A Mathematician's Refutation of Bell's Theorem

[Joy Christian]

Bell did not found a religion.

Neither did Marx or Christ. But the followers of Bell, Marx, and Christ did. The most damaging religion is founded by the followers of Bell. Bell would have been deeply disappointed.
.

[FrediFizzx]

Bell did not found a religion.

Neither did Marx or Christ. But the followers of Bell, Marx, and Christ did. The most damaging religion is founded by the followers of Bell. Bell would have been deeply disappointed.

[minkwe]

It's the same well-known story. Formally the bound is 4 but the statistics converge to a bound of 2 with enough trials.

Actually, I disagree with the second part of that. The key question is "the statistics" of what? There are tons of simulations showing that the statistics do not converge to a bound of 2. Why is that? Because it is important to understand the "what"? In Adenier's paper, he asks an important question:

To begin, the exact meaning of the simultaneous presence of different arguments in a CHSH function must be clarified. Basically, there are two possible interpretations, the strongly objective interpretation and the weakly objective
interpretation [12, 13]:
- Strongly Objective Interpretation implies that all correlation functions are relevant to the same set of N particle
pairs, that is, all four pairs of directions are considered simultaneously relevant to each particle pair. As such
they cannot be relevant to actual experiments but rather with what result would have been obtained if measured
on the same set of N particle pairs along different directions.
- Weakly Objective Interpretation implies that each correlation function is actually to be measured on distinct
sets of N particle pairs. Each set of N particle pairs pertains to only one pair of arguments, that is, for each
pair only one joint spin measurement is executed.

Notwithstanding current claims of disavowal by him, he is correct. This is a crucial point and even Bell believers do not agree among themselves what the correct interpretation is. Even Bell himself is opaque on the issue. Besides, it is obvious from looking at Bell's arithmetic that the correct answer is a mixture.

You can start with P(a,b) - P(a,c) within the weakly objective interpretation as Bell claims that he does, and then through arithmetic manipulation arrive at P(b,c) which is stitched from parts of P(a,b) and P(a,c) as Bell did. In that case, the final inequality containing P(a,b), P(a,c), and P(b,c) is not entirely weakly objective as Bell claims in his reply to critics. It can't be. What Bell's followers conveniently ignore is the fact that Bell did not take three weakly objective terms place them in a box, shake them vigorously, and out fell the inequality. He placed only two weakly objective terms in that box (if any). The third therm appearing there can't be independent of the other two and therefore can't be weakly objective as he later claims, or as Justo claims now.

[Justo]

The third therm appearing there can't be independent of the other two and therefore can't be weakly objective as he later claims, or as Justo claims now.

I show explicitly, for the CHSHS case, why Bell's derivation can be understood as weakly objective in this paper https://doi.org/10.1007/s10701-021-00488-z
Perhaps somebody would want to tell me where I went wrong. I can very well be mistaken. The story that is correct because it was peer reviewed is not valid for me. I'll be happy to recognize any mistake if the argument convinces me.
Marian Kupczynski told me that he was going to issue a comment on my mistakes. I told him that would welcome his criticisms explaining by mistakes. I am still waiting.

[gill1109]

You can start with P(a,b) - P(a,c) within the weakly objective interpretation as Bell claims that he does, and then through arithmetic manipulation arrive at P(b,c) which is stitched from parts of P(a,b) and P(a,c) as Bell did. In that case, the final inequality containing P(a,b), P(a,c), and P(b,c) is not entirely weakly objective as Bell claims in his reply to critics. It can't be. What Bell's followers conveniently ignore is the fact that Bell did not take three weakly objective terms place them in a box, shake them vigorously, and out fell the inequality. He placed only two weakly objective terms in that box (if any). The third therm appearing there can't be independent of the other two and therefore can't be weakly objective as he later claims, or as Justo claims now.

Michel,

There are many ways to derive a mathematical formula. Bell first of all writes down some physical hypotheses which tell him about existence of functions A, B and rho and lead him to the formula P(a, b) = integral….. Observe that B must be the negative of A because P(a, a) = -1 for all a. Now pick any a, b, c and write down formulas for P(a,b), P(a,c), and P(b,c). The same formula three times with different arguments filled in. Now do some simple algebra and calculus. Get his original three correlations inequality. That little derivation is a piece of mathematical formula manipulation. Its validity does not depend on any physical interpretation of any of the intermediate expressions.

Now notice that the inequality you got is violated by QM predictions. Notice that the QM predictions are confirmed in experiments. Conclusion: those physical hypotheses are invalid.

The three expressions P(a,b), P(a,c), and P(b,c) are not *mathematically independent* because they are built up out of some common ingredients: a probability distribution over a set containing all values of some unobserved physical variable lambda, which does not depend on the settings, and a measurement function.

Computer simulations which violate the inequality do so by violating the assumptions. They could in principle correspond to a physically reasonable explanation of the results of some experiments.

Justo is right. Moreover Bell is very clear what he is doing. The objections people raise today were also raised in the early years, and Bell answered his critics, in my opinion quite adequately, though very succinctly. In effect, he underscored the distinction between mathematical-physical modelling on the one hand, and analysing a given mathematical model, mathematically, on the other hand. He does *not* suppose that polarisation of a given pair of photons could be measured simultaneously in many directions at once. His results match the physical fact that one cannot do that - because those local hidden variables just do not exist.

I have corresponded a great deal over the years with Marian Kupczynski, who I met long ago at Växjö. And we have corresponded again in recent months about some of his most recent papers. He might be slowly refining his opinions about these matters.

[FrediFizzx]

... Now notice that the inequality you got is violated by QM predictions. ...

It's pure nonsense. No one has ever noticed that. It is mathematically impossible. It's the old bait and switch trick.
.

[local]

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.

This guy whines about ad hominems in his first sentence, and then delivers one in his next sentence. It's narcissistic blindness. These people never look within; it's always the other guy.

...he's not a young man anymore, so communication is slow.

Now he projects his slowness onto others. Remember, guys, the narc's stock-in-trade is gaslighting, muddying, and projection.

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".

And now this guy delivers a totally out-of-place insult to an entire country. He's oh-so-clever, don't you know?

[local]

... Now notice that the inequality you got is violated by QM predictions. ...

It's pure nonsense.

Yes, Fred, of course it is nonsense. The quantum mysterians want us to believe that a joint measurement can be achieved with separated measurements. They won't acknowledge that "the quantum prediction" may vary depending on the conditions of the experiment. If you have separated measurements, the joint prediction cannot be applied (Graft). If you resort to Luders projection then you violate Einstein's special relativity. The mysterians try to evade that by calling the projected information "passion". A tragic joke on science.

[local]

... even Bell believers...

When an argument appeals to rhetoric it's likely false.

[gill1109]

... Now notice that the inequality you got is violated by QM predictions. ...

It's pure nonsense.

Yes, Fred, of course it is nonsense. The quantum mysterians want us to believe that a joint measurement can be achieved with separated measurements. They won't acknowledge that "the quantum prediction" may vary depending on the conditions of the experiment. If you have separated measurements, the joint prediction cannot be applied (Graft). If you resort to Luders projection then you violate Einstein's special relativity. The mysterians try to evade that by calling the projected information "passion". A tragic joke on science.

You violate Einstein's special relativity if you take the wave function as being "real", and its collapse as being real and as being located in ordinary 3D space and happening in ordinary time. If you only "use" the usual rules to get empirical predictions you are not violating anything. If the predictions moreover turn out to be correct then apparently you are onto a good thing. You don't have to *imagine* spookiness or weird passion. And you may call it what you like. It doesn't change the facts.

The standard statistical predictions of QM are entirely compatible with special relativity. Donald Graft and many others before him have said that "if you have separated measurements, the joint prediction cannot be applied". Nobody expected Aspect's experiment to produce the singlet correlations. Of course, anybody is allowed to write their own rule book, but they can't impose it on anyone else. The interesting question is whether their rule book gives the right predictions. Answer: Graft's rule book does not give the right predictions. The fact is that the conventional joint prediction is confirmed by experiment. Good. So the physicist's job is to find a way to explain it. QM does not explain much. It tells you how states evolve in time, in that sense it is a "mechanics". But QM does not explain *how* the Born rule comes to be true, it does not describe what actually happens at the level of individual realisations. Quantum states live in complex Hilbert spaces. Born rule probabilities are supposed to predict experimentally observed statistics. They do a good job at that modest aim.

[local]

Such predictable mysterian nonsense! Sounding desperate now.

Show us the derivation of -a.b for separated measurements. That will require transfer of information. For a space-like separation that information will have to be transferred superluminally. There is no escape.

Here we have a "mathematical statistician" telling us that a joint distribution can be sampled with separated (marginal) measurements. The same guy we had to school on copulas. Is it any wonder he has been called third-rate?

Now cite the one definitive EPRB experiment that you claim proves the joint prediction. Piling up a bunch of ridiculous flawed experiments proves nothing. You mention Aspect, but that experiment was discredited decades ago. Is that the experiment you want to hang your hat on? Or perhaps you prefer Weihs' nonsense? Or maybe the experiment you admitted needs to be ten times longer? Or maybe the experiments for which the authors refuse to make available the full raw data (it's too big, don't you know?) Pathetic!

Finally, you can spare us your trite little lectures on QM and other stuff we already know. Nobody is impressed by your feigned erudition.

[local]

Actually, I disagree with the second part of that. The key question is "the statistics" of what? There are tons of simulations showing that the statistics do not converge to a bound of 2.

Can you please cite the best one out of the tons you claim? I expect that it will simply demonstrate one of the well-known "loopholes", such as the detection or coincidence "loopholes". In the absence of these pathologies there will be convergence to 2.

[minkwe]

Actually, I disagree with the second part of that. The key question is "the statistics" of what? There are tons of simulations showing that the statistics do not converge to a bound of 2.

Can you please cite the best one out of the tons you claim? I expect that it will simply demonstrate one of the well-known "loopholes", such as the detection or coincidence "loopholes". In the absence of these pathologies there will be convergence to 2.

Not sure what you mean by "best one". But here are just a few of the multitude :

"Event-by-event simulation of experiments to create entanglement and violate Bell inequalities", Proc. SPIE 8832, The Nature of Light: What are Photons? V, 88321M (1 October 2013); https://doi.org/10.1117/12.2021863


Discrete-Event Simulation of an Extended Einstein-Podolsky-Rosen-Bohm Experiment
Front. Phys., 12 May 2020 | https://doi.org/10.3389/fphy.2020.00160

Clauser-Horne/Eberhard inequality violation by a local model
Adv. Sci. Eng. Med. 8, 496-502 (2016)

I myself have written two "unpublished" local realistic simulations which "violate" the inequalities and produce results very similar to QM.

[local]

Thank you for your reply. I have limited time to look into these things so I am asking which one you personally consider to be the most definitive and illuminating of your claim. Then we can discuss that one. As I said, I expect to be able to quickly identify the "loophole" that is being invoked. In the absence of such pathologies, the statistics converge to 2.

[minkwe]

All of them. Pick one.

[local]

That's non-responsive. Not playing that game.

[minkwe]

Michel,

There are many ways to derive a mathematical formula.

That's your problem. The same mathematical formulas can represent completely different things in physics. One can represent a strongly objective correlation on the same pair of particles as the others, while another similar-looking formula can represent weakly objective correlations on disjoint sets of particle pairs. The formulas may look the same but the *values* may be completely different. Just because a mathematical formula shows up in an equation does not mean it *represents* the same thing as a similar-looking formula from somewhere else.

Bell first of all writes down some physical hypotheses which tell him about existence of functions A, B and rho and lead him to the formula P(a, b) = integral….. Observe that B must be the negative of A because P(a, a) = -1 for all a. Now pick any a, b, c and write down formulas for P(a,b), P(a,c), and P(b,c). The same formula three times with different arguments filled in. Now do some simple algebra and calculus. Get his original three correlations inequality. That little derivation is a piece of mathematical formula manipulation. Its validity does not depend on any physical interpretation of any of the intermediate expressions.

All true but completely irrelevant. The validity of Bell's inequality is uncontested. What is contested is the physical interpretation of its meaning and application.

Now notice that the inequality you got is violated by QM predictions. Notice that the QM predictions are confirmed in experiments. Conclusion: those physical hypotheses are invalid.

Wrong! For two of the terms, QM gives you a prediction. For the third term in the inequality, you have used the wrong QM prediction to claim violation. You are making an error in your application of your albeit valid inequality to the physical situation described by QM and observed in experiments. You are doing a bait and switch.

The three expressions P(a,b), P(a,c), and P(b,c) are not *mathematically independent* because they are built up out of some common ingredients: a probability distribution over a set containing all values of some unobserved physical variable lambda, which does not depend on the settings, and a measurement function.

Again, this is a subterfuge. P(a,b) and P(a,c) being weakly objective (as Bell claims) are independent in ways in which P(b,c) is not relative to P(a,b) and P(a,c). This much is very obvious. Bell starts with P(a,b) and P(b,c) and from those two he derives P(b,c). P(b,c) in the inequality is more restricted than P(a,b) and P(a,c) due to the cyclic nature of the terms. This is the core ingredient of all variants of Bell's theorem. They include a hidden reduction of independence that is simply ignored when comparing the results with experimental data where no such reduction in independence is present.

Why must the terms be cyclical? Why has nobody been able to "prove" Bell's theorem without relying on a cyclicity? What manner of "non-realism" or "non-locality" is this that only shows up when terms are cyclically related? I would have expected more curiosity from you on such topics.

Computer simulations which violate the inequality do so by violating the assumptions. They could in principle correspond to a physically reasonable explanation of the results of some experiments.

Oh so now you agree with me that it is very important to know "What" statistics converge to 2? You admit that there are local realistic statistics that converge to 2 and non-local statistics that do not converge to 2?

Justo is right. Moreover Bell is very clear what he is doing. The objections people raise today were also raised in the early years, and Bell answered his critics, in my opinion quite adequately,

He did not. Here is what he did. Critics argued that he was using a single 3xN spreadsheet instead of 3 disjoint 2xN spreadsheets. He replied that he was using 3 disjoint 2xN spreadsheets. But based on his equations, that is false. He is using 2 2xN spreadsheets and from each of them he separates one column, recombines them to generate a third 2xN spreadsheet that is not independent of the other two in the same way the first two are independent from each other. While it appears to diffuse the criticism, it does not eliminate it. Perhaps he did not understand the root of the problem.

[minkwe]

That's non-responsive. Not playing that game.

Not playing it either. It is your game. You asked for citations I gave you three it's very easy to pick one of them unless you just want to argue.

[minkwe]

The third therm appearing there can't be independent of the other two and therefore can't be weakly objective as he later claims, or as Justo claims now.

I show explicitly, for the CHSHS case, why Bell's derivation can be understood as weakly objective in this paper https://doi.org/10.1007/s10701-021-00488-z
Perhaps somebody would want to tell me where I went wrong. I can very well be mistaken. The story that is correct because it was peer reviewed is not valid for me. I'll be happy to recognize any mistake if the argument convinces me.
Marian Kupczynski told me that he was going to issue a comment on my mistakes. I told him that would welcome his criticisms explaining by mistakes. I am still waiting.

I already explained it to you in the other thread but you were too distracted to follow carefully. Perhaps you want to review the thread and the discussion therein: viewtopic.php?f=6&t=482

[local]

I gave you three it's very easy to pick one of them unless you just want to argue.

Two of them invoke the coincidence "loophole". That has been uninteresting for many years as the recent experimental protocols eliminate it.