jreed wrote:If you want to find out where CHSH comes from, you should read the article by Bell, "Bertlmann's socks and the nature of reality". It's in his book. This explains it all very well. I've read it and it makes sense, but I won't try to give all the details here. Basically it says that for certain measurements the joint probability P(A,B|a,b,lambda) can be written as:

P1(A|a,lambda)*P2(B|b,lambda) where lambda is a hidden variable. The rest follows from this.

This post reads -- word by word -- as if it were written by Richard Gill. I wouldn't be surprised

at all if it were actually written -- word by word -- by Richard Gill, even though he is banned from this forum (as he is banned from many other forums and blogs for misbehaving).

I want to make one other sociological point clear to John Reed, and to anyone else who might be reading this, because I have had enough of the lectures given to me by John Reed about CHSH and Bell inequalities. I wrote my PhD thesis with Prof. Abner Shimony, the "S" in the CHSH. Do you know what that means? That means I am an expert on the foundations of quantum mechanics, and in particular on Bell's theorem. I learned about Bell's theorem not only from Abner Shimony --- the foremost expert on Bell's theorem until he passed away last month --- but from Bell himself, who was a frequent visitor to our research group in the 1980's, until 1990 when he passed away. His famous book came out during that decade, but we were intimately familiar with all the papers in it long before they were republished in that book, from the closed seminars Bell gave to our research group during that decade. I am elaborating on this to stress that I don't need lectures on Bell's theorem or on CHSH from you, John Reed, who has learned about them yesterday, from the dishonest, incompetent, and psychologically disturbed statistician like Richard Gill. And since Gill is lurking on this forum, I am elaborating this also for his benefit. In any case, I learned about "Bertlmann's socks and the nature of reality" from John Bell himself, in a closed seminar to our research group in the 1980's, when that paper had just been published. So don't ever dare to give me a lecture, Gill, about Bell's theorem.

Now about the probabilistic point made in the above post by John Reed -- dictated by Richard Gill. This point has been thoroughly addressed and refuted by Michel Fodje on this forum. See, for example,

this thread, and there are plenty more threads like this by Michel on this forum.

But even if we don't accept Michel's argument, all one has to do is to look at my analytical model, as Fred has pointed out above. Just look at the explicit derivation of the bound

on CHSH in my "

Reply to Gill" [cf. Eq. (26)]. Better still, look at the derivation of the actual correlation E(a, b) = -a.b in Eq. (B10) of that paper. This is explicit analytical derivation, giving correlation between the standard scalar events A(a, s) = +/-1 and B(b, s) = +/-1, where s is the "hidden variable" or initial state.

So get this through your head, Richard Gill. Bell's theorem is dead. It was actually stillborn. And It's corps was put to rest permanently on the 20th of March 2007.