Bell on Bell's theorem: The changing face of nonlocality

Harvey R. Brown and Christopher G. Timpson

Submitted to “Quantum Nonlocality and Reality – 50 Years of Bell’s theorem”

Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation. Full text

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2 Responses

  1. Avatar of Gregg Jaeger
    Gregg Jaeger at | |

    Fellows,

    I think you do a service in your paper, by emphasizing that Bell was careful to distinguish between the ‘no-superluminal-signalling’ condition and ‘local causality,’ (as I have also taken care to do recently, cf. my discussion of this in Quantum Objects). I was unaware, however, like many---as you point out---of just how suspicious was Bell of the factorability condition. So, that point is particularly good to have made and I thank you for it.

    Also, I realize that you have already added a number of detailed footnotes to your paper, but now mention here that one could add (for others reading the results of this workshop) that the terminology of "outcome independence" and "parameter independence" applied to the Jarrett conditions (mentioned in Footnote 21) is due to Shimony (as discussed in his Search for a Naturalistic World View) in the context you discuss in your Section 8 here.

    I also commend you on the clarity of your discussion of Reichenbach's Common Cause principle, which helps the reader better understand the subtlety and reasons behind the particular form in which Reichenbach came to give it in his writings.

    Finally, I agree with what you say in your paper which is most novel, namely, that "the Everett picture of quantum mechanics can play an illuminating role in understanding the significance of factorizability." Yet, your statement in the abstract goes much further than that in stating "In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation." So, I now ask, could one not do equally well in this understanding in a (in my view) far less metaphysically troublesome possible worlds scenario than what the Everett picture requires (at least of a realist like Bell) in that regard?

    My best regards,

    Gregg

    1. Avatar of Christopher Timpson
      Christopher Timpson at | |

      Hi Gregg,

      Many thanks for your comments.

      We do mention Shimony, but you are right that it might have been more elegant to do so earlier than we do.

      Regarding your closing query the answer is - perhaps - but I'm not sure exactly what kind of position you have in mind.

      Cheers,
      Chris

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