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The role of lambda in Bell (1964) and experiments

  1. Mar 29, 2012 #1
    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.

    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 a+ [= +1] is a spin-up output for Alice with her detector in the a direction; b- [= -1] is a spin-down output for Bob with his detector in the b direction; 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?

    The ab outcome combinations are a+b+, a+b-, a-b+, a-b-. The angle between the outputs a+ and b- is θ + ∏; etc.

    How does this show that you are not confused?

    Well cos2θ 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).

    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: 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.
     
    Last edited: Mar 29, 2012
  2. jcsd
  3. Mar 29, 2012 #2
    My apologies for any added confusion. I'm happy to do this via direct email for awhile to knock off some rough edges.

    WRT your: "Afaik, wrt optical Bell tests, λ, the hidden variable denotes an underlying polarisation." IMHO, if you carried this analysis through (which I encourage you to do) you will get the classical example in https://www.physicsforums.com/showthread.php?t=590249. But note that such photons are not entangled.
     
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