Bell Proof Against Hidden Variables in EPR

[msumm21]

I have a question regarding the paper by John Bell (www.drchinese.com/David/Bell_Compact.pdf‎ ) in which he shows that a certain hidden variable approach cannot reproduce the expectation values predicted by QM for a pair of particles in the singlet state.

After eqn 15 on page 4, I don't understand the logic. Why can't $P(b,c)$ be stationary at the point $b=c$? Seems like $P$ could have a minimum at $b=c$ and hence be a stationary point. How does $P(b,c)$ being the order of $|b-c|$ around $b=c$ prevent that? I guess I'm missing something big here.

 

[Bryan Sanctuar]

Hi Actually saying Bell's theorem rules out local hidden variables is today's take. Bell viewed the violation of his inequalities as a failure of local causality of Special Relativity.

To me your question is just this: as b and c get close, then the difference b-c will take all sorts of small values and in Bell's words is not stationary.

I think this is a mathematical point: apply two colinear fields at b=c and the correlation will also be non stationary.

This point was addressed, if I recall, by CHSH who derived their inequalities to remove this point. However please note that this case (b=c) is very rare and the violation of the CHSH requires b and c to be orgononal, not colinear. Hence their magnitude is |b-c| = root(2)--look familiar.

hope this helps