A Mathematician's Refutation of Bell's Theorem

[Joy Christian]

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We do not need any more refutations of Bell's theorem in this forum. Some of us are convinced already that it is a worthless piece of junk. I myself have provided both counterexamples to it and also formal refutations of it, in my own way. See, for example, my recent talk summarising my work of the past fourteen years: http://dx.doi.org/10.13140/RG.2.2.21753.39529.

However, Bell's theorem continues to dominate the mainstream as well as the semi-popular opinion. A certain statistician, in particular, has doggedly hounded me personally as well as my work, claiming that mathematically Bell's theorem is not refutable. While there is some truth in this claim, in this thread I want to promote a mathematician's refutation of Bell's theorem.

The mathematician is called Frank Lad. He is a Senior Lecturer in Mathematical Statistics, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.

While I have yet to read his papers, I have read their abstracts and found them interesting:

1) Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect, Journal of Modern Physics, 2021, 12, 1109-1144,

https://doi.org/10.4236/jmp.2021.128067.

2) Quantum Mysteries for No One, Journal of Modern Physics, 2021, 12, 1366-1399,

https://doi.org/10.4236/jmp.2021.129082.

Let me know what you think of them if you have a chance to read them. I will do the same if I get a chance to read them.
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[gill1109]

I read Frank Lad’s papers. I don’t think much of them. The interesting question would be: what does he think of Joy Christian’s papers?

He refers to the shrinking band of anti-Bellists, such as Marian Kupczynski and Karl Hess and (perhaps) Andrei Khrennikov. But nobody else.

[Joy Christian]

I read Frank Lad’s papers. I don’t think much of them.

That is not a criticism. That is a statement of your faith in your religion.
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[Heinera]

It's basically the same misunderstanding as minkwe and Joy are displaying. It merely shows that not every mathematician understand Bell's theorem.

[Joy Christian]

It's basically the same misunderstanding as minkwe and Joy are displaying. It merely shows that not every mathematician understand Bell's theorem.

What Lad's papers and Heinera's statement proves is that Bell's so-called "theorem" is not a theorem in mathematics at all, but merely a sociologically and politically sustained belief system.

PS: By the way, my views are very different from Lad's, and they are explained in Section II of my first IEEE Access paper as well as in this preprint: https://arxiv.org/pdf/1704.02876.pdf.
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[gill1109]

It's basically the same misunderstanding as minkwe and Joy are displaying. It merely shows that not every mathematician understand Bell's theorem.

What Lad's papers and Heinera's statement proves is that Bell's so-called "theorem" is not a theorem in mathematics at all, but merely a sociologically and politically sustained belief system.

PS: By the way, my views are very different from Lad's, and they are explained in Section II of my first IEEE Access paper as well as in this preprint: https://arxiv.org/pdf/1704.02876.pdf.

As you yourself admitted, Joy, there is a true mathematical theorem at the core of Bell’s works. George Boole and Arthur Fine both proved indisputably true mathematical theorems. Of course, their metaphysical meaning for physicists is part of an ongoing debate in the Philosophy of Science, as well as an establishment dogma, or if you prefer, presently dominant religion.

NB, according to some scientists/philosophers of science, the theorems in question are both true and not true. ZFC is inconsistent. The real numbers don’t actually exist. Personally, I think that that argument is not tenable.

[minkwe]

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We do not need any more refutations of Bell's theorem in this forum. Some of us are convinced already that it is a worthless piece of junk. I myself have provided both counterexamples to it and also formal refutations of it, in my own way. See, for example, my recent talk summarising my work of the past fourteen years: http://dx.doi.org/10.13140/RG.2.2.21753.39529.

However, Bell's theorem continues to dominate the mainstream as well as the semi-popular opinion. A certain statistician, in particular, has doggedly hounded me personally as well as my work, claiming that mathematically Bell's theorem is not refutable. While there is some truth in this claim, in this thread I want to promote a mathematician's refutation of Bell's theorem.

The mathematician is called Frank Lad. He is a Senior Lecturer in Mathematical Statistics, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.

While I have yet to read his papers, I have read their abstracts and found them interesting:

1) Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect, Journal of Modern Physics, 2021, 12, 1109-1144,

https://doi.org/10.4236/jmp.2021.128067.

2) Quantum Mysteries for No One, Journal of Modern Physics, 2021, 12, 1366-1399,

https://doi.org/10.4236/jmp.2021.129082.

Let me know what you think of them if you have a chance to read them. I will do the same if I get a chance to read them.
.

I hadn't read this paper before and will be reading it shortly but from the abstract, the argument appears similar to the argument I made recently about "Franken-Correlations" that got the quantum mysterians tizzy-up.

[gill1109]

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We do not need any more refutations of Bell's theorem in this forum. Some of us are convinced already that it is a worthless piece of junk. I myself have provided both counterexamples to it and also formal refutations of it, in my own way. See, for example, my recent talk summarising my work of the past fourteen years: http://dx.doi.org/10.13140/RG.2.2.21753.39529.

However, Bell's theorem continues to dominate the mainstream as well as the semi-popular opinion. A certain statistician, in particular, has doggedly hounded me personally as well as my work, claiming that mathematically Bell's theorem is not refutable. While there is some truth in this claim, in this thread I want to promote a mathematician's refutation of Bell's theorem.

The mathematician is called Frank Lad. He is a Senior Lecturer in Mathematical Statistics, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.

While I have yet to read his papers, I have read their abstracts and found them interesting:

1) Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect, Journal of Modern Physics, 2021, 12, 1109-1144,

https://doi.org/10.4236/jmp.2021.128067.

2) Quantum Mysteries for No One, Journal of Modern Physics, 2021, 12, 1366-1399,

https://doi.org/10.4236/jmp.2021.129082.

Let me know what you think of them if you have a chance to read them. I will do the same if I get a chance to read them.
.

I hadn't read this paper before and will be reading it shortly but from the abstract, the argument appears similar to the argument I made recently about "Franken-Correlations" that got the quantum mysterians tizzy-up.

The first paper already in the abstract states "The [CHSH] inequality pertains to a linear combination of four polarization products on the same pair of photons arising in a gedankenexperiment". I think this is a completely faulty interpretation. The CHSH inequality does not pertain to a thought experiment in which four polarization products on one and the same pair of photons are combined. The CHSH inequality is derived by assuming that correlations have a certain form; the form being motivated by *physical* assumptions: determinism with at most local pseudo-randomness. The physical assumptions mean that the correlations observed in each of the four possible experiments (combining one of Alice's two settings with one of Bob's two settings, and measuring very many photon pairs) are built up from the same two functions A and B and the same probability measure rho, in the familiar way: corr(a, b) = int A(a, lambda)B(b, lambda) rho(d lambda).

Bell himself in his paper answering his critics already discussed this common misunderstanding, very clearly.

[minkwe]

Richard says in his Statistical Science paper about Bell's Theorem:

its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

Yet he has never pointed out which terms in the "formulation" of the inequality correspond to outcomes of measurements not actually performed.

Obviously, Richard has abandoned the arguments made in the Statistical Science paper.

[gill1109]

Richard says in his Statistical Science paper about Bell's Theorem:

its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

Yet he has never pointed out which terms in the "formulation" of the inequality correspond to outcomes of measurements not actually performed.

Obviously, Richard has abandoned the arguments made in the Statistical Science paper.

I stand behind the arguments given there. All of the terms refer to outcomes of measurements which might have been performed. The mathematical model does not assume that any particular measurement is actually performed. Maybe Alice and Bob each take a break and have a cup of coffee.

Please read Bell's "Reply to critics", last half of last page.
https://cds.cern.ch/record/980330/files ... 061609.pdf
Bell writes: “These authors say ‘Clearly, since A, A′, B, B′ are all evaluated for the same λ, they must refer to four measurements carried out on the same electron–positron pair. We can suppose, for instance, that A′ is obtained after A, and B′ after B’. But by no means. We are not at all concerned with sequences of measurements on a given particle, or of pairs of measurements on a given pair of particles. We are concerned with experiments in which for each pair the ‘spin’ of each particle is measured once only. The quantities A(a', lambda), B(b', lambda) are just the same functions A(a, lambda), B(b, lambda) with different arguments.”

Excerpt From: Bell, J. S. “Speakable and Unspeakable in Quantum Mechanics”. Apple Books. My emphasis!

By the way, in the Statistical Science paper I was assuming no memory effects, no time trends, no time jumps. I kept it simple by way of introduction, and because I wanted to survey a great many more applications of statistics in Bell experiments. My 20 years earlier papers allow for those phenomena, introducing martingale methods so as to get p-values which depend only on the randomness of the setting choices; not on assumptions about randomness of the hidden variables.

https://arxiv.org/abs/1207.5103
Statistics, Causality and Bell's Theorem
Statistical Science 2014, Vol. 29, No. 4, 512-528
DOI: 10.1214/14-STS490

https://arxiv.org/abs/quant-ph/0301059
Time, Finite Statistics, and Bell's Fifth Position
pp. 179-206 in: Proc. of "Foundations of Probability and Physics - 2", Ser. Math. Modelling in Phys., Engin., and Cogn. Sc., vol. 5/2002, Växjö Univ. Press, 2003

https://arxiv.org/abs/quant-ph/0110137
Accardi contra Bell (cum mundi): The Impossible Coupling
pp. 133-154 in: Mathematical Statistics and Applications: Festschrift for Constance van Eeden. Eds: M. Moore, S. Froda and C. Léger. IMS Lecture Notes -- Monograph Series, Volume 42 (2003)
https://doi.org/10.1214/lnms/1215091935

[FrediFizzx]

@gill1109 A bunch of freakin' nonsense! I should just delete it by I will leave that up to Michel.
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[gill1109]

@gill1109 A bunch of freakin' nonsense! I should just delete it but I will leave that up to Michel.

Thanks, Fred. I'm looking forward to Michel's reaction.

By the way: here's a link to a round table discussion at the last Vaxjo meeting:

https://play.lnu.se/media/t/0_27j4ufvm
Round Table: Is quantum theory nonlocal? - QIP

[Justo]

.

While I have yet to read his papers, I have read their abstracts and found them interesting:

1) Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect, Journal of Modern Physics, 2021, 12, 1109-1144,

https://doi.org/10.4236/jmp.2021.128067.
.

Like Joy, I also find it interesting. I only have to read the abstract to understand what is going on. It all reduces to the infamous counterfactual definteness problem again. The author says :
"Designed to assess consequences of Einstein’s principle of local realism, the inequality pertains to a linear combination of four polarization products on the same pair of photons arising in a gedankenexperiment"

I totally agree, you do not have to be a mathematician to realize that this interpretation is meaningless. In my opinion, the best paper explaining this misinterpretation concerning the absurdity of counterfactual definiteness is Adenier's paper: paperhttps://www.worldscientific.com/do ... 10809_0002 w

[local]

Thank you for the interesting post, Justo.

Corrected the link:

https://www.worldscientific.com/doi/abs/10.1142/9789812810809_0002

The paper is available here too:

https://arxiv.org/abs/quant-ph/0006014

Dr. Adenier explained at a conference in 2009 that he no longer fully endorses the views of that paper. It's the same well-known story. Formally the bound is 4 but the statistics converge to a bound of 2 with enough trials. At the conference he presented a paper showing that photons could manifest both bosonic and fermionic characteristics depending on the conditions of the experiment, and demonstrated the effect experimentally. One might think that would garner a lot of interest and follow-up. Alas, not. He later left the field due to the bias against local realists and the need to make a good living for his new family. A brilliant and very friendly guy. Always very helpful to amateurs like myself. We need more people like him in quantum foundations.

[Joy Christian]

Formally the bound is 4 but the statistics converge to a bound of 2 with enough trials.

That is correct and it is the ace up the sleeves of Bell-believers, especially those who are statistically inclined. However, the bound of 2 cannot be derived without an additional assumption of the additivity of expectation values, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I explain here: https://arxiv.org/pdf/1704.02876.pdf.
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[gill1109]

Formally the bound is 4 but the statistics converge to a bound of 2 with enough trials.

That is correct and it is the ace up the sleeves of Bell-believers, especially those who are statistically inclined. However, the bound of 2 cannot be derived without an additional assumption of the additivity of expectation values, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I explain here: https://arxiv.org/pdf/1704.02876.pdf.

Dear Joy,

You write "Bell identified the above sum of four separate averages of real numbers (to be recorded, for example, in experimental runs performed on four different days) with the following single average"

He did no such thing. That's what you do. But nobody obliges you to do so.

I think that your argument is a nice example of a straw-man argument.

"local" put his finger on the crucial point. You don't have to be "statistically inclined" but it is essential to know some basic probability and statistics.

Giullaume Adenier is indeed a very nice guy. He is working in data-science and AI and still in quantum theory. He is very statistically inclined; indeed, gifted.

https://www.linkedin.com/in/guillaumeadenier/?locale=fr_FR
https://scholar.google.com/citations?hl=en&user=Zt5B-CMAAAAJ&view_op=list_works&sortby=pubdate

See for instance the very nice paper:

Test of the no-signaling principle in the Hensen loophole-free CHSH experiment
Guillaume Adenier, Andrei Yu. Khrennikov,
First published: 18 April 2017 https://doi.org/10.1002/prop.201600096
Abstract: We analyze the data from the loophole-free CHSH experiment performed by Hensen et al., and show that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger.

That experiment has to be redone with a ten times larger sample size and better random setting generators.

Richard

[Joy Christian]

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The bound of 2 on the CHSH correlator cannot be derived without an additional assumption of the additivity of expectation values over and above statistics, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I have explained here: https://arxiv.org/pdf/1704.02876.pdf. This shows that Bell's theorem is never proved but only assumed.
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[gill1109]

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The bound of 2 on the CHSH correlator cannot be derived without an additional assumption of the additivity of expectation values over and above statistics, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I have explained here: https://arxiv.org/pdf/1704.02876.pdf. This shows that Bell's theorem is never proved but only assumed.

Nope, you're wrong. Good luck with getting your work published.

[Joy Christian]

.
The bound of 2 on the CHSH correlator cannot be derived without an additional assumption of the additivity of expectation values over and above statistics, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I have explained here: https://arxiv.org/pdf/1704.02876.pdf. This shows that Bell's theorem is never proved but only assumed.

Nope, you're wrong. Good luck with getting your work published.

I couldn't care less whether my paper is published or not. What is important is that it recognizes the obvious flaw in Bell's argument and the double standards maintained by his followers.
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[gill1109]

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The bound of 2 on the CHSH correlator cannot be derived without an additional assumption of the additivity of expectation values over and above statistics, the assumption that Bell himself called "silly" in the context of von Neumann's theorem, as I have explained here: https://arxiv.org/pdf/1704.02876.pdf. This shows that Bell's theorem is never proved but only assumed.

Nope, you're wrong. Good luck with getting your work published.

I couldn't care less whether my paper is published or not. What is important is that it recognizes the obvious flaw in Bell's argument and the double standards maintained by his followers.

Bell did not found a religion. Saying that his "followers" maintain "double standards" is an ad hominem argument, ie, not an argument at all. Maybe it would work in an Oxford students' debating club. But not in academic discourse.

I'm having a delightful exchange of emails with fellow mathematical statistician Frank Lad. He's in New Zealand, and like me, he's not a young man anymore, so communication is slow. I hope to be able to report on our exchanges in a few days.

There is a nice joke about New Zealand. As you approach the airport the airline hostess calls "we are now approaching Auckland. Please set your clocks back fifty years".