Moved from https://www.physicsforums.com/showthread.php?t=590249&page=3 to avoid confusion with the classical example in its OP. ThomasT and I are mainly discussing Bell (1964) here.(adsbygoogle = window.adsbygoogle || []).push({});

The example discussed relates to 2 spin-half particles in the original EPR-Bohm example, see Bell (1964). The outcomes are spin-up or spin-down. The typical notations then are +1 and -1. But in trying to sort out any confusion, imho, it helps to maintain the detector orientations and the orientations of the outcomes in your analysis. So ThomasT said: ↑The individual outputs will be either that a detection has been registered, or that a detection hasn't been registered. You can denote that however you want, but the conventional notations are +1,-1 or 1,0, corresponding to detection, nondetection, respectively.a+[= +1] is a spin-up output for Alice with her detector in theadirection;b-[= -1] is a spin-down output for Bob with his detector in thebdirection; etc.

The angle between any Alice-Bob output combinations may also be expressed as a function of θ; see earlier example involving ∏. You seem to miss this important point? ThomasT said: ↑I don't know what you mean by thefull physical significance of θ. θ just refers to the angular difference between the polarizer settings, afaik.

The ThomasT said: ↑I don't know what this means. Theabcombinationsareθ. I don't have any idea what thea+b-stuff means or where ∏ comes into it.aboutcome combinations area+b+,a+b-,a-b+,a-b-. The angle between the outputsa+andb-is θ + ∏; etc.

How does this show that you are not confused? ThomasT said: ↑Well, I don't think I'm confused. P(A,B) is a function that refers to the independent variable θ. And, in the ideal, wrt optical Bell tests, P(A,B) = cos^{2}θ.

Well cos ThomasT said: ↑Of course it's obvious. Because, in the ideal, this is the QM prediction. Rate of coincidental detection varies as cos^{2}θ.^{2}θ in some experiments; other functions of θ in others.

This is wrong; a big misunderstanding. This does not hold in entangled experiments. It would hold if λ denoted a polarisation but entangled particles are unpolarised (quoting Bell). ThomasT said: ↑The relation of λ to A is denoted as P(A) = cos^{2}|a-λ| .

The underlying parameters λ has given up the ghost, gone, been burnt off, in the production of each output. Having done its job, it exists no more. What remains are the outputs, which may be paired in 4 combinations: ThomasT said: ↑As I said, I don't think you understand what I'm saying. Namely, that the underlying parameter that determines rate ofindividualdetectionis notthe underlying parameter that determines rate ofcoincidentaldetection.a+b+,a+b-,a-b+,a-b-. The angle between the output in each pair is a function of θ, and nothing else. It follows that, depending on the source, the overall output correlation will also be a function of θ alone; θ the difference between the detector orientations.

Plant a seed (input) λ; the seed λ is not in the subsequent fruit (output)a+= +1; etc.

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# The role of lambda in Bell (1964) and experiments

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