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50th anniversary of Bell's theorem

  1. Nov 8, 2014 #1
    A special issue on 50 years of Bell's theorem has been published in Journal of Physics with free access to all articles:


    http://iopscience.iop.org/1751-8121/47/42
     
  2. jcsd
  3. Nov 8, 2014 #2

    jedishrfu

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    Thanks for the reference. I'm sure others here will enjoy it.
     
  4. Nov 8, 2014 #3

    atyy

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    Lots of good articles, I love Bertlmann's :)
     
  5. Nov 10, 2014 #4

    Demystifier

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    I like the Maudlin's Reply to Comment.
     
  6. Nov 10, 2014 #5
    Cool :)
    I bet this is going to generate new discussions. ;)
     
  7. Nov 10, 2014 #6
    R. Werner just wrote a follow-up piece to that paper by Maudlin:

    What Maudlin replied to
    http://arxiv.org/pdf/1411.2120.pdf
     
  8. Nov 11, 2014 #7
    Interesting! Can someone guide me towards an elaboration of "algebraic quantum field theory provides an example of a theory with full relativistic signal locality and clear violations of Bell inequalities." ?
     
  9. Nov 11, 2014 #8
    Here is Stapp's paper on that idea:

    Bell’s Theorem Without Hidden Variables
    http://arxiv.org/pdf/quant-ph/0010047v2.pdf

    I think the major controversial area still appears to be with respect to whether the Bell theorem includes 'realism' among its assumptions. Part of the difficulty may be due to delineating what one means by 'realism'.
     
  10. Nov 12, 2014 #9

    Demystifier

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    A rather clear explanation of 'realism' is given in
    http://lanl.arxiv.org/abs/1212.5214 [Am. J. Phys. 81, 854 (2013)]:
    "Let us define “counterfactual-definite” [14, 15] a the-
    ory whose experiments uncover properties that are pre-
    existing. In other words, in a counterfactual-definite
    theory it is meaningful to assign a property to a sys-
    tem (e.g. the position of an electron) independently of
    whether the measurement of such property is carried
    out. [Sometime this counterfactual definiteness property
    is also called “realism”, but it is best to avoid such philo-
    sophically laden term to avoid misconceptions.]
    Bell’s theorem can be phrased as “quantum mechanics
    cannot be both local and counterfactual-definite”. A log-
    ically equivalent way of stating it is “quantum mechanics
    is either non-local or non counterfactual-definite”
    "
     
  11. Nov 12, 2014 #10
    Thanks a lot! - looking at the date I likely have seen this one before, but a quick look tells me that indeed it elaborates on Bell's so-called "reality" assumption (which he based on E-P-R's earlier arguments), and which subtly goes beyond the standard meaning of "reality". In earlier discussions on this forum we (or just me?) could not get a good grip on that issue. "Counterfactuals" and things like that. Maybe if I study this (again?) it will be possible to get a grip on this!
     
    Last edited: Nov 12, 2014
  12. Nov 12, 2014 #11

    Demystifier

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    For a long time I was not able to understand how a physical theory can be non-counterfactual-definite (except by rejecting to talk about counterfactual definiteness), until I constructed my own model:
    http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]
     
  13. Nov 12, 2014 #12
    This is the part that is confusing me. Aren't such pre-existent properties (e.g. non-contextual) already ruled by Kochen-Specker theorem? This is what I take Laudisa to be arguing where he writes:
    Non-Local Realistic Theories and the Scope of the Bell Theorem
    http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf
     
  14. Nov 12, 2014 #13

    atyy

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    One of the things I misunderstood about Bell's theorem is that I thought it rules out hidden variables which are relativistically covariant. Maudlin discusses that this is not ruled out by Bell's theorem in the first of his articles in this collection. The first time I came across this possibility was in Demystifier's work, which I originally thought contradicted Bell. I haven't studied the work well enough to understand if it is correct, but I think I now understand Bell's theorem well enough to know that the possibility is not ruled out. The other case that Maudlin cites is the relativistic spontaneous collapse theory which violates a Bell inequality.
     
  15. Nov 12, 2014 #14

    Demystifier

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    No. Kochen-Specker excludes properties which are both
    1) pre-existent before the measurement, and
    2) unchanged by the measurement.

    Both KC and Bell agree that if 1) is satisfied then 2) is not. In other words, they both say that if properties exist before the measurement, then they must change by the measurement. But Bell goes a step further by proving that the required change must be non-local. That's why the Bell theorem is compatible with KC theorem, but also much stronger (and hence more important) than KC theorem.
     
  16. Nov 12, 2014 #15

    DrChinese

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    I agree: a very well worded description. In case anyone has a hard time finding where realism or counterfactual definiteness is explicitly assumed in Bell, look after his (14). He adds c as another unit vector and references it an equation in which a and b are also present. The assumption is that a, b and c all exist simultaneously.
     
  17. Nov 12, 2014 #16
    Demystifier,
    Do you think that Bell's theorem includes any "realism" among its assumptions? (And for "realism" you can substitute objectivity/classicality/counterfactual definiteness, etc.).
     
  18. Nov 12, 2014 #17

    morrobay

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    Can you post a link for (14) ? thanks
     
  19. Nov 12, 2014 #18
    I believe DrChinese is referring to equation 14 of Bell's famous 1964 paper. It is after equation 14 where Bell introduces unit vector c. DrChinese has argued that is where Bell brings in "realism". But this is far from being clear. See:

    http://www.drchinese.com/David/Bell.pdf
     
  20. Nov 13, 2014 #19

    Demystifier

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    Yes I do. (In the paper in post #11 I substituted realism for non-solipsism and explained in detail how locality can be saved with a price of adopting solipsism.)
     
  21. Nov 13, 2014 #20

    DrChinese

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    As bohm2 says, it is from the original paper. After a bit of manipulation, it becomes the more well known form presented as Bell's (15):

    1 + P(b,c) >= | P(a,b) - P(a,c) |

    There really is nothing to question about the realism assumption present here. There is a, b and c which must exist for this equation to make sense.

    This is a direct representation of what EPR called the elements of reality, which they said did NOT need to be simultaneously predictable with certainty to be accepted as elements of reality (they said any other view was unreasonable). Bell is making this explicit by saying: they simultaneously exist even through they cannot be simultaneously observed.
     
  22. Nov 13, 2014 #21

    stevendaryl

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    I don't like this definition. There is a connection between "realism" and "counterfactual-definite", but I don't think they mean the same thing. To me, the word "counterfactual-definite" should mean that counterfactual questions have definite answers. I assume that's where the phrase "counterfactual-definite" comes from. So even though Alice happened to measure spin along axis [itex]\vec{a}[/itex], we can ask the counter-factual question "What result would she have gotten if she measured it along axis [itex]\vec{b}[/itex] instead?" If such questions have answers, then your theory is counterfactually definite.

    But a nondeterministic theory would not be counterfactually definite, although a nondeterministic theory can still be realistic.
     
  23. Nov 13, 2014 #22
    OK I've now looked a bit longer at that paper. Probably I once saw it, but never read it! However perhaps I still don't "get" it: I don't see how such statements as "some kind kind of faster-than-light influence" and "This result places a strong condition on theoretical models that reproduce the predictions of quantum theory. This condition is similar to the failure of locality associated with Bell’s theorem" can be compatible with Einstein's SR ("Einstein-local"). I'm afraid that he merely argues, like Tim Maudlin, that no unreasonable "back-in-time" influences are necessary for QM interpretations that only at face-value are compatible with SR (or, only compatible with a to QM adapted version of SR, as in Maudlin's book). If so, then Einstein as well as Lorentz would have disagreed with calling that idea "full relativistic".
     
  24. Nov 13, 2014 #23

    morrobay

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    OK, and the elements of reality that are being counted in the above inequality are vector components of a,b,and c from Bell's (14) and (15)
    Physical quantities like magnetic spin and polarization, both of which have different values that depend on theta at time of measurement.
    So if P(b,c) , P(a.b) , P(a,c) are functions of theta then is there is a classical explanation whether inequality holds ?
     
  25. Nov 13, 2014 #24

    atyy

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    I think this shows why it is contested whether the realism assumption is present. If I use your definition that there is a meaningful equation in which a, b and c are present, then there is such an equation in quantum mechanics. One such example is Tsirelson's bound http://en.wikipedia.org/wiki/Tsirelson's_bound. So I think by this definition, quantum mechanics is a realistic theory, which would mean that quantum mechanics is nonlocal in the sense of Bell.
     
  26. Nov 14, 2014 #25

    Demystifier

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    First let me note that the Tsirelson's bound is an upper bound on quantum non-locality, so it cannot be used as a proof of non-locality even when some reality assumptions are taken for granted. If it tells something about locality or non-locality at all, it only tells that non-locality, if there is any, cannot be arbitrarily large.

    But the note above is actually red herring, because the crucial question here is whether Tsirelson's bound assumes reality, by the definition used by DrChinese. Is there an important difference between your example and DrChinese's example? Your example talks about quantities such as <AB>, which are average values. DrChinese's example talks about quantities such as p(A,B), which are probabilities. So the question reduces to the following one: Can we say that probabilities are somehow more "real" than average values? We could say so if we could argue that average value is only a property of a statistical ensemble, while probability is a property of a single member of an ensemble. But can we find a convincing argument for such a claim? I am not sure that we can.

    So I kind of agree with you that DrChinese's argument is not totally convincing. The question of reality assumption in the Bell theorem is more subtle than he explained.
     
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