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What can we say about Bell theorem?

  1. Jun 4, 2013 #1
    Bell theorem say that there is a contradiction between the locality principle in special relativity theory and quantum mechanics.So one theory must be incomplete describable theory.Then which theory(special relativity or quantum theory) is incomplete describable theory?
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  3. Jun 4, 2013 #2


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    Bell's theorem does not say that special relativity and quantum mechanics are incompatible. Special relativity and quantum mechanics are compatible.

    Last edited: Jun 5, 2013
  4. Jun 5, 2013 #3
    So the nonlocality in special relativity theory is not always meaning the sending a signal with velocity equaling infinity?Because Bell's theorem says the quantum mechanics contradicts the locality in special relativity theory.
  5. Jun 5, 2013 #4
    Bell's theorem states that measurements performed at spacelike separated (causally separated) events have correlations that can't be explained by any classical (local and bounded by c) interactions, but these 'superluminal' connections between measurements cannot be used to send information between spacelike separated observers. The latter caveat is what allows compatibility with SR.
    Last edited: Jun 5, 2013
  6. Jun 5, 2013 #5
    So we must classify the normal information and 'superluminal' information,the first propagates with velocity < c?
  7. Jun 5, 2013 #6


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    As pointed out, in a strict reading of QM and SR there is no contradiction. It is true that there is an implied contradiction but that involves extending the domains of these theories so they overlap, perhaps more than they should be.

    This can be seen by considering the following: there are interpretations of QM in which SR is not violated. Examples are Many Worlds and Time Symmetric types. So QM is usually considered to be "quantum non-local" which is to say there are quantum effects which appear to be non-local.
  8. Jun 5, 2013 #7
    In standard SR nothing physical can go faster than c. IOW, SR and QM do not directly contradict each concerning predictions (which is a practical compatibility), but according to Bell they are incompatible in their modelling. SR implies "Einstein locality" and QM seems to break that. See also the book of Tim Maudlin, Quantum Non-Locality and Relativity.
    "Modern physics was born from two great revolutions: relativity and quantum theory. Relativity imposed a locality constraint on physical theories: since nothing can go faster than light, very distant events cannot influence one another. Only in the last few decades has it become clear that quantum theory violates this constraint. The work of J. S. Bell has demonstrated that no local theory can return the predictions of quantum theory. Thus it would seem that the central pillars of modern physics are contradictory.
    Quantum Non-Locality and Relativity examines the nature and possible resolution of this conflict. [..]"
  9. Jun 5, 2013 #8
    Harrylin, if you open the book you reference (Maudlin), you'll see he gives several alternatives for exactly what the assumptions of SR are. He does consider the strict definition you give (everything bounded by c), and in addition he also considers the one I said (information transfer bounded by c). You are right Bell's Theorem violates the former, but all the physics of SR is in the second definition too, so why is it necessary to extend the definition to include things beyond information as being limited in transmission by c? Stick with the more limited definition and then SR and Bell's theorem are compatible-don't throw away the baby with the bath water.
  10. Jun 7, 2013 #9
    Hi Jolb what I said plus the summary that I cited largely implies what you say here. However, I dont think that I "extended" the definition of SR; for sure it was a common definition (or qualifier) in the early days. I have not seen any book or paper on SR from before the Bell theorem discussion that defines SR as limited by "information transfer bounded by c" (did you?). And clearly explaining the issue has nothing to do with "throwing away the baby with the bath water"!
  11. Jun 7, 2013 #10
    For historical reasons, you make a valid point, but I do not think that what you said clearly explains the issue. Your answer does not make it clear that you are adopting an obsolescent view of SR which has been replaced in the literature since the time of Bell--instead it seems to stress that QM and SR are incompatible. (I've never studied a relativity text older than Bell's Theorem--why bother with such relics? Even MTW came out in 1973.)

    When two theories are incompatible, this is usually an indication that at least one of them is wrong, we must choose one or the other. If QM and SR were incompatible, then we would think that something is wrong with one or the other. Are we to throw away QM or SR, despite the fact that both are wildly successful? (This would be "throwing away the baby with the bathwater" because it doesn't separate out the "bathwater" that causes the incompatibility.)

    Luckily we can avoid having to choose QM or SR since a slightly modified version of SR can save compatibility. The modification that is needed is the one I said--abandon the strict SR assumption in the antique books and instead adopt a slightly looser SR definition that works to make the two theories compatible, without modifying any of the predictions of SR. In effect, we just cut the junk that got us in trouble out of the definition. (This is "throwing away the bathwater" without throwing away either of the QM or SR "babies".) This is the modern approach, and most textbooks from the last forty years will simply sidestep the whole problem by never bothering to state the antique SR definition.

    In fact the historical development of this redefining of SR is a nice allegory for why we shouldn't bother stressing the antique assumptions of SR. The adherents of the antique view (everything bounded by c) said that Bell's theorem is incompatible with SR, and (assuming Bell's Theorem was derived correctly from QM) an experiment would support one or the other theory. I imagine that the SR guys were even excited that there might be an experiment which could verify the classical-relativistic physical picture and show that there is a problem with the more controversial QM physical picture. A few years later, Alain Aspect did the experiment, and lo and behold, there were superluminal correlations observed in the data. So QM is right! So the SR guys had to change their theory to save it. That is where the theory is now.

    Do we bother talking about how generations of physicists believed in negative-mass matter called Phlogiston? Or do we just skip right to the modern view?
    Last edited: Jun 7, 2013
  12. Jun 8, 2013 #11


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    You forgot the option of non-realism in interpreting the Bell experiments results. By giving up the narrow and
    limited definition of Bell/EPR realism, locality can be saved. There is no known physical mechanism for a
    superluminal signal and is bizarre
  13. Jun 8, 2013 #12


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    Not so sure about that.

    I think strictly speaking SR says information can't be sent FTL (I think that's what Jolb is correctly pointing out). Strange correlations in QM that imply some kind of non locality can't be used to send information so really it doesn't violate SR. But still its a rather desperate sort of an out.

    Last edited: Jun 8, 2013
  14. Jun 8, 2013 #13


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    I think what you are getting at here is the more modern treatments I have seen on SR based solely on the symmetry's implied by the POR (for example - Rindler - Introduction To Special Relativity - but its not the only one). With that assumption alone you can derive SR - the speed of light thing emerges as a constant that naturally occurs in its development - namely the maximum speed information can be sent in an inertial frame - by the POR that must be the same in all frames. Its simply a constant we fix by experiment and turns out to be the speed of light. Since quantum correlations can't be used to send information (and that's what you need to for example sync clocks) then its not really a problem.

    If that's what you are getting at then yes I agree.

    Actually any speed can be used in that derivation - the maximum speed particles can be accelerated to is another one. The key point is it must define some kind of velocity - it can be shown there is only one invariant speed - the correlations of QM can't be used to define a velocity since that requires syncing clocks.

    Last edited: Jun 8, 2013
  15. Jun 21, 2013 #14
    Indeed, that was the simple point that we made...
  16. Jun 21, 2013 #15
    Just for the record: Bill did not cite me but the book summary.
  17. Jun 21, 2013 #16
    but the problem is strong with general relativity.
    change gravity, QM ?
  18. Jun 22, 2013 #17
    Related to all this, seems to me that it isn't reasonable to say that "instantaneous" means the same as "faster than c". Maybe simplistic, but there is no such thing as "instant speed".
  19. Jun 22, 2013 #18


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    Well, IF Special Relativity is correct, THEN a signal that is faster-than-c in one frame is instantaneous in another frame. Of course, that might be an uninteresting point, since faster-than-c signals imply that Special Relativity is wrong.
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