Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Mathematical formulation of local non-realism

  1. Mar 1, 2017 #1
    Hi.

    Bell formulated local realism as follows: The probability of a coincidence between separated measurements of particles with correlated (e.g. identical or opposite) orientation properties can be written as
    $$P(a,b)=\int{d\lambda\cdot \rho(\lambda)\cdot p_A(a,\lambda)\cdot p_B(b,\lambda)}\enspace .$$

    To get a better understanding of the terms "local" and "realistic", I'm trying to adapt this formula. So I'd say a theory that realistic, but not necessarily local, would satisfy
    $$P(a,b)=\int{d\lambda\cdot \rho(\lambda)\cdot p_{AB}(a,b,\lambda)}\enspace ,$$
    i.e. ##p_{AB}(a,b,\lambda)## is not necessarily a product distribution. As far as I can see quantum expectation values satisfy this probability distribution.

    How would this formula look like for a nonrealistic (or not necessarily realistic), but local theory? Or is local realism not something that can be split up into locality and realism?
     
  2. jcsd
  3. Mar 1, 2017 #2

    Demystifier

    User Avatar
    Science Advisor

    If ##a## and ##b## are spatially separated, then, according to the local non-realistic interpretation, there is no such thing as ##P(a,b)##. Namely, there is no single observer who can measure ##P(a,b)##, and things which nobody measures don't exist according to non-realistic interpretations.

    If ##a## and ##b## are not spatially separated and a single observer measures both ##a## and ##b##, then, according to the same interpretation,
    $$P(a,b)=p_{AB}(a,b)$$
    which is almost a tautology.
     
    Last edited: Mar 1, 2017
  4. Mar 1, 2017 #3
    So in this interpretation it's not allowed that both observers make individual, spatially separated measurements and then construct ##P(a,b)## by comparing their results locally at a later time?

    Do both observers need to assume the other one stays in a superposition until they compare their results over a classical channel?
     
  5. Mar 2, 2017 #4

    Demystifier

    User Avatar
    Science Advisor

    It's allowed, but then the observables that are really compared are no longer spatially separated. According to non-realistic interpretations, there is no correlation until one observes the correlation.

    In non-realistic interpretations (I am not a proponent of such interpretations, I just explain what such interpretations are), you don't assume anything about things which you don't observe.
     
  6. Mar 2, 2017 #5
    But in order to agree with experimentally verifiable QM predictions, observer ##A## needs a way to compute the correlations ##P(a,b)## that ##A## and ##B## will find when they later compare their measurements locally. So will he describe everything on ##B##'s side as a unitary time evolution (i.e. with local Hamiltonians) and only use projective measurements when they meet (or talk over a classical channel)?

    If I was a hardcore non-realist, would I need to assume I'm the only one in the whole universe capable of making QM measurements and everything else evolutes unitarily?
     
  7. Mar 2, 2017 #6

    Demystifier

    User Avatar
    Science Advisor

    Yes, exactly.

    That would be a kind of solipsism, and yes, I also think that hardcore non-realism leads to solipsism. See also
    http://lanl.arxiv.org/abs/1112.2034
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Mathematical formulation of local non-realism
  1. Local Realism After Bell (Replies: 24)

Loading...