CHSH Bell inequality derivation

[d_bar_x]

TL;DR

Does the CHSH derivation of Bell's inequality make sense?

Has anyone else tried to make sense of the Clauser, Horne, Shimony, Holt derivation of Bell's inequality (Physics. Rev. Left. 23, 15, 1969)?
The CHSH version is said to be a more practical application of Bell's inequality, which could be used to describe the polarization correlations that Aspect observed in his famous experiment. I'm currently frustrated trying to make good sense of it.

There are two polarizers on each side of the calcium atom which emits two entangled photons, one to each side. Each photon is randomly directed to one or the other of the polarizers by a water wave transducer. Depending on which way each photon goes CHSH write the result as A(a) = +- 1 on one side, and B(b) = +- 1 on the other side. They include in their derivation the variables a' and b' which I suppose are particular values of a and b. I haven't yet make sense of the b' which they say somehow specifies the efficiency of the measurement process, since the joint probability of b and b', P(b, b') is very close to 1. Can one measure the joint probability for b and b' in the experiment and discover which values of b' lead to inefficiency? And, what is their variable, c? They don't define it do they? Is it another particular value for either a, or b, or for both a and b at some point?

Does someone else understand this derivation better than I do?

Thanks.

 

[pines-demon]

TL;DR Summary: Does the CHSH derivation of Bell's inequality make sense?

Has anyone else tried to make sense of the Clauser, Horne, Shimony, Holt derivation of Bell's inequality (Physics. Rev. Left. 23, 15, 1969)?
The CHSH version is said to be a more practical application of Bell's inequality, which could be used to describe the polarization correlations that Aspect observed in his famous experiment. I'm currently frustrated trying to make good sense of it.

There are two polarizers on each side of the calcium atom which emits two entangled photons, one to each side. Each photon is randomly directed to one or the other of the polarizers by a water wave transducer. Depending on which way each photon goes CHSH write the result as A(a) = +- 1 on one side, and B(b) = +- 1 on the other side. They include in their derivation the variables a' and b' which I suppose are particular values of a and b. I haven't yet make sense of the b' which they say somehow specifies the efficiency of the measurement process, since the joint probability of b and b', P(b, b') is very close to 1. Can one measure the joint probability for b and b' in the experiment and discover which values of b' lead to inefficiency? And, what is their variable, c? They don't define it do they? Is it another particular value for either a, or b, or for both a and b at some point?

Does someone else understand this derivation better than I do?

Thanks.

Are you reading this from the original paper? They should have clearly defined their variables. Have you tried any other explanation of the CHSH, they usually define their variables too.

 

[Haborix]

I quickly read the paper and the only talk about efficiencies has to do with "photoelectric efficiencies," which I'm inclined to believe is referring to the technology for detecting photons; hence their redefining A and B to refer to emergence/non-emergence from a filter.

 

[Nugatory]

Has anyone else tried to make sense of the Clauser, Horne, Shimony, Holt derivation of Bell's inequality (Physics. Rev. Left. 23, 15, 1969)?

The Wikipedia article on the CHSH inequality says "The original 1969 derivation will not be given here since it is not easy to follow...."

 

[d_bar_x]

It's the original paper that I find so obtuse. They do not define all their variables. I agree that there are now much better derivations, particularly in the book Quantum Computation and Quantum Information