The Mistakes by Bell and von Neumann are Identical

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: The Mistakes by Bell and von Neumann are Identical

Postby JohnDuffield » Sun Mar 08, 2020 10:42 am

There's lots of other errors in physics. Joy. Some of them are so utterly stupid it's like criminal insanity. For example we use the local motion of light to define the second. then we use the second to measure the local motion of light. So we say the speed of light is constant even though it isn't. It varies in the room you're in. If it didn't, your pencil wouldn't fall down. See this and this for further examples in gravitational physics and particle physics. We live in a dark age. Physics is an idiocracy.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Mon Mar 09, 2020 1:31 am

Joy Christian wrote:Let R, S, T, and U be Hermitian operators whose eigenvalues are r = AB, s = AB', t = A'B, and u = A'B', where A, B, A', and B' = +1 or -1 are the measurement results observed by Alice and Bob. Now, in the proof of Bell's "theorem," it is assumed that the sum of the individual eigenvalues, (r + s + t - u), is an eigenvalue of the sum (R + S + T - U) of the corresponding operators. Without this assumption, the stringent bounds of -2 and +2 on the CHSH correlator cannot be derived. But this assumption is simply false. No such correspondence between the Hermitian operator (R + S + T - U) and the sum (r + s + t - u) of individual eigenvalues exists mathematically.

Bell, working within a mathematical framework satisfying a property called Local Realism, does *not* assume any correspondence between measurements and Hermitian operators. Quantum mechanics *does* make such an assumption. You are explaining, correctly, why QM can violate Bell inequalities.

Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

In the real world, Bell's inequalities can be violated. So QM is a viable description of the real world, LR isn't.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Mon Mar 09, 2020 2:36 am

gill1109 wrote:
Joy Christian wrote:Let R, S, T, and U be Hermitian operators whose eigenvalues are r = AB, s = AB', t = A'B, and u = A'B', where A, B, A', and B' = +1 or -1 are the measurement results observed by Alice and Bob. Now, in the proof of Bell's "theorem," it is assumed that the sum of the individual eigenvalues, (r + s + t - u), is an eigenvalue of the sum (R + S + T - U) of the corresponding operators. Without this assumption, the stringent bounds of -2 and +2 on the CHSH correlator cannot be derived. But this assumption is simply false. No such correspondence between the Hermitian operator (R + S + T - U) and the sum (r + s + t - u) of individual eigenvalues exists mathematically.

Bell, working within a mathematical framework satisfying a property called Local Realism, does *not* assume any correspondence between measurements and Hermitian operators. Quantum mechanics *does* make such an assumption. You are explaining, correctly, why QM can violate Bell inequalities.

Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

In the real world, Bell's inequalities can be violated. So QM is a viable description of the real world, LR isn't.

Your comments reveal total cluelessness about what the hidden variable program is all about. They reveal a total lack of background in the history of the program starting from the debate between Einstein and Bohr in the 1920s and culminating in the EPR argument in 1935. One of the most important contributions in that debate was von Neumann's alleged proof against hidden variable theories. One of the key assumptions on which von Neumann's (by now discredited) proof is based is the following assumption:

Let R, S, T, and U be Hermitian operators on a Hilbert space and a, b, c, and d be real numbers. Then, von Neumann correctly assumed that, for a given state vector | psi >,

a < psi | R | psi > + b < psi | S | psi > + c < psi | T | psi > + d < psi | U | psi > = < psi | a R + b S + c T + d U | psi >.

As noted, this is a correct assumption. But von Neumann then went on to assume that it would be true also for the corresponding eigenvalues r, s, t, and u of the operators, giving

a < r > + b < s > + c < t > + d < u > = < a r + b s + c t + d u >,

where < . > is ordinary average within a hidden vriable theory. But as Einstein, Bell, Grete Hermann, and many others pointed out, the latter assumption does not hold for individual eigenvalues of operators. In particular, a r + b s + c t + d u is not an eigenvalue of the operator a R + b S + c T + d U. Thus von Neumann's alleged proof is based on a major blunder.

But that is precisely what Bell and his followers unwittingly assume to derive the bounds of -2 and +2 on the Bell-CHSH correlator. Of course, they do not tell us that they are implicitly assuming exactly what von Neumann had assumed. Instead, they use a sleight of hand, an outright deception, to justify the claim that bounds on the Bell-CHSH correlator would be -2 and +2. But that claim is wrong. The correct bounds on the Bell-CHSH correlator are -2\/2 and +2\/2, the same as those predicted by quantum mechanics. Thus there is absolutely no difference between the bounds predicted by quantum mechanics and those predicted by local realism. Therefore, both quantum mechanics and local realism are equally viable descriptions of the real world as far as the strong or quantum correlations are concerned. For more details you really ought to read my paper very carefully: https://arxiv.org/abs/1704.02876.

gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

But that assumption is manifestly wrong for any EPR-Bohm type experiment. The observables R, S, T, and U do not commute in such experiments. That is the Achilles heel of Bell's theorem.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby JohnDuffield » Mon Mar 09, 2020 1:54 pm

-2√2 and +2√2
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Mon Mar 09, 2020 2:32 pm

Joy Christian wrote:
gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

But that assumption is manifestly wrong for any EPR-Bohm type experiment. The observables R, S, T, and U do not commute in such experiments. That is the Achilles heel of Bell's theorem.


The spin operators R, S, T, and U do not commute in the EPRB experiments. This is a fact. But suppose one denies this fact. Suppose one insists --- just to be difficult --- that R, S, T, and U are commuting operators in the EPRB experiments. But in that case, even quantum mechanics predicts the bounds of -2 and +2 on the CHSH correlator:

By definition, we have R = AB, S = AB', T = A'B, and U = A'B'. Then the CHSH operator is simply CHSH = \sqrt{ 4 + [ A, A' ] [ B', B ] }, which reduces to +\-2 if R, S, T, and U are commuting.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Tue Mar 10, 2020 12:25 am

Joy Christian wrote:
Joy Christian wrote:
gill1109 wrote:Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

But that assumption is manifestly wrong for any EPR-Bohm type experiment. The observables R, S, T, and U do not commute in such experiments. That is the Achilles heel of Bell's theorem.

The spin operators R, S, T, and U do not commute in the EPRB experiments. This is a fact. But suppose one denies this fact. Suppose one insists --- just to be difficult --- that R, S, T, and U are commuting operators in the EPRB experiments. But in that case, even quantum mechanics predicts the bounds of -2 and +2 on the CHSH correlator: By definition, we have R = AB, S = AB', T = A'B, and U = A'B'. Then the CHSH operator is simply CHSH = \sqrt{ 4 + [ A, A' ] [ B', B ] }, which reduces to +\-2 if R, S, T, and U are commuting.

Yes, exactly. We agree yet again! The spin operators R, S, T, and U do not commute in EPR-B experiments, *if* you assume Bohm's conventional QM model of those experiments. If you start by assuming the absolute reality of the QM description of the world, then the case of commuting operators is a special case, and within that special case, you can use QM to derive the CHSH inequality.

Bell was careful to be agnostic in his "scientific" conclusions. He wrote that Bohr would have said "told you so!" in answer to Bell's theorem. Bell's *personal* inclination was to go for a non-local non-conspiratorial realistic description. But he carefully distinguished his opinions from his logical/mathematical deductions. The latter are always conditional, anyway - conditional on assumptions or axioms.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Tue Mar 10, 2020 1:43 am

gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

gill1109 wrote:
The spin operators R, S, T, and U do not commute in EPR-B experiments, *if* you assume Bohm's conventional QM model of those experiments. If you start by assuming the absolute reality of the QM description of the world, then the case of commuting operators is a special case, and within that special case, you can use QM to derive the CHSH inequality.

You are not going to escape the inescapable by making contradictory statements. Bohm's conventional quantum model is the only model for the EPRB experiment universally accepted by the physics community. So we agree that R, S, T, and U do not commute in those experiments. It is then inescapable that (r + s + t - u) is not an eigenvalue of the operator (R + S + T - U). But assuming that (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) is necessary for deriving the bounds of -2 and +2 on the CHSH correlator. In other words, assuming something patently wrong is necessary for deriving the conclusion of Bell's theorem. Here is a nice story illustrating what is wrong with that:

The famous British philosopher Bertrand Russell, in a lecture on logic, mentioned that in the sense of material implication, a false proposition implies any proposition.

A student raised his hand and said: "In that case, given that 1 = 0, prove that you are the Pope."

Russell immediately replied:

"Add 1 to both sides of the equation: then we have 2 = 1. The set containing just me and the Pope has 2 members. But 2 = 1, so it has only 1 member; therefore, I am the Pope."

The moral of the story is that you can prove anything and claim anything about anything if you start out with a false assumption, such as R, S, T, and U commute in the EPRB experiments.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Sat Mar 14, 2020 7:24 am

By the way, Jeffrey Bub has published a paper entitled "Is Von Neumann’s “No Hidden Variables” Proof Silly?"

He argues very carefully (and takes 15 pages to do this) that Bell (and others) misunderstood von Neumann's argument, which, he argues, is a whole lot more subtle than superficially appears.

Bub, J. (2011). Is Von Neumann's “No Hidden Variables” Proof Silly? In H. Halvorson (Ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation (pp. 393-408). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976971.012

For more recent work by Bub see
https://arxiv.org/abs/1804.03267
In Defense of a "Single-World" Interpretation of Quantum Mechanics
Jeffrey Bub
(Submitted on 9 Apr 2018)
In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then "we are forced to give up the view that there is one single reality." Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent "single-world" interpretation of the theory.
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics,
2018,
https://doi.org/10.1016/j.shpsb.2018.03.002.
(http://www.sciencedirect.com/science/ar ... 9817301788)
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Sat Mar 14, 2020 7:46 am

gill1109 wrote:
By the way, Jeffrey Bub has published a paper entitled "Is Von Neumann’s “No Hidden Variables” Proof Silly?"

He argues very carefully (and takes 15 pages to do this) that Bell (and others) misunderstood von Neumann's argument, which, he argues, is a whole lot more subtle than superficially appears.

Bub, J. (2011). Is Von Neumann's “No Hidden Variables” Proof Silly? In H. Halvorson (Ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation (pp. 393-408). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976971.012

I know Jeff Bub very well. A student of David Bohm. We were together at the Perimeter Institute and I also visited him at the University of Western Ontario when he was a professor there.

Unfortunately, in recent years Jeff has become a firm believer in quantum information theory and also a firm believer in Bell's fallacious theorem. So he has his own reasons for arguing what he is arguing in the paper you have linked. No one in the foundations of quantum mechanics is persuaded by his argument. In fact, it has been thoroughly debunked by David Mermin and Rudiger Schack in this fine paper: https://link.springer.com/article/10.10 ... 018-0197-5. So, nice try, but you will not be able to save Bell's "theorem" by invoking Jeff Bub's argument.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Sun Mar 15, 2020 4:20 am

Joy Christian wrote:
gill1109 wrote:By the way, Jeffrey Bub has published a paper entitled "Is Von Neumann’s “No Hidden Variables” Proof Silly?"He argues very carefully (and takes 15 pages to do this) that Bell (and others) misunderstood von Neumann's argument, which, he argues, is a whole lot more subtle than superficially appears.
Bub, J. (2011). Is Von Neumann's “No Hidden Variables” Proof Silly? In H. Halvorson (Ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation (pp. 393-408). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976971.012

I know Jeff Bub very well. A student of David Bohm. We were together at the Perimeter Institute and I also visited him at the University of Western Ontario when he was a professor there. Unfortunately, in recent years Jeff has become a firm believer in quantum information theory and also a firm believer in Bell's fallacious theorem. So he has his own reasons for arguing what he is arguing in the paper you have linked. No one in the foundations of quantum mechanics is persuaded by his argument. In fact, it has been thoroughly debunked by David Mermin and Rudiger Schack in this fine paper: https://link.springer.com/article/10.10 ... 018-0197-5. So, nice try, but you will not be able to save Bell's "theorem" by invoking Jeff Bub's argument.

Thanks for the link. Here is another voice from the past:
Some local models for correlation experiments, Arthur Fine, Synthese volume 50, pages 279–294 (1982)
SOME LOCAL MODELS FOR CORRELATION EXPERIMENTS
ABSTRACT. This paper constructs two classes of models for the quantum correlation experiments used to test the Bell-type inequalities, synchronization models and prism models. Both classes employ deterministic hidden variables, satisfy the causal requirements of physical locality, and yield precisely the quantum mechanical statistics. In the synchronization models, the joint probabilities, for each emission, do not factor in the manner of stochastic independence, showing that such factorizability is not required for locality. In the prism models, the observables are not random variables over a common space; hence these models throw into question the entire random variables idiom of the literature. Both classes of models appear to be testable.

Behind a paywall but if anyone wants a pdf they can PM me.

It occurred to me in this time of Corona virus how frail we all are and how vulnerable (perhaps?) are small independent institutions like the Einstein centre. http://einstein-physics.org/. The prime minister of the UK is counting on herd immunity. I suppose that he believes that the 1 million deaths which will be needed to achieve that would all occur in the herd, ie among the people who vote for him, and not among his friends, who are running the UK show and no doubt profiting from it mightily in one way or another. Having advance knowledge of draconian government interventions would certainly be useful for those able to deploy lots of cash on the stock-market.

Anyway, I would recommend you populate your board of scientific advisors and establish and publish some rules of transparent governance. In this time of populism and fake news, we need independent research organisations which dare to deviate from establishment scientific opinions. Even if they are merely a "thorn in the side" (in Dutch we say "a louse in the fur"). I hope all the participants and lurkers on this forum take good care of their health, keep calm and keep smiling, and carry on passionately seeking truth.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby JohnDuffield » Tue Mar 17, 2020 2:59 pm

There's a copy of Arthur Fine's paper here.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Wed Mar 18, 2020 11:13 am

Joy Christian wrote:
gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.

gill1109 wrote:
The spin operators R, S, T, and U do not commute in EPR-B experiments, *if* you assume Bohm's conventional QM model of those experiments. If you start by assuming the absolute reality of the QM description of the world, then the case of commuting operators is a special case, and within that special case, you can use QM to derive the CHSH inequality.

You are not going to escape the inescapable by making contradictory statements. Bohm's conventional quantum model is the only model for the EPRB experiment universally accepted by the physics community. So we agree that R, S, T, and U do not commute in those experiments. It is then inescapable that (r + s + t - u) is not an eigenvalue of the operator (R + S + T - U). But assuming that (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) is necessary for deriving the bounds of -2 and +2 on the CHSH correlator. In other words, assuming something patently wrong is necessary for deriving the conclusion of Bell's theorem.

So here is an extraordinary fact. For more than half a century the physics community has believed in Bell's so-called "theorem" as something written in stone. Any attempt to challenge it has been ridiculed, disdained, rejected, and suppressed with contempt. And this is often done anonymously, behind the closed doors of editorial offices and peer-reviewer desks. It is not difficult to imagine how many legitimate research papers would have been rejected by the journals, sometimes even without a review, simply for challenging Bell's conclusions. A typical response of a peer-reviewer, if a response is even provided, goes like this:

Reviewer # 2 wrote:
This paper attempts to disprove Bell’s theorem, one of the fundamental results of quantum mechanics. Bell’s theorem cannot be disproved, just like, e.g., Pythagorean theorem. In fact, the proof of Bell’s theorem is simple and straightforward. The theorem imposes restrictions (inequalities) on the correlations functions under assumptions of local realism and the existence of hidden variables. Numerous experiments done in the past thirty or so years show clearly that quantum systems violate Bell’s inequalities, thus violating at least one of the assumptions of Bell's theorem. Therefore, I cannot recommend this paper for publication.

I have received literally hundreds of reviewer reports like the above for the past thirteen years in my attempts to convince the physics community that they have been duped by Bell and his followers. And now it turns out that Bell's "theorem", however Bell's followers try to spin it, relies on an undeniable falsehood. Namely, (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) even if R, S, T, and U are non-commuting operators. I think President Trump and Prime Minister Johnson can learn a thing or two from the followers of Bell who claim to be geniuses.

If you don't believe me, then please read this short paper and think for yourself: https://arxiv.org/abs/1704.02876.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby FrediFizzx » Wed Mar 18, 2020 12:15 pm

Bell's junk physics theory is not the only shell game in physics. Renormalization is the other big one that John brought up recently.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Sun Mar 22, 2020 4:26 am

Joy Christian wrote:You are not going to escape the inescapable by making contradictory statements.

I don't think I'm contradicting myself. I do do that sometimes, maybe even often, but not right now.
Joy Christian wrote:Bohm's conventional quantum model is the only model for the EPRB experiment universally accepted by the physics community. So we agree that R, S, T, and U do not commute in those experiments. It is then inescapable that (r + s + t - u) is not an eigenvalue of the operator (R + S + T - U).

Yes, I can agree with that. More precisely, I would say: they do not commute in the agreed model for those experiments. Of course, what everyone in some scientific community agrees may well be wrong. It has happened before... (e.g. whether or not the Earth is the centre of the universe, or the planets move in circles, or the earth is flat, or that physics is essentially finished with aside for a triple of little issues which will be fixed easily very soon).
Joy Christian wrote:But assuming that (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) is necessary for deriving the bounds of -2 and +2 on the CHSH correlator. In other words, assuming something patently wrong is necessary for deriving the conclusion of Bell's theorem.

No, that assumption is not used to derive the CHSH inequality. The proof of Bell's theorem uses the very different assumption of local realism to derive a contradiction with the predictions of quantum mechanics (and nowadays we can add to that, a contradiction with the observations of experimenters).

What you are saying, I think, is that if you are OK with QM then there is not a problem. As Bell said: "Niels Bohr would have said, I told you so". I can agree with that.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Sun Mar 22, 2020 4:49 am

***
I hear that John S. Bell has been beatified by the church of Quantum Fraudation and it is only a matter of time before he will be declared a saint --- Saint John of nonlocality and nonreality.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby gill1109 » Mon Mar 23, 2020 12:47 am

Joy Christian wrote:I hear that John S. Bell has been beatified by the church of Quantum Fraudation and it is only a matter of time before he will be declared a saint --- Saint John of nonlocality and nonreality.

Yes, indeed. That's my church. This is also called quantum Buddhism. It's a kind of solipsism.

Talking of churches, yesterday, deep in the forest, I saw 25 Christians in a very tight circle playing musical instruments and singing and recording this on a smartphone. All ages - from very old to very young. All very close to one another.

Maybe they got some special information from Jesus which most of us are not privy to.

I live in the Dutch bible belt. Not far, there are small villages where nobody is vaccinated. Does this give me some herd immunity?
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Mon Mar 23, 2020 6:13 am

***
I have worked out the correct eigenvalue of the operator (R + S + T - U) relevant for the Bell's implicit assumption [cf. eq. (16) or (29) of this paper: https://arxiv.org/abs/1704.02876].

The correct eigenvalue of the operator (R + S + T - U) is

(1) ,

where , and l, m, n, o, p, and q are the eigenvalues of the operators L = RS - SR, M = RT - TR, N = TS - ST, O = US - SU, P = UR - RU, and Q = UT - TU, respectively.

Now, implementing what they think is the demand of local realism, Bell and his followers assume that the eigenvalue of the operator (R + S + T - U) is (r + s + t - u). But that is true if and only if the operators R, S, T, and U commute with each other. This is easy to see from the above eq. (1). When R, S, T, and U all commute with each other, then z = 0 and the eigenvalue reduces to (r + s + t - u). But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. So Bell and his followers assume a wrong eigenvalue of the operator (R + S + T - U) and thus incorrectly implement Einstein's notion of local realism. It is a simple mathematical mistake. And it invalidates the bounds of -2 and +2 on the CHSH correlator. The correct bounds follow if we use the correct eigenvalue (1) worked out above. The correct bounds work out to be and , exactly as those predicted by quantum mechanics. Thus there is no incompatibility between quantum mechanics and local realism.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby Heinera » Mon Mar 23, 2020 9:02 am

Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]

Well, they do commute in a macroscopic experiment with colorful exploding balls.
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Re: The Mistakes by Bell and von Neumann are Identical

Postby Joy Christian » Mon Mar 23, 2020 9:10 am

Heinera wrote:
Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]

Well, they do commute in a macroscopic experiment with colorful exploding balls.

That kind of deflection is not going to help the Bell-believers. It would be much more honest and dignified to recognize the silly mistake Bell and his followers have made and apologize to the physics community for misleading them for over fifty years.

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Re: The Mistakes by Bell and von Neumann are Identical

Postby Heinera » Mon Mar 23, 2020 10:30 am

Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]

Well, they do commute in a macroscopic experiment with colorful exploding balls.

That kind of deflection is not going to help the Bell-believers. It would be much more honest and dignified to recognize the silly mistake Bell and his followers have made and apologize to the physics community for misleading them for over fifty years.

***

Why do you think it is a deflection? Se the paper below, where just such a macroscopic experiment is proposed, and where a violation of the Bell inequalities is predicted.

https://arxiv.org/abs/1211.0784v4
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