Is Bell's 1971 CHSH the same as Gill's CHSH version?

[gill1109]

Final version submitted to Statistical Science, and posted on arXiv (v5) http://arxiv.org/abs/1207.5103

[minkwe]

http://arxiv.org/abs/1207.5103

Violation of Bell's inequality in experiments such as that of Aspect et al. (1982) provides empirical proof of non-locality in the real world.
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The paper starts with a proof of a strong, finite sample, version of Bell's inequality and thereby also of Bell's theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism, and freedom

The paper argues that Bell's theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.

So: Bell is not responsible for the so-called Bell's theorem.
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(b) I did not write on that page the usual statement of what is usually called Bell's theorem, which is displayed there, slavishly following the literature (so-called "reliable sources"). You can change it if you like but as long as 99.99% of all physicists out there think that the so-called theorem written there is (a) true and (b) Bell's theorem, then Wikipedia will say so too. Don't blame me. Blame Wikipedia policies if you like.

Yet in your paper, you attribute the theorem to Bell.

Bell's (1964) theorem states that certain predictions of quantum mechanics are incompatible with the conjunction of three fundamental principles of classical physics which are sometimes given the short names \realism", \locality" and \freedom".

You deny that it is a theorem to begin with, yet you claim to prove it in your paper.

You say in your paper that you reject realism. You say in your paper that experiments have been done which successfully violate given inequalities. I've asked you to provide a dataset from any source which violates the inequality. I've offered you a chance to prove that what you write in your paper is not a fib by writing a simulation or providing the data which demonstrates that non-realism can violate the bound. If you really believed what you wrote was true, you would simply ask the authors of the Giustina experiment and obtain the data for us to scrutinize according to the guidelines laid out in your own LG paper.

So what is it going to be? Are you going to go ahead and publish a paper, which you know for a fact contains falsehoods?

[gill1109]

Bell's (1964) theorem states that certain predictions of quantum mechanics are incompatible with the conjunction of three fundamental principles of classical physics which are sometimes given the short names \realism", \locality" and \freedom".

You deny that it is a theorem to begin with, yet you claim to prove it in your paper.

I prove a mathematical theorem in my paper. It's new. I state my theorem and give the proof. If words like "statistics" and "probability" are not in your vocabulary, then you will not even be able to make sense of the statement of the theorem.

No-one even conjectured this theorem before.

Every true mathematical theorem can be considered a tautology. What it has to say about the real world depends on building a bridge between mathematical concepts and empirical things. Even philosophy has this problem: we reason with words, using logic, but the bridge between the words we use, and our actual experiences in the world, might be more tricky than first appears.

In the rest of the papaer I discuss the relation between my new theorem, metaphysics, experimental physics, and simulation models. What is usually called Bell's (1964) theorem is a piece of folklore. Bell was not a physicist and never proved a theorem. Clauser et al., physicists all four of them, were the first to name something "Bell's theorem". If you actually read Bell you will see that Bell completely disagrees with them.

My paper is written for statisticians, for whom this whole topic is completely new. In the abstract I give them a few key words and phrases to hold on to, to motivate them to read the rest of the paper. If I carefully defined every phrase used in the abstract, the abstract would be longer than the paper itself.

[minkwe]

Richard, you actually attributed Bell's theorem to Bell. You do not say anywhere in your paper that Bell disagrees with it. You claim that you are proving Bell's theorem even though you believe Bell's theorem is not a theorem. This is what I'm talking about.

I'm not arguing with you about what Bell believed or didn't believe. I'm simply pointing inconsistencies and contradictions between what you claim on these forums and what you write in your paper. Unless you don't really believe what you write here, and it's all just for argumentation purposes.

[gill1109]

Richard, you actually attributed Bell's theorem to Bell. You do not say anywhere in your paper that Bell disagrees with it. You claim that you are proving Bell's theorem even though you believe Bell's theorem is not a theorem. This is what I'm talking about.

I'm not arguing with you about what Bell believed or didn't believe. I'm simply pointing inconsistencies and contradictions between what you claim on these forums and what you write in your paper. Unless you don't really believe what you write here, and it's all just for argumentation purposes.

In the paper I wrote for Statistical Science I was allowed 20 something pages and I already exceeded the original limit repeatedly in one revision after another because the referees kept asking for more stuff. You were not asked to referee the paper. If you had been, you could have asked for a discussion of this point and I would have gladly added it. I'm not going to ask the editors for another two pages, now.

Maybe I will write a supplement and put it on arXiv.