Pedagogical proofs of Bell's theorem
Posted: Mon Aug 30, 2021 4:14 am
I don't like discussing Bell's original 1964 paper. At only six pages, it is way to succinct for many people to fully understand. The were of course enough smart people that did understand it, and so subsequently produced clearer proofs of their own.
My favorite pedagogical line of proof can be sketched like this:
1. Show that the CHSH urn experiment¹ has an upper bound of 2 for the CHSH expression when N goes to infinity. It seems that everyone one the forum agree with this, so I'll skip the proof (although it is pretty simple).
2. A CHSH urn experiment can not produce the correlations of QM, i.e. a CHSH expression 2.8284 (this is a trivial corollary of 1).
3. Any LHV model can be reduced to a CHSH urn experiment (just replace the paper slips with the sequence [A(a1, lambda), A(a2, lambda), B(b1, lambda), B(b2, lambda)] and start drawing lambdas).
4. An LHV model can not produce the correlations of QM (this is a trivial consequence of 2 and 3).
Anyone who claims Bell's theorem is wrong must disagree with one of these steps. Which is it?
¹) Explained elsewhere on this forum
My favorite pedagogical line of proof can be sketched like this:
1. Show that the CHSH urn experiment¹ has an upper bound of 2 for the CHSH expression when N goes to infinity. It seems that everyone one the forum agree with this, so I'll skip the proof (although it is pretty simple).
2. A CHSH urn experiment can not produce the correlations of QM, i.e. a CHSH expression 2.8284 (this is a trivial corollary of 1).
3. Any LHV model can be reduced to a CHSH urn experiment (just replace the paper slips with the sequence [A(a1, lambda), A(a2, lambda), B(b1, lambda), B(b2, lambda)] and start drawing lambdas).
4. An LHV model can not produce the correlations of QM (this is a trivial consequence of 2 and 3).
Anyone who claims Bell's theorem is wrong must disagree with one of these steps. Which is it?
¹) Explained elsewhere on this forum