where an anti-Bellist could object to some of the rules

I never saw how you met the challenge so please reproduce it here. Thanks.

[Joy Christian]

Sorry Joy, I met it immediately, but you apparently could not understand my argument.

I recommend you reformulate your challenge ...

[Joy Christian]

Sorry Joy, I met it immediately, but you apparently could not understand my argument. It was a simple argument using Fourier analysis, from one of the founders of Geometric Algebra. I recommend you reformulate your challenge so that an independent jury of unbiased observers can objectively determine whether or not a challenge is succesful. That is a difficult job, I know! I gave the "reverse" challenge a lot of thought, and even as it is, I can see issues where an anti-Bellist could object to some of the rules

I never saw how you met the challenge so please reproduce it here. Thanks.

He means this nonsense: viewtopic.php?f=6&t=275#p6695

It is pathetic!

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[gill1109]

Sorry Joy, I met it immediately, but you apparently could not understand my argument. It was a simple argument using Fourier analysis, from one of the founders of Geometric Algebra. I recommend you reformulate your challenge so that an independent jury of unbiased observers can objectively determine whether or not a challenge is succesful. That is a difficult job, I know! I gave the "reverse" challenge a lot of thought, and even as it is, I can see issues where an anti-Bellist could object to some of the rules

I never saw how you met the challenge so please reproduce it here. Thanks.

He means this nonsense: viewtopic.php?f=6&t=275#p6695

It is pathetic!

One person's evaluation is "pathetic", another person's is "pure genius". I'm referring to the genius of Steve Gull who wrote those four overhead slides http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf.

I explored Gull's ideas in https://arxiv.org/abs/1312.6403. I never submitted this to a journal. It ends with a lot of open problems, really I am looking for someone who is interested in collaborating with me to explore these ideas even further.

Steve Gull, one of the great pioneers of Geometric Algebra, presented his brilliant idea at a "max ent" conference. It was about an exam question he used to give to students. Jaynes was there and very very impressed and excited. He wrote that it would take many decades to digest the meaning of this extraordinary result, which completely overturned his earlier judgements on Bell's theorem. (He had earlier, rather arrogantly, written that Bell had simply got in a muddle about the difference between independence and conditional independence.)

My paper https://arxiv.org/abs/1312.6403 is entitled "The triangle wave versus the cosine (how to optimally approximate EPR-B correlations by classical systems)"
Author: Richard D. Gill
(Submitted on 22 Dec 2013 (v1), last revised 27 Dec 2013 (this version, v2))
Abstract: The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind are striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind are a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained for free: they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a ``spinning coloured disk'' model, and a research programme: describe these functions in a concise analytic way.
Comments: v2: changed title (saw tooth became triangle)
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Applications (stat.AP)
Cite as: arXiv:1312.6403 [quant-ph]
(or arXiv:1312.6403v2 [quant-ph] for this version)
Submission history
From: Richard D. Gill [view email]
[v1] Sun, 22 Dec 2013 16:51:33 UTC (36 KB)
[v2] Fri, 27 Dec 2013 06:52:53 UTC (36 KB)

[Joy Christian]

One person's evaluation is "pathetic", another person's is "pure genius". I'm referring to the genius of Steve Gull who wrote those four overhead slides http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf.

This is garbage all the same. Garbage in, garbage out, as I explained here: viewtopic.php?f=6&t=275#p6695

There is a nice proof of Bell's theorem by Steve Gull which uses Fourier analysis instead of the usual algebra.

http://www.mrao.cam.ac.uk/~steve/maxent2009/
http://www.mrao.cam.ac.uk/~steve/maxent ... s/bell.pdf

This sketch of the "proof" does not meet my challenge above.

To begin with, the "proof" violates my condition (2) right from the start. Secondly, it says, with emphasis, that "This is a mathematical project. There are no physical assumptions." I couldn't care less about a mathematical project in this context. I am talking about the physically realisable EPR-Bohm type experiment. Thirdly, I see no derivation of the bounds on the CHSH correlator at all in the "proof." Finally, there actually exists an explicit, clear-cut local-realistic model, trivially derived and verified in several independent event-by-event computer simulations: http://arxiv.org/abs/1405.2355.

Therefore the above "proof" cannot possibly have any physical significance.

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Stephen Gull left academia after my disproof of Bell's theorem appeared, never to return back. Such was the impact of my work on him!

My challenge to all Bell-believers remains open. Meet it or Beat it: viewtopic.php?f=6&t=275#p6681
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[gill1109]

Stephen Gull left academia after my disproof of Bell's theorem appeared, never to return back. Such was the impact of my work on him!

Stephen Gull retired, and did *not* leave academia as far as I know. I rather imagine that Steve now spends his time just how he himself likes, as far as his health permits. https://www.astro.phy.cam.ac.uk/directory/prof-steve-gull

Michael Atiyah recently did leave academia quite definitively, and his passing was a bit sad, because many thought and moreover said that his last work should never have been publicised. But I think he was perfectly right to tell the world what his most recent ideas were, even if everyone *at this moment* thinks they are wrong.

I'm sure that you too, Joy, are not going to leave academia till your last breath! Keep on going, keep on fighting, keep on searching for the truth and telling the world what you've found.

[gill1109]

This was the challenge:

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My challenge to all Bell-believers is simply this:

Prove the Bell-CHSH inequality with the bounds of +/-2 without violating the following two conditions:

(1) You are not permitted to surreptitiously replace the sum E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) of four separate averages with the following single average:

E( a, b, a', b' ) = << A(a)B(b) + A(a)B(b' ) + A(a' )B(b) - A(a' )B(b' ) >>

(2) You are not permitted to obfuscate this simple challenge by invoking unnecessary concepts from probability theory.

I think the challenge should be slightly re-formulated. The interesting thing about Bell's work is not an inequality. Such an inequality was just an intermediate step. You can disagree with it, sure, but so what. The important thing is Bell's immediately claimed corollary of his inequality - the incompatibility of QM and LHV (or LR). That's what everyone is interested in.

So I answered the question: can we prove the incompatibility of QM and LHV without going via BI and without using probability theory?

I think the answer is yes, and Steve Gull's little exercise to Part III students of theoretical physics in Cambridge provides the proof that the answer is yes.

Gull proves Bell's corollary without making any use whatsoever of BI.

He does not use concepts from probability theory, or for that matter, perish the thought, from statistics.

He uses "Fourier analysis" which I hope everyone agrees is not an "unnecessary concept from probability theory".

It is a pretty fundamental "technology" of theoretical physics, and it has been that way since the 18th century. It is "modern mathematics" (i.e. post 16th century).

Fourier analysis is essential Bachelor level Maths for Physicists, Maths for Engineers, Maths for Computer Scientists, even: Maths for Statisticians. STEM subjects. Theoretical biologists have to know about it. Philosophers and historians of science have to know about it.

"Bell's corollary" (that QM and LR are incompatible) in short is a pretty easy theorem of mathematics and/or computer science, which is relevant to physics, since QM and LR (or LHV) are mathematical structures which physicists want to use to describe (or mimic some aspects of) physical reality as it is understood by them through experiment and analysis.

[Joy Christian]

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My challenge to all Bell-believers is simply this:

Prove the Bell-CHSH inequality with the bounds of +/-2 without violating the following two conditions:

(1) You are not permitted to surreptitiously replace the sum E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) of four separate averages with the following single average:

E( a, b, a', b' ) = << A(a)B(b) + A(a)B(b' ) + A(a' )B(b) - A(a' )B(b' ) >>

(2) You are not permitted to obfuscate this simple challenge by invoking unnecessary concepts from probability theory.

I think the challenge should be slightly re-formulated.

I am not impressed by such deflection tactics (cf. https://arxiv.org/abs/1704.02876). My challenge to all Bell-believers remains open. Meet it or Beat it: viewtopic.php?f=6&t=275#p6681

In addition to stealing Boole's inequalities without giving him any credit, Bell claimed that the strong quantum correlations cannot be reproduced by any local-realistic model. That claim of Bell is utter nonsense, as I have demonstrated many times during the past eight years with an explicit and constructive local-realistic model:

https://arxiv.org/abs/1103.1879

https://arxiv.org/abs/1211.0784

https://arxiv.org/abs/1405.2355

https://arxiv.org/abs/1806.02392

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[gill1109]

I am not impressed by such deflection tactics.
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In addition to stealing Boole's inequalities without giving him any credit, Bell claimed that the strong quantum correlations cannot be reproduced by any local-realistic model. That claim of Bell is utter nonsense, as I have demonstrated many times during the past eight years with an explicit and constructive local-realistic model:

https://arxiv.org/abs/1103.1879

https://arxiv.org/abs/1211.0784

https://arxiv.org/abs/1405.2355

https://arxiv.org/abs/1806.02392

Joy, you are unkind. Those were not deflection tactics by me. Please don't make such allegations. We want to discuss science civilly, at a public symposium, right?

Boole's *famous* inequality is absolutely trivial in probability theory. His name is attached to it, to honour him. The Bell-CHSH inequalities are trivial corollaries, "original Bell" being given in Boole's book as an elementary exercise for the reader. The famous 1850-whatever book which nobody reads any more does not include solutions to the exercises, nor did old George publish an "instructor's manual". Please don't insult the memory of J.S. Bell by suggesting that he consciously *stole* someone else's work.

Itamar Pitowsky (RIP) was, I believe, the first person who actually read Boole's magnum opus and saw the connection to Bell and all that and successfully publicised the fact.

Now, here comes the important stuff. You then say:

"... Bell claimed that the strong quantum correlations cannot be reproduced by any local-realistic model. That claim of Bell is utter nonsense, as I have demonstrated many times during the past eight years with an explicit and constructive local-realistic model".

Indeed. That's the point I tried to make earlier today. The point I wanted to make, which you have just implicitly agreed to, is that "Bell's claim" is much, much, more interesting than "Bell's inequality".

So perhaps you can tell us: what is the mistake in Gull's argument? You indeed have been implicitly claiming, for at least eight years, that Gull's "theorem" (exam question for Part III students at Cambridge), is wrong. None of your papers even mentions Gull's proof. Gull does not use probability theory, and he does not use CHSH. His "proof" is, therefore, a valid response to the challenge which you've just implicitly admitted is much more interesting.

So I would like to ask you, yet again, what is wrong with Gull's proof?

It appears that Edwin Thompson Jaynes was flabbergasted by it. He seems to have admitted that he hadn't actually realised what Bell was on about at all. And that actually, Bell was onto something which, if he (Bell) was right, appeared to Jaynes rather important and subtle and deep.

[Joy Christian]

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There is no "Gull's proof." There is not even a sketch of a proof. At best, it is just wishful thinking by Gull.

One obvious problem with Gull's wishful thinking is that his argument ignores the geometry and topology of the physical space in which EPR-Bohm type experiments are performed.

As for my claim of "stealing", the fact remains that neither Bell nor the early followers of Bell ever gave any credit to Boole for his inequality. That is "stealing" in my book.

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