FrediFizzx wrote:
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 is 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.
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.
"
(3)
With these local forms, it is not possible to find functions A and B and a probability distribution 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.
.
gill1109 wrote:
When Bell himself talked about his *theorem* he usually meant his *inequality*.
gill1109 wrote:
Bell himself knew that one had to rule out super-determinism or to say it in a positive sense, to assume the existence of something which some people like to call “free will” ...
Joy Christian wrote:FrediFizzx wrote:
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 is 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.
I of course agree with your conclusion. But just to be the devil's advocate (because the devils seem to have fled the battleground), what the Bell-believers would say is that by considering four EPR-Bohm type experiments and assuming only locality and realism (aka "counterfactual definiteness") they are able to derive the bounds of +/-2 on the CHSH correlator. The theorem, they claim, is then that no local functions of the form and can be used to exceed those bounds.
...
***
FrediFizzx wrote:Joy Christian wrote:FrediFizzx wrote:
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 is 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.
I of course agree with your conclusion. But just to be the devil's advocate (because the devils seem to have fled the battleground), what the Bell-believers would say is that by considering four EPR-Bohm type experiments and assuming only locality and realism (aka "counterfactual definiteness") they are able to derive the bounds of +/-2 on the CHSH correlator. The theorem, they claim, is then that no local functions of the form and can be used to exceed those bounds.
...
***
It's trivial that if you have local A and B functions that produce the QM correlation of -a.b, you will exceed the bounds of CHSH also. So, all it takes is Bell's original "theorem" that I have shown above. With that disproven, all of the rest of it also falls into junk physics theory territory.
Joy Christian wrote:FrediFizzx wrote:Joy Christian wrote:FrediFizzx wrote:
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 is 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.
I of course agree with your conclusion. But just to be the devil's advocate (because the devils seem to have fled the battleground), what the Bell-believers would say is that by considering four EPR-Bohm type experiments and assuming only locality and realism (aka "counterfactual definiteness") they are able to derive the bounds of +/-2 on the CHSH correlator. The theorem, they claim, is then that no local functions of the form and can be used to exceed those bounds.
...
***
It's trivial that if you have local A and B functions that produce the QM correlation of -a.b, you will exceed the bounds of CHSH also. So, all it takes is Bell's original "theorem" that I have shown above. With that disproven, all of the rest of it also falls into junk physics theory territory.
Sure. But to recognize that elementary fact requires honesty, scientific integrity, and competence in physics. That is asking too much from those irrationally committed to Bell orthodoxy.
***
gill1109 wrote:Joy Christian wrote:
Sure. But to recognize that elementary fact requires honesty, scientific integrity, and competence in physics. That is asking too much from those irrationally committed to Bell orthodoxy.
Competence in physics involves having certain broad mathematical skills (and even statistical skills).
Heinera wrote:
Sabine Hossenfelder has a recent post about nonlocality and Bell's theorem on her blog:
http://backreaction.blogspot.com/2020/0 ... 3-non.html
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.
"
(3)
With these local forms, it is not possible to find functions A and B and a probability distribution 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.
.
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.
"
(3)
With these local forms, it is not possible to find functions A and B and a probability distribution 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.
.
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.
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.
***
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.
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.
Joy Christian wrote:Your waffle describes a religion, not science.
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.
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."
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