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OK Corral: Local versus non-local QM

  1. Feb 19, 2007 #1

    wm

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    Preamble: I have yet to find a reason to abandon my support of a LOCAL interpretation of QM; especially in relation to EPRB. It is therefore my hope that we might here bring the issue to a head. Given the frequent verbal misunderstandings across the LOCAL--NONLOCAL divide, it is also my hope that we might resolve the issue in the beautiful (and usually clearer) language and logic of mathematics.

    PS: I suggest we constrain our discussion on this thread to the EPR-Bohm experiment with spin-half particles; it being the source of Bell's (1964) theorem. So:

    On another thread, I (wm) wrote:

    DrChinese replied:

    (Emphasis added.)

    1. Causally correlated?? DrC, note that I said that the detector settings are correlated by their diifferential setting. If detector A on the left is set at a (a unit vector) and detector B' on the right is set at b' (another unit vector), then the detector settings are correlated by a function of (a, b'): that is, by a function of the differential setting.

    For example: If we took cos(a, b') as the correlation function; +1 indicates a parallel setting; -1 indicates an antiparallel correlation; etc.

    Of course the correlation that counts is that established by the respective detector-settings at the instant of arrival of each particle: set in any manner of your choosing.

    2. Was the outcome of a particular detector setting determined when the particle pair was created?? The outcome was determined when the particle and the detector interacted LOCALLY.

    So could I ask you to provide the detailed maths by which you derive the EPRB correlation function? So that I might see where you believe that nonlocality enters (in the language of maths.)?

    3. How does the answer at one point get transmitted to the other point? ??

    Well, in that we have not introduced Alice and Bob to the discussion thus far: it does not get transmitted! How could it?

    Trust this all helps to convince you of the need for your mathematical derivation of the EPRB correlation function,

    With best regards, wm
     
    Last edited: Feb 19, 2007
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  3. Feb 19, 2007 #2

    Hurkyl

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    I can answer this one.

    There is a lot of information in the universe. There is information about Alice's laboratory, there is information about Bob's laboratory, there is information about the Andromeda galaxy, etc.

    Alice can measure anything in her laboratory, but she can't (directly) measure anyting in Bob's laboratory. Nor can she directly measure anything in the Andromeda galaxy.

    When we take the state of the universe and discard the information that isn't (directly) accessible to Alice, what remains is what we call Alice's world.

    In particular, it isn't like Star Trek where we have a parallel "universe" in which our evil twins live.


    If the entire universe consisted of the pair of photons in the experiment, then the state of the universe might be

    (3/5) |01> + (4/5) |10>

    Alice's world is the first coordinate. If we take the partial trace along the second coordinate to obtain the state of Alice's world, we get the statistical mixture

    36% chance of |0>
    64% chance of |1>

    Similarly, Bob's world is the statistical mixture

    64% chance of |0>
    36% chance of |1>
     
    Last edited: Feb 19, 2007
  4. Feb 20, 2007 #3

    wm

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    Clarifying the MW in MWI?

    Dear hurkyl, I appreciate this answer very much!

    BUT I wonder: How long before someone comes to clobber us in this common belief. Dare I summarise that belief as: Many private local worlds, one common local universe?

    AND I wonder that I've not seen such a clear delineation of the MW in MWI before? That is: I wonder if dedicated MWIers will accept it?

    For, if I'm not mistaken, you allow that the overlap in Alice and Bob's private worlds may increase when they get on the phone to discuss their respective results: in full accord with locality.

    And in full accord with the common-sense response to DrC's question re information (answers) about Alice's result (in Alice's world) being transferred to Bob (in Bob's world); and vice-versa: There being no virtual/mysterious/magical/non-local/Star-Trek universes built from virtual Alices and Bobs ... ad infinitum.

    Hoping I've understood you correctly, many thanks, wm
     
  5. Feb 20, 2007 #4

    Demystifier

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    There are local and nonlocal *interpretations* of quantum mechanics (QM).
    But what can we say about QM (non)locality independently on the interpretation?
    We can say that a (many-particle) state is described by a wave function of the form psi(x_1,...,x_n), i.e., that, in general, there is no wave function for each particle, but that there is only one wave function describing all particles together. Isn't that an interpretation-independent sign of NONlocality?

    Of course, if you start to deal with interpretations, you may say that quantum physics is only about correlations, and that only the correlations are the entities which are nonlocal. But if the only entities quantum mechanics is about are nonlocal, then obviously quantum mechanics IS nonlocal, isn't it?

    And if QM is *not* only about the correlations, then what is it about? Whatever *clear* answer to that question you choose, it seems that you cannot avoid the conclusion that this thing must be nonlocal. The only way to save locality is to advocate an interpretation that avoids a clear answer to the question - what is QM about?!
     
  6. Feb 20, 2007 #5

    Demystifier

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    Let me also explain why I claim that correlations are nonlocal. If two particles spacially separated are correlated, then this correlation is nonlocal. Clearly, in the EPR(B) setup this is the case. It is also clear that the Schrodinger equation allows entangled wave functions without local interactions between particles. In that regard see also
    http://arxiv.org/abs/quant-ph/0304031
     
  7. Feb 20, 2007 #6

    vanesch

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    I've been giving my PoV on this issue at least a dozen of times, so I'm not going to do so here again...
     
  8. Feb 20, 2007 #7

    Demystifier

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    Then let me put a summary of my view of your PoV. It is MWI and local and is in agreement with what I said above. Namely, it involves a fundamental role of conscious observers, but their role is not *clearly* explained. Instead, their role remains somewhat mysterious. In other words, just as I said above, you save locality by avoiding a *clear* answer to the question - what is QM about?!

    But of course, it does not mean that your PoV is wrong. It may be a fundamental property of consciousness that it is uncomprehensible and logically unexplainable. In that case, QM can indeed be local, while apparent nonlocality can be merely an artefact of misleading attempts to find a non-existing complete comprehensible model of nature.
     
    Last edited: Feb 20, 2007
  9. Feb 20, 2007 #8

    Demystifier

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    Let me also say the following. If QM is both local and comprehensible, then there must exist a formulation of QM in which this locality is manifest in *every* equation. In particular, it should not contain many-particle wave functions that cannot be reduced to a collection of single-particle wave functions. But no one ever constructed such a formulation of QM. Thus, I conclude that QM is either nonlocal or noncomprehensible (or possibly both). This conjecture is nothing but a somewhat stronger variant of the well-known *theorem* (Bell, Hardy, ...) that QM is either nonlocal or nonrealistic (or possibly both).

    But if you accept the option that QM is noncomprehensible, then you come to the teritory of religion-like arguments. Whenever scientists give a logical argument against some religion dogma, religious people reply that the logical argument does not disprove anything, because God is not comprehensible by humans. I respect such arguments as long as they are used consistently, but then physicists advocating locality of QM should not pretend that they find QM fully comprehensible. Locality is compatible with QM in the same way as religion is compatible with science.
     
    Last edited: Feb 20, 2007
  10. Feb 20, 2007 #9

    Demystifier

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    What I cannot understand is WHY some physicists so desperately seek for a local interpretation of QM? What is so sacred about locality? Before getting familiar with Einstein theory of relativity, (almost) nobody had problems with accepting the Newton nonlocal theory of gravity or the Coulomb nonlocal law of electrostatics. So, why locality could not be only an approximative principle valid only in a restricted domain? Why many physicists find so dangerous or even unacceptable to have nonlocal laws of physics?
     
  11. Feb 20, 2007 #10

    DrChinese

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    I am not defending non-locality. I simply defend Bell's Theorem. I would be willing to discuss the topic in this light. Basically, Bell says that:

    No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

    Further, experimental results are within the range of the predictions of QM. If you are a proponent of locality, then you should reject the existence of hidden variables. If you are asserting that there ARE local hidden variables, then you should demonstrate that Bell's Theorem is wrong. The proof of Bell's Theorem has been presented many times, and I provide a couple of versions of it on my website:

    Bell's Theorem (following Bell)

    Bell's Theorem (following Mermin)
     
  12. Feb 20, 2007 #11

    vanesch

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    The one and only reason is the one you give yourself: relativity. Its basic principles require locality, and it is difficult to restore all the confirmed results of relativity in a natural way (I mean: following from some principle, and not one by one put in by hand to make things come out AS IF) if you violate locality in interaction.

    After all, the idea is to distill some fundamental principles on which to build physics. If we do not do this, and allow for a "deus ex machina" each time that we *seem* to have a principle, but which we'd like to violate somehow, which makes things come out nevertheless AS IF that principle were valid, then you can just as well go all the way: there are no laws of physics. There's just a big bag of events, and there happen to be correlations between them, but there's no real reason for that, there's no structure behind it, and if we find some, then that's a funny coincidence. What we think are cause-effect relationships are just coincidences, and their apparently systematic relationship is just by good (or bad) fortune. Tomorrow, things may be totally different. Or not.

    So, if we want to avoid the above viewpoint (which, after all, could be "true"), we'd better try to find rigorous principles, and be wary each time we find funny relationships that don't seem to rely on such a principle. This quest is not guaranteed to work, of course. But when we HAVE such a principle, and we have no absolute reason to reject it, we shouldn't reject it carelessly! Now, the relativity principle seems to be ok: there's no known, observed violation of anything that's derived from it, and it is extremely powerful in explaining a lot of stuff. So that's why people are very reluctant to dump it for no good reason but just some bad feeling about certain interpretations of quantum theory.

    Now, that said, Newton himself had a lot of troubles with his own "action-at-a-distance" ! In his principia, he states:

    So, locality does have some attractiveness, apart from its necessity in relativity.
     
  13. Feb 20, 2007 #12

    Demystifier

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    Vanesch, I agree, relativity looks as a nice and general physical principle with which we could start.
    But the existence of objective reality also looks as a nice and even *more general* physical principle with which we could start as well.
    On the other hand, the Bell theorem proves that at least one of these two nice principles is wrong.
    Isn't it more natural to retain the more general principle and to crucify the less general one?
    In addition, if you abandon the general principle of the existence of objective reality, then the existence of spacetime may not be objectively real as well, which means that even the principle of relativity (or locality) may not be objectively real, so you may lose *both* nice principles, which is certainly not what you want. (For an expanded version of this idea see also
    http://arxiv.org/abs/quant-ph/0607057 )
     
  14. Feb 20, 2007 #13

    Hurkyl

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    I'm not sure about the semantics anymore: I (thought I) had gotten it straight from Wikipedia, but I don't see it there anymore. MWIers will certainly agree with what I said, but they might disagree that's the definition of a "world".
     
  15. Feb 20, 2007 #14
    Or to presume that your interpretation of QM is wrong in some as yet undefined way. Not that I think it is definitely, but it's a possibility; that only our practically limited understanding of what exactly is going on, is clouding our theoretical approach to what is actually going on, in other words we're making incorrect assumptions.

    On the other hand of course we could just assume that QM is correct and there is something enigmatic(not necessarily a hidden variable as we might think of it, but something intrinsic we're missing) Which with our current technology we cannot reveal, that would make sense of the seemingly unusual or non common sense ideas.

    Perhaps we need to decouple ourselves from current reason and accept that probability or energy and matter may well work in as yet incomprehensible ways we cannot yet grasp at our current level. Maybe we're unfortunate enough to be living in a time where our reach exceeds our grasp?

    I honestly have no idea, and probably will not have any more the more I come to learn about QM in depth.
     
  16. Feb 20, 2007 #15

    Demystifier

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    Schrodinger's Dog, but there *is* something very general that is proved rigorously by the Bell theorem:
    If the results of measurements are manifestation of *some* objective reality (*whatever* this reality might be), then this reality must be nonlocal. This generality of the Bell theorem expressed by my words "some" and "whatever" is what makes this theorem so strong.
     
  17. Feb 20, 2007 #16
    Oh I agree given what we currently know the Bell theorem makes a pretty strong case for non locality, that's not something I would presume to argue about as it's a pretty air tight thought experiment, the only thing I suggested is that it might not necessarily be based on a true picture, and therefore we could be making flawed assumptions, which of course is entirely speculatory.

    We assume that there is something based on our logic system at work, without knowing if there is something else going on we can't possibly account for given our current technology, for example, it's like Newton looking at light without understanding it's duality so he claims it's a particle, and then Young claims it must be a wave because of his experiment, both are wrong, because both don't have the bigger picture.

    This doesn't mean there is some hidden variable or locality exists with QM, but I think it's possible that QM could be mistaken in some key area so I don't discount anything without having the 100% picture. Obviously this is just an example where nothing is 100% air tight, particularly when we don't have all the books in our collection.

    I'm not disagreeing with anything, just keeping an open mind.

    If Bell's theorem is not falsifiable then it is not a theorem :smile:
     
    Last edited: Feb 20, 2007
  18. Feb 20, 2007 #17
    I have a question- how can you test for realism? Is it falsifiable? You would say, realism is a false assumption if everybody does not 'see the same elephant', but if 'everybody hears everybody else stating that they see the same elephant they see', then you can't then know if the elephant has an objective reality. It certainly seems that the elephant is an objective thing, say from A's point of view, especially if B is saying it's an elephant, but a completely different consistent set of obsevations is perfectly possible- B seeing a wombat, and hearing A say that it's a wombat.

    Locality is certainly falsifiable, and has been tested, so it would surely make more sense to get rid of realism than locality.
     
  19. Feb 20, 2007 #18
    Is the elephant pink?
     
  20. Feb 20, 2007 #19

    vanesch

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    Yes, this is about correct (if you make the implicit hypothesis of no super-determinism, but which I think is necessary to make if we are going to draw ANY conclusion from observation): one has to choose between giving up the objective (and unique!) existence of outcomes of measurement, OR non-locality. Now, given that we can more or less cope with the first without hurting the known principles of physics (namely, MWI), but that, when accepting non-locality, we have to throw out the whole formal machinery of relativity, I would say that the requirement of objective and unique outcomes is for sure an esthetic and philosophically very satisfying one, but not absolutely strictly required by what we know, formally, about physics. However, the second (locality), is.

    So it seems that Bell + experimental confirmation (which is suggestively strong, but I'm not sure it is 100% watertight) makes us choose between:
    - a philosophically satisfying concept, that "what we see, IS there, and ONLY that" OR
    - the formal principle of relativity.

    I would say that as a human being, I'd go for the first, but as a physicist, I go for the second. Because the first principle doesn't bring me any FORMAL confort, while the second one is formally useful... at least as long as there isn't another principle from which we can get the *results* of relativity without its founding principle (which is the 4-dim spacetime manifold).
     
    Last edited: Feb 20, 2007
  21. Feb 20, 2007 #20

    vanesch

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    I love that :!!) :approve:
    It is exactly my critique on Rovelli's RQM.
     
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