Bell's Theorem Begs the Question

[Joy Christian]

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I have written up a new critique of Bell’s theorem: https://www.researchgate.net/publicatio ... e_Question

It demonstrates that Bell’s theorem assumes its conclusion and thus harbors a logical fallacy (𝘱𝘦𝘵𝘪𝘵𝘪𝘰 𝘱𝘳𝘪𝘯𝘤𝘪𝘱𝘪𝘪). While Gleason’s theorem and its corollary vindicate Bohr’s view by necessitating local contextuality, Bell’s “theorem” does not necessitate non-locality or rule out Einstein’s local realism even when statistical independence of sub-experiments is respected.

Here is the abstract of my paper:

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

Have a Happy New Year!

Joy Christian
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[FrediFizzx]

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I have written up a new critique of Bell’s theorem: https://www.researchgate.net/publicatio ... e_Question

It demonstrates that Bell’s theorem assumes its conclusion and thus harbors a logical fallacy (𝘱𝘦𝘵𝘪𝘵𝘪𝘰 𝘱𝘳𝘪𝘯𝘤𝘪𝘱𝘪𝘪). While Gleason’s theorem and its corollary vindicate Bohr’s view by necessitating local contextuality, Bell’s “theorem” does not necessitate non-locality or rule out Einstein’s local realism even when statistical independence of sub-experiments is respected.

Sure. However, I think Einstein and Bell and others got sidetracked by the assumption that quantum mechanics needs hidden variables to be completed to be local. It seems that all that is needed is 3 or 7 sphere topology.

viewtopic.php?p=886#p886
http://dx.doi.org/10.13140/RG.2.2.22142.25927

So, Bell's whole hidden variable program is indeed a bunch of junk physics.

Happy New Year!
.

[Joy Christian]

.
I have written up a new critique of Bell’s theorem: https://www.researchgate.net/publicatio ... e_Question

It demonstrates that Bell’s theorem assumes its conclusion and thus harbors a logical fallacy (𝘱𝘦𝘵𝘪𝘵𝘪𝘰 𝘱𝘳𝘪𝘯𝘤𝘪𝘱𝘪𝘪). While Gleason’s theorem and its corollary vindicate Bohr’s view by necessitating local contextuality, Bell’s “theorem” does not necessitate non-locality or rule out Einstein’s local realism even when statistical independence of sub-experiments is respected.

Sure. However, I think Einstein and Bell and others got sidetracked by the assumption that quantum mechanics needs hidden variables to be completed to be local. It seems that all that is needed is 3 or 7 sphere topology.

viewtopic.php?p=886#p886
http://dx.doi.org/10.13140/RG.2.2.22142.25927

So, Bell's whole hidden variable program is indeed a bunch of junk physics.

Happy New Year!
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Sure, Fred. The idea behind my paper is to demonstrate that Bell-believers are wrong even within their own game!
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[FrediFizzx]

Who was it that started the hidden variable nonsense?

[Joy Christian]

Who was it that started the hidden variable nonsense?

It was von Neumann, inspired by the debate between Einstein and Bohr in the 1920s.
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[Joy Christian]

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The bottom line is, Bell's theorem is based on a hefty dose of cheating and dishonesty. Not to mention aggressive defense and gaslighting by its advocates.
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[Joy Christian]

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Here is a slightly revised version of my paper: https://doi.org/10.48550/arXiv.2302.09519


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[Dirkman2]

Sabine Hossenfelder, in her 9th of July youtube video about Bell, said that the conclusion is we can either have a) or b), and the nobel was actually awarded for proving that we have either a) or b)

a)measurement independence=>violation of local causality
b)local causality=>violation of measurement independence

[Joy Christian]

Sabine Hossenfelder, in her 9th of July youtube video about Bell, said that the conclusion is we can either have a) or b), and the nobel was actually awarded for proving that we have either a) or b)

a)measurement independence=>violation of local causality
b)local causality=>violation of measurement independence

Sabine is a friend of mine, but I do not agree with her on this point. She, like 't Hooft, is a proponent of what is usually referred to as "superdeterminism", which amounts to assuming a "violation of statistical independence." Sabine has now invented a new name for "statistical independence" and calls it "measurement independence." That is a rhetorical trick. But "What's in a name? That which we call a rose by any other name would smell as sweet."

Whatever we call it, mathematically "measurement independence" means the following condition on the probability distribution:

p(h | a, b) = p(h),

where "h" stands for "hidden variables" (which I prefer to call "the initial state of the system"), "a" and "b" are the experimental settings, and p(h) is the probability distribution of the hidden variables (or the initial states) "h".

Unless Sabine allows violation of the above condition assumed by Bell, she cannot do her superdeterminism stuff. Indeed, Bell inequalities are derived assuming p(h | a, b) = p(h) explicitly. So Sabine wants to abandon this condition. And voila, Bell inequalities can no longer be derived!

That sounds pretty innocent but it is not. Because a violation of the above condition introduces a subtle form of non-locality. This is very well known. So, by violating "measurement independence" Sabine violates local causality after all. She has not got rid of the problem --- just renamed it. Sorry, Sabine.
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[FrediFizzx]

"Hidden variables" are a red herring. Bell screwed up.

[Joy Christian]

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I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

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[FrediFizzx]

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I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves.
.

[FrediFizzx]

.
I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves.

And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.
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[Joy Christian]

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I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:

Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves.

And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.
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I think by hidden variable you mean something else than what is usually meant by it. I think you mean the orientation "lambda" of the old version of the 3-sphere model. But the symbol "lambda" is not of any significance for the general meaning of the hidden variable. In the latest version of the 3-sphere model, the hidden variable is the direction s1 = s2 = s of the axis about which the spins L1 and L2 are rotating. So the model is based on a statistical distribution of the direction s1 = s2 = s of the spin initially emerging from the source. But that direction is precisely what Bell used in his local model. What we have symbolized as s1 = s2 = s is what Bell symbolized as vector lambda in the local model he presented in Section 3 of his 1964 paper. So there is indeed a hidden variable even in the latest version of the 3-sphere model. But it is symbolized as s1 = s2 = s rather than as vector lambda.

But you are right about entanglement. It is not a fundamental feature of Nature. It is just a placeholder for correlations. It is not at all mysterious.
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[FrediFizzx]

Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves.

And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.

I think by hidden variable you mean something else than what is usually meant by it. I think you mean the orientation "lambda" of the old version of the 3-sphere model. But the symbol "lambda" is not of any significance for the general meaning of the hidden variable. In the latest version of the 3-sphere model, the hidden variable is the direction s1 = s2 = s of the axis about which the spins L1 and L2 are rotating. So the model is based on a statistical distribution of the direction s1 = s2 = s of the spin initially emerging from the source. But that direction is precisely what Bell used in his local model. What we have symbolized as s1 = s2 = s is what Bell symbolized as vector lambda in the local model he presented in Section 3 of his 1964 paper. So there is indeed a hidden variable even in the latest version of the 3-sphere model. But it is symbolized as s1 = s2 = s rather than as vector lambda.

But you are right about entanglement. It is not a fundamental feature of Nature. It is just a placeholder for correlations. It is not at all mysterious.

Well, quantum mechanics knows about the singlet vector, s, and s1 and s2. So, I'm not sure how that would be classified as hidden. Let's see if we can find an agreeable definition of hidden variable... Boy! That was pretty unsatisfying! "Possibly unobservable" is maybe the best. Other descriptions don't have the variable all that hidden. Anyways, s, s1 and s2 can be used in both classical and quantum mechanics solutions for the correlations so let's not count them as hidden variables. So, I stand by the fact that hidden variables as far as the EPR scenario goes is a bunch of junk physics.

But we still have the strong correlations predicted by both classical and quantum mechanics and no need for hidden variables. Now..., how about superposition?
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[FrediFizzx]

The "hidden variables" saga gets even stranger... EPR was claiming that quantum mechanics is incomplete so it needs hidden variables to complete it. So, why did Bell put hidden variables on a classical mechanics scenario? He did it backwards!!!!
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[Joy Christian]

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I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be.

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.
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[FrediFizzx]

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I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be.

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.

After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.
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[Joy Christian]

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I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be.

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.

After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.

Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.
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[FrediFizzx]

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I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be.

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.

After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.

Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.

Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?
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