## What exactly is Bell's Theorem?

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### Re: What exactly is Bell's Theorem?

Joy Christian wrote:
gill1109 wrote:No, it is not all I can do. Participate in our conference and help us re-formulate Bell's theorem.https://gill1109.com/2020/10/02/time-reality-and-bells-theorem/

Fred, if I were you, I wouldn't touch Gill's "conference" with a barge pole. No matter how one tries to "re-formulate" garbage, it remains garbage. A dog born in a barn remains a dog.

The conference is organised by Sabine Hossenfelder, Ivette Fuentes, Jay Yablon and Jan-Ake Larsson. I am merely a facilitator. And I plan to give a birthday party. Klaas Landsman is going to give a talk. He said to me "Joy would probably like my lecture, by the way ...". Referring to his prize-winning essay, which he says destroys the whole meeting. "I am finished with Bell", he said to me. https://fqxi.org/community/essay/winners/2020.1. Time to bury the hatchet, I would say! Come and smoke the peace pipe. We have good stuff in the Netherlands, it's even legal... If I'm a dog born in a barn, I'm proud of that.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
No, it is not all I can do. Participate in our conference and help us re-formulate Bell's theorem.https://gill1109.com/2020/10/02/time-reality-and-bells-theorem/

Fred, if I were you, I wouldn't touch Gill's "conference" with a barge pole. No matter how one tries to "re-formulate" garbage, it remains garbage. A dog born in a barn remains a dog.

***

### Re: What exactly is Bell's Theorem?

FrediFizzx wrote:
gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:Not all physicists will agree that *every* self-adjoint operator must correspond to a physical observable. But OK, if you do take that as axiomatic, then there is indeed an issue here. If you go that way, then your argument is a proof of a version of the Kochen-Specker theorem. It’s nothing to do with locality. Nice! Congratulations.

My conclusion, to put it in my words, which appear in the last line of my (yet to be published) arXiv paper, is that "what is ruled out by Bell-test experiments is not local realism, but the additivity of expectation values (21), which does not hold for hidden variable theories to begin with."

Exactly. Why should it? That's what I am saying. It depends, of course, on what you mean by "a hidden variable theory". Which depends on what you mean by a whole load of other things. The maths is clear. The "meaning" you give to it is up to you. The meaning of the maths is socially, culturally, determined. It's relative to a more or less shared world view. That's challenging, that's diversity!

What a bunch of mumbo jumbo. Is that all you can do? Mumbo jumbo?

No, it is not all I can do. Participate in our conference and help us re-formulate Bell's theorem.https://gill1109.com/2020/10/02/time-reality-and-bells-theorem/

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:
Not all physicists will agree that *every* self adjoint operator must correspond to a physical observable. But OK, if you do take that as axiomatic, then there is indeed an issue here. If you go that way, then your argument is a proof of a version of the Kochen-Specker theorem. It’s nothing to do with locality. Nice! Congratulations.

My conclusion, to put it in my words, which appear in the last line of my (yet to be published) arXiv paper, is that "what is ruled out by Bell-test experiments is not local realism, but the additivity of expectation values (21), which does not hold for hidden variable theories to begin with."

***

Exactly. Why should it? That's what I am saying. It depends, of course, on what you mean by "a hidden variable theory".Which depends on what you mean by a whole load of other things.

The maths is clear. The "meaning" you give to it is up to you.The meaning of the maths is socially, culturally, determined. It's relative to a more or less shared world view. That's challenging, that's diversity!

What a bunch of mumbo jumbo. Is that all you can do? Mumbo jumbo?
.

### Re: What exactly is Bell's Theorem?

Joy Christian wrote:
gill1109 wrote:
Not all physicists will agree that *every* self adjoint operator must correspond to a physical observable. But OK, if you do take that as axiomatic, then there is indeed an issue here. If you go that way, then your argument is a proof of a version of the Kochen-Specker theorem. It’s nothing to do with locality. Nice! Congratulations.

My conclusion, to put it in my words, which appear in the last line of my (yet to be published) arXiv paper, is that "what is ruled out by Bell-test experiments is not local realism, but the additivity of expectation values (21), which does not hold for hidden variable theories to begin with."

***

Exactly. Why should it? That's what I am saying. It depends, of course, on what you mean by "a hidden variable theory".Which depends on what you mean by a whole load of other things.

The maths is clear. The "meaning" you give to it is up to you.The meaning of the maths is socially, culturally, determined. It's relative to a more or less shared world view. That's challenging, that's diversity!

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
Not all physicists will agree that *every* self adjoint operator must correspond to a physical observable. But OK, if you do take that as axiomatic, then there is indeed an issue here. If you go that way, then your argument is a proof of a version of the Kochen-Specker theorem. It’s nothing to do with locality. Nice! Congratulations.

My conclusion, to put it in my words, which appear in the last line of my (yet to be published) arXiv paper, is that "what is ruled out by Bell-test experiments is not local realism, but the additivity of expectation values (21), which does not hold for hidden variable theories to begin with."

***

### Re: What exactly is Bell's Theorem?

Not all physicists will agree that *every* self adjoint operator must correspond to a physical observable. But OK, if you do take that as axiomatic, then there is indeed an issue here. If you go that way, then your argument is a proof of a version of the Kochen-Specker theorem. It’s nothing to do with locality. Nice! Congratulations.

### Re: What exactly is Bell's Theorem?

Joy Christian wrote:
gill1109 wrote:
Joy Christian wrote:Here is ... an irrefutable scientific argument: The additivity of expectation values is not a valid or acceptable assumption for any hidden variable theory, regardless of locality or reality. On the other hand, the only way to derive the bounds of +/-2 on the CHSH correlator is by assuming the additivity of expectation values. If the additivity of expectation values is not assumed, then the bounds on the CHSH correlator are +/-4, not +/-2. In the experiments, the bounds of +/-2 are exceeded. Therefore the assumption of the additivity of expectation values is ruled out by the experiments. Locality and realism remain untouched and unscathed, contrary to what Bell and his followers believe.

The argument is easily refutable. A hidden variable theory is a theory in which outcomes which would be observed if various different measurements were done are all defined, or more generally, can all be defined. Moreover, this is done in such a way that the theory predicts the same correlations between jointly observable variables as quantum mechanics does; or at least, it predicts the same correlations up to very close approximation. Additivity of expectation values is not an assumption. Joint existence (in a mathematical sense) is the central assumption of a hidden variables theory. Your own hidden variables theories are of this kind. You define functions A(a, lambda) and B(b, lambda) etc etc etc.

Linearity of expectations is now a corollary.

In a hidden variable theory, all observables have definite values and those values must be eigenvalues of the corresponding quantum mechanical operators. The eigenvalue x(r,s,t,u) of the observable that correponds to the quantum mechanical operator R+S+T+U and appears on the right-hand side of the assumption of additivity of expectation values in the derivation of the CHSH inequalities is not a linear combination r+s+t+u of the eigenvalues of R, S, T, and U. But Bell and followers wrongly assume that it is a linear combination r+s+t+u and use that to derive the wrong bounds of +/-2. The use of wrong eigenvalue leads them to wrong bounds. It is a rookie mistake. For the correct derivation of the correct bounds +/-2\/2, see my paper:

https://arxiv.org/abs/1704.02876.

gill1109 wrote:
Indeed. But the “observable” R+S+T+U is not observed directly, hence its eigenvalues are irrelevant. This is a quite subtle point. Joy is really the first person who brings it clearly out into the open. We only *deduce* things about that “observable”, by making the working assumption that a local hidden variable model is possible. We reach a contradiction, exactly the contradiction which Joy discusses. Hence our no-go theorem. The working assumption must be rejected. Proof by contradiction. To prove something is impossible, you assume it to be true, and see where that brings you.

According to the Hilbert space formulation of quantum theory, the correspondence between observables and self-adjoint operators is one-to-one. Now, it is correct that R+S+T+U is never observed in any Bell-test experiments that test singlet correlations. But in the Hilbert space of the singlet state, the sum R+S+T+U is a self-adjoint operator because R, S, T, and U are all self-adjoint operators themselves, and therefore R+S+T+U is observable in principle, at least counterfactually. In other words, a "God" can observe it, at least counterfactually. Therefore, the eigenvalue of the operator R+S+T+U is anything but irrelevant in a local or nonlocal hidden variable theory in which counterfactual possibilities are on par with the actual occurrences.

***

### Re: What exactly is Bell's Theorem?

Indeed. But the “observable” R+S+T+U is not observed directly, hence its eigenvalues are irrelevant. This is a quite subtle point. Joy is really the first person who brings it clearly out into the open. We only *deduce* things about that “observable”, by making the working assumption that a local hidden variable model is possible. We reach a contradiction, exactly the contradiction which Joy discusses. Hence our no-go theorem. The working assumption must be rejected. Proof by contradiction. To prove something is impossible, you assume it to be true, and see where that brings you.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
Joy Christian wrote:Here is ... an irrefutable scientific argument: The additivity of expectation values is not a valid or acceptable assumption for any hidden variable theory, regardless of locality or reality. On the other hand, the only way to derive the bounds of +/-2 on the CHSH correlator is by assuming the additivity of expectation values. If the additivity of expectation values is not assumed, then the bounds on the CHSH correlator are +/-4, not +/-2. In the experiments, the bounds of +/-2 are exceeded. Therefore the assumption of the additivity of expectation values is ruled out by the experiments. Locality and realism remain untouched and unscathed, contrary to what Bell and his followers believe.

The argument is easily refutable. A hidden variable theory is a theory in which outcomes which would be observed if various different measurements were done are all defined, or more generally, can all be defined. Moreover, this is done in such a way that the theory predicts the same correlations between jointly observable variables as quantum mechanics does; or at least, it predicts the same correlations up to very close approximation. Additivity of expectation values is not an assumption. Joint existence (in a mathematical sense) is the central assumption of a hidden variables theory. Your own hidden variables theories are of this kind. You define functions A(a, lambda) and B(b, lambda) etc etc etc.

Linearity of expectations is now a corollary.

In a hidden variable theory, all observables have definite values and those values must be eigenvalues of the corresponding quantum mechanical operators. The eigenvalue x(r,s,t,u) of the observable that correponds to the quantum mechanical operator R+S+T+U and appears on the right-hand side of the assumption of additivity of expectation values in the derivation of the CHSH inequalities is not a linear combination r+s+t+u of the eigenvalues of R, S, T, and U. But Bell and followers wrongly assume that it is a linear combination r+s+t+u and use that to derive the wrong bounds of +/-2. The use of wrong eigenvalue leads them to wrong bounds. It is a rookie mistake. For the correct derivation of the correct bounds +/-2\/2, see my paper:

https://arxiv.org/abs/1704.02876.

gill1109 wrote:
“Bell followers” are not members of some religious sect.

In the light of the above rookie mistake, it is clear that Bell’s theorem is a politically sustained belief system. Therefore, in my books, the followers of Bell are members of a religious sect.

***

### Re: What exactly is Bell's Theorem?

Joy Christian wrote:Here is ... an irrefutable scientific argument: The additivity of expectation values is not a valid or acceptable assumption for any hidden variable theory, regardless of locality or reality. On the other hand, the only way to derive the bounds of +/-2 on the CHSH correlator is by assuming the additivity of expectation values. If the additivity of expectation values is not assumed, then the bounds on the CHSH correlator are +/-4, not +/-2. In the experiments, the bounds of +/-2 are exceeded. Therefore the assumption of the additivity of expectation values is ruled out by the experiments. Locality and realism remain untouched and unscathed, contrary to what Bell and his followers believe.

The argument is easily refutable. A hidden variable theory is a theory in which outcomes which would be observed if various different measurements were done are all defined, or more generally, can all be defined. Moreover, this is done in such a way that the theory predicts the same correlations between jointly observable variables as quantum mechanics does; or at least, it predicts the same correlations up to very close approximation. Additivity of expectation values is not an assumption. Joint existence (in a mathematical sense) is the central assumption of a hidden variables theory. Your own hidden variables theories are of this kind. You define functions A(a, lambda) and B(b, lambda) etc etc etc.

Linearity of expectations is now a corollary.

Itamar Pitowsky tried to escape this by assuming non measurability so that expectation values could not be defined in the way of modern measure-theoretic probability theory (Kolmogorov). Others try to escape this by assuming some inconsistency in the usual ZFC axioms of set theory. My own work shows that by assuming randomness only in the setting choices, Bell’s theorem follows without any probabilistic assumptions on the hidden variables model at all. Only standard discrete (finite, counting) probability is needed.

“Bell followers” are not members of some religious sect. No modern scientist is a “Bell follower”. There are hundreds of proofs of hundreds of variants of Bell’s theorem. The maths and the logic are not difficult. The problem is that nobody can claim to *understand* quantum mechanics, though one can become familiar with the mathematical structure.

I suppose that you are also not the leader of a religious sect, but a scientist.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
Joy Christian wrote:Your waffle describes a religion, not science.

That is not acceptable language to use in scientific discourse. It seems to me to be a value judgement, an opinion. You are welcome to your opinion. I have my own. I think your argument is faulty. It seems you don’t want to address arguments. Perhaps someone else on the forum is interested to actually enter into the arguments.

Ok, forget my first sentence. Here is the rest of what I wrote, and it is an irrefutable scientific argument:

Joy Christian wrote:
"The additivity of expectation values is not a valid or acceptable assumption for any hidden variable theory, regardless of locality or reality. On the other hand, the only way to derive the bounds of +/-2 on the CHSH correlator is by assuming the additivity of expectation values. If the additivity of expectation values is not assumed, then the bounds on the CHSH correlator are +/-4, not +/-2. In the experiments, the bounds of +/-2 are exceeded. Therefore the assumption of the additivity of expectation values is ruled out by the experiments. Locality and realism remain untouched and unscathed, contrary to what Bell and his followers believe."

***

### Re: What exactly is Bell's Theorem?

Joy Christian wrote:Your waffle describes a religion, not science.

That is not acceptable language to use in scientific discourse. It seems to me to be a value judgement, an opinion. You are welcome to your opinion. I have my own. I think your argument is faulty. It seems you don’t want to address arguments. Perhaps someone else on the forum is interested to actually enter into the arguments.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
I agree that the moon is there when I’m not looking. Linearity of expectation values follows immediately from the definition of expectation values. See https://en.m.wikipedia.org/wiki/Expected_value and the many links there. But one has to realise than in present context, “realism” is not a practical, obvious concept. It’s idealistic. Tsirelson and others suggest we use the term “counterfactual definiteness”. Even if, contrary to fact, we did not measure the momentum of a particle, but only measure its position, it still can be thought to have a position. This is not a claim about reality. It’s a claim about mathematical descriptions of reality. They can be augmented in a consistent (and not to forget, local) way with descriptions of alternative realities. A deterministic description allows such augmentation. We can put the planets in a different configuration from where they are today and the equations of motion still tell us where they would then be tomorrow. Also, stochastic descriptions allow this, if the random disturbances can be imagined to be independent of the deterministic parts of the model. From Bohr’s point of view, which you could say found its logical fulfilment with David Bohm’s, the whole debate with Einstein was a waste of time, since everything is interconnected. David Bohm went on to show that the mathematical structure of QM could be augmented so as to make the universe interconnected and deterministic. Bell showed any augmentation *has* to have nonlocal features. I think physicists have to get used to the facts of life. I think actually, most do.

Your waffle describes a religion, not science. The additivity of expectation values is not a valid or acceptable assumption for any hidden variable theory, regardless of locality or reality. On the other hand, the only way to derive the bounds of +/-2 on the CHSH correlator is by assuming the additivity of expectation values. If the additivity of expectation values is not assumed, then the bounds on the CHSH correlator are +/-4, not +/-2. In the experiments, the bounds of +/-2 are exceeded. Therefore the assumption of the additivity of expectation values is ruled out by the experiments. Locality and realism remain untouched and unscathed, contrary to what Bell and his followers believe.

***

### Re: What exactly is Bell's Theorem?

I agree that the moon is there when I’m not looking. Linearity of expectation values follows immediately from the definition of expectation values. See https://en.m.wikipedia.org/wiki/Expected_value and the many links there. But one has to realise than in present context, “realism” is not a practical, obvious concept. It’s idealistic. Tsirelson and others suggest we use the term “counterfactual definiteness”. Even if, contrary to fact, we did not measure the momentum of a particle, but only measure its position, it still can be thought to have a position. This is not a claim about reality. It’s a claim about mathematical descriptions of reality. They can be augmented in a consistent (and not to forget, local) way with descriptions of alternative realities. A deterministic description allows such augmentation. We can put the planets in a different configuration from where they are today and the equations of motion still tell us where they would then be tomorrow. Also, stochastic descriptions allow this, if the random disturbances can be imagined to be independent of the deterministic parts of the model. From Bohr’s point of view, which you could say found its logical fulfilment with David Bohm’s, the whole debate with Einstein was a waste of time, since everything is interconnected. David Bohm went on to show that the mathematical structure of QM could be augmented so as to make the universe interconnected and deterministic. Bell showed any augmentation *has* to have nonlocal features. I think physicists have to get used to the facts of life. I think actually, most do.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:
The easiest proof of the CHSH inequality shows it is a mathematical triviality, following directly from the assumptions of local realism and a basic probability theory inequality called Boole’s inequality. Bell’s earlier three correlations inequality is even more so, a triviality. It’s a special case of CHSH. Boole has it as an exercise in his book from 18-whatever. “Bell’s theorem” is the equally trivial logical corollary that local realism and quantum mechanics are incompatible. A local realist model does generate in a local way individual outcomes of measurements whose correlations are the same as the correlations predicted by QM. Now, superdeterminism, retrocausality, and postselection (detection loophole) are all ways to get out of Bell’s theorem. They are collectively thought of as conspiratorial, or violations of the freedom of the experimenters to choose whatever settings they like and then get to see a pair of outcomes.

This is complete and utter nonsense. None of the Bell inequalities follow from local realism and basic probability theory. For example, if you assume local realism and basic probability theory for the CHSH correlator, you end up with the bounds of +/-4. A further assumption of the additivity of expectation values is required to reduce the bounds of +/-4 to the bounds of +/-2. But the additivity of expectation values is not a valid assumption for any hidden variable theory, regardless of the assumption of local realism. Thus Bell's theorem is a non-starter.

To put this differently, what is ruled out by the Bell-test experiments is not local realism. What is ruled out by the Bell-test experiments is the additivity of expectation values.

***

Additivity of expectation values is, in my book, part of basic probability theory. But of course everything depends here also on your definition of “local realism”. If your definition is different from that of everyone else, then (a) nobody will understand you, (b) Bell’s theorem can switch between true and false, and similar, Bell’s inequality too. Perhaps everyone who participates in this thread should start by giving some precise definitions of what they understand by “Bell’s theorem”. They should also point out if they agree or disagree with various definitions given by what usually might be considered “authoritative sources”. Standard text books and the like.

Whichever book additivity of expectation values belongs to, it has been ruled out by the Bell-test experiments. No one has ruled out local realism. The moon is there when I am not looking.

***

### Re: What exactly is Bell's Theorem?

Joy Christian wrote:
gill1109 wrote:
The easiest proof of the CHSH inequality shows it is a mathematical triviality, following directly from the assumptions of local realism and a basic probability theory inequality called Boole’s inequality. Bell’s earlier three correlations inequality is even more so, a triviality. It’s a special case of CHSH. Boole has it as an exercise in his book from 18-whatever. “Bell’s theorem” is the equally trivial logical corollary that local realism and quantum mechanics are incompatible. A local realist model does generate in a local way individual outcomes of measurements whose correlations are the same as the correlations predicted by QM. Now, superdeterminism, retrocausality, and postselection (detection loophole) are all ways to get out of Bell’s theorem. They are collectively thought of as conspiratorial, or violations of the freedom of the experimenters to choose whatever settings they like and then get to see a pair of outcomes.

This is complete and utter nonsense. None of the Bell inequalities follow from local realism and basic probability theory. For example, if you assume local realism and basic probability theory for the CHSH correlator, you end up with the bounds of +/-4. A further assumption of the additivity of expectation values is required to reduce the bounds of +/-4 to the bounds of +/-2. But the additivity of expectation values is not a valid assumption for any hidden variable theory, regardless of the assumption of local realism. Thus Bell's theorem is a non-starter.

To put this differently, what is ruled out by the Bell-test experiments is not local realism. What is ruled out by the Bell-test experiments is the additivity of expectation values.

***

Additivity of expectation values is, in my book, part of basic probability theory. But of course everything depends here also on your definition of “local realism”. If your definition is different from that of everyone else, then (a) nobody will understand you, (b) Bell’s theorem can switch between true and false, and similar, Bell’s inequality too. Perhaps everyone who participates in this thread should start by giving some precise definitions of what they understand by “Bell’s theorem”. They should also point out if they agree or disagree with various definitions given by what usually might be considered “authoritative sources”. Standard text books and the like.

### Re: What exactly is Bell's Theorem?

gill1109 wrote:
The easiest proof of the CHSH inequality shows it is a mathematical triviality, following directly from the assumptions of local realism and a basic probability theory inequality called Boole’s inequality. Bell’s earlier three correlations inequality is even more so, a triviality. It’s a special case of CHSH. Boole has it as an exercise in his book from 18-whatever. “Bell’s theorem” is the equally trivial logical corollary that local realism and quantum mechanics are incompatible. A local realist model does generate in a local way individual outcomes of measurements whose correlations are the same as the correlations predicted by QM. Now, superdeterminism, retrocausality, and postselection (detection loophole) are all ways to get out of Bell’s theorem. They are collectively thought of as conspiratorial, or violations of the freedom of the experimenters to choose whatever settings they like and then get to see a pair of outcomes.

This is complete and utter nonsense. None of the Bell inequalities follow from local realism and basic probability theory. For example, if you assume local realism and basic probability theory for the CHSH correlator, you end up with the bounds of +/-4. A further assumption of the additivity of expectation values is required to reduce the bounds of +/-4 to the bounds of +/-2. But the additivity of expectation values is not a valid assumption for any hidden variable theory, regardless of the assumption of local realism. Thus Bell's theorem is a non-starter.

To put this differently, what is ruled out by the Bell-test experiments is not local realism. What is ruled out by the Bell-test experiments is the additivity of expectation values.

***

### Re: What exactly is Bell's Theorem?

FrediFizzx wrote:
FrediFizzx wrote:The Wikipedia entry for Bell's Theorem gives,

"If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

Which is from the book "Speakable and Unspeakable in Quantum Mechanics" page 65 which actually says,

"But if his extension is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says."

However, in the paragraph before this statement, Bell gives another description of the so-called theorem.

"$A({\bf a}, \lambda)$
$B({\bf b}, \lambda)$ (3)

With these local forms, it is not possible to find functions A and B and a probability distribution $\rho$ which give the correlation (1). This is the theorem."

Correlation (1) is of course the quantum mechanical prediction of -a.b. Now..., someone with proper definitions could possibly make this into a rigorous mathematical theorem. But there not much point in that since Joy has already found local A and B functions that do give the QM correlation. This should really be the end of the debate.
.

For some unknown reason, the Bell fans don't want to even accept Bell's own definition of the "theorem". So, now we have Gill's "theorem" which is basically that a local model can't simulate Nature and the experiments. But quantum mechanics can't predict correct individual outcome events for A and B either. So, what is the point? Now what is more, Jay Yablon has successfully demonstrated that quantum mechanics is local for the EBR-Bohm scenario so locality is no longer an issue. QM and... Nature must be local so non-local simulations are completely out.
.

The easiest proof of the CHSH inequality shows it is a mathematical triviality, following directly from the assumptions of local realism and a basic probability theory inequality called Boole’s inequality. Bell’s earlier three correlations inequality is even more so, a triviality. It’s a special case of CHSH. Boole has it as an exercise in his book from 18-whatever. “Bell’s theorem” is the equally trivial logical corollary that local realism and quantum mechanics are incompatible. A local realist model does generate in a local way individual outcomes of measurements whose correlations are the same as the correlations predicted by QM. Now, superdeterminism, retrocausality, and postselection (detection loophole) are all ways to get out of Bell’s theorem. They are collectively thought of as conspiratorial, or violations of the freedom of the experimenters to choose whatever settings they like and then get to see a pair of outcomes.

### Re: What exactly is Bell's Theorem?

FrediFizzx wrote:The Wikipedia entry for Bell's Theorem gives,

"If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

Which is from the book "Speakable and Unspeakable in Quantum Mechanics" page 65 which actually says,

"But if his extension is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says."

However, in the paragraph before this statement, Bell gives another description of the so-called theorem.

"$A({\bf a}, \lambda)$
$B({\bf b}, \lambda)$ (3)

With these local forms, it is not possible to find functions A and B and a probability distribution $\rho$ which give the correlation (1). This is the theorem."

Correlation (1) is of course the quantum mechanical prediction of -a.b. Now..., someone with proper definitions could possibly make this into a rigorous mathematical theorem. But there not much point in that since Joy has already found local A and B functions that do give the QM correlation. This should really be the end of the debate.
.

For some unknown reason, the Bell fans don't want to even accept Bell's own definition of the "theorem". So, now we have Gill's "theorem" which is basically that a local model can't simulate Nature and the experiments. But quantum mechanics can't predict correct individual outcome events for A and B either. So, what is the point? Now what is more, Jay Yablon has successfully demonstrated that quantum mechanics is local for the EBR-Bohm scenario so locality is no longer an issue. QM and... Nature must be local so non-local simulations are completely out.
.

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