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EPR and QFT

  1. May 10, 2005 #1
    Hi,
    I have a question: The EPR experiment told us the world is nonlocal. And as we know, the QFT is a local theory, there is a principle that measurement do not affect each other between spacelike points. Do the two conflict? And can we say "we can not find an experiment for now which does not support the QFT?"
    Thank you very much!
    wangyi
     
  2. jcsd
  3. May 10, 2005 #2

    dextercioby

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    Well,how can the EPR(-type) experiments fit in with the relativistic quantum mechanics...?I have no idea.Remember that the postulates of nonrelativistic quantum mechanics which lead Einstein,Podolsky & Rosen to formulate that Gedankenexperiment do not take into account the second (and neither the first,actually,but the second is much more relevant) postulate of SR,which was formulated by Einstein himself... :surprised Therefore,i think Einstein had something against the whole theory... :rolleyes:

    So far,so good with the QFT,at least its SM part.

    Da
     
    Last edited: May 10, 2005
  4. May 10, 2005 #3
    I think you are mixing two kinds of locality here. QM being non local directly applies to the measurements in QM. In other words, it applies to the observables, eg the EPR paradox. In the QFT-case, locality means that the gauge symmetry needs to be respected at each and every space time coordinate. Don't forget that QFT completely incorporates the principles of QM, as well as those of SR

    regards
    marlon
     
  5. May 10, 2005 #4

    vanesch

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    As I pointed out in some other thread, EPR results do NOT tell us the world is non-local ! This is only one of the possible explanations, but Bell made *several* assumptions to deduce his inequalities.
    The unitary dynamics in QFT is indeed completely local. However, QFT is just an application of quantum theory in general (you know, the Hilbert space, the operators, the states, the superposition principle...).
    What people working in elementary particles often forget, is that it is a full-fledged quantum theory in which the superposition principle is universally valid ; usually one works with asymptotic incoming and outgoing momentum states. As such, no "change in basis" is required for the calculation of most quantities, and hence the typical mysteries that are apparent in non-relativistic quantum theory (in the style of the Young slits, EPR and so on) are not made very visible in most treatments on QFT ; the mathematical machinery being already difficult and heavy as it is. But all of these things are also present in QFT.
    QFT being an application of quantum theory to a specific model, of course the general conceptual difficulties of quantum theory are the same for QFT as they are for non-relativistic quantum theory ; in particular the resolution of the measurement problem, and all discussion of the projection postulate and so on is just as actual in QFT as it is in non-relativistic QM.
    So if you stick to Copenhagen quantum theory, where a measurement induces a collapse of the wavefunction, then this introduces just as much non-locality in QFT as it does in NR QM.

    What I tried to argue in the other thread (on entanglement) is that a relative-state interpretation of quantum theory (and thus of QFT) leads naturally to the resolution of the EPR riddle *WITHOUT* violating locality. Of course the price to pay is that you have to accept the conceptual weirdness of a relative-state interpretation. I would like to underline, especially in QFT, the importance of this result. Locality (lorentz invariance) is such a strong guiding principle in all of QFT that it would be very very strange that we would finally introduce a rule (the projection postulate) that bluntly violates it. It simply doesn't make sense that you require lorentz invariance for the lagrangian formulation, that you require space-like field operators to commute etc... and that suddenly, you throw all that in the dustbin and bluntly project the entire field state reaching to the boundaries of the visible universe onto one of its components, simply because you, on earth, did a "measurement".

    cheers,
    Patrick.
     
  6. May 10, 2005 #5

    vanesch

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    Yup ! I'm exactly of the same opinion.

    I take it as one of the lessons of quantum theory, that has been with it from the very start, and that people have systematically tried to wipe out until it hit us in the face with EPR.
    I think the basic lesson from quantum theory is that "observations are relative" and only make sense to ONE observer, in the same way as "time is relative" was the message of relativity.
    I have probably been pushing a bit hard here, with consciousness and stuff like that, to illustrate the idea, and I'm affraid this ended up being counter-productive because it was thought to be mixed in with too much mysticism.
    Quantum theory, as it stands, allows you to explain YOUR specific observation history. We are used to take it for granted that this observation history is all there is to the world (which is probably the definition of "realism" in the Bell sense), and that anybody else necessarily needs to possess a similar observation history, because there IS only one observation history, which corresponds to "reality". But we could just as well be on our "personal voyage" through different possibilities, which doesn't need to coincide with "other" voyages by other observers. Only, whenever we CROSS such another observer, we WILL have common observation histories. So the Alice-state that will meet a Bob state will be in agreement with whatever that Bob state has observed.
    We get strange results (a la Bell violations) when we take different observation histories, by different observers, together, in the same way as we get strange results when we mix time variables of different observers in relative motion in special relativity.

    I think that this is the "lack of realism" content. What our observation history tells us is not "what happened". It is what "we observed what happened" and this is a very personal history. When we encounter another observer, then we should be aware of what he tells us happened to him is not necessarily what "happened" for short. It could be that us "meeting him" is part of our personal history ; and that there are other "hims" which we will NOT encounter. As such, our meeting him has already introduced a certain bias in which histories he's going to tell us. And that bias turns out to be the correlations we find when we compare our observations to his observation history.

    It is of course a disturbing idea that all we know, feel and see is just a personal story, and is not a view on the "real world". But this is what quantum mechanics has been yelling at us already for 80 years. Only, we found excuses as for why ELECTRONS "didn't have a position" until we observed them. Or why neutrons didn't have a position (when they diffracted at a crystal lattice). Or why an entire lattice of atoms in a crystal didn't have individual motions but acted as a whole (phonons).
    Well, now I think we came to the point where Alice has to accept that Bob didn't have a definite measurement result until she asked him. And vice versa!

    cheers,
    Patrick.
     
  7. May 10, 2005 #6
    I think I have a explanation, and it does not quite related with QFT, accually.
    the equation [phi(x),phi(y)]=0 for x,y spacelike only tells that the possibility of measuring the state with phi at x equals to the same measurment on condition that at point y the state has already been measured, it only indicates that the possibility is the same, but not the two measurement unrelated. For example, if we measure a system with J_z=0 using spin along z axis at x and y, the two must get the related(opposite) result, but both of them thinks the possibility is 50%, and no matter the measurment at x has taken place or not, the possibility at y is always 50%, because he doesn't know the information at x.

    Is my explanation right? thank you!
     
  8. May 10, 2005 #7

    vanesch

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    It is correct that measurements, locally at x, have probabilities which are not altered by whatever is decided to be measured at y. So as you point out, X sees half of the particles spin up, and half of them spin down, no matter what happens at y.
    However, the simple case you present (both measure along the z-axis) can also be explained by local realist models: namely for all couples sent out, half of them have a +z spin which is sent off in the x direction, and the corresponding -z spin in the y direction, and the other half have exactly the opposite. Each particle then determines in advance what will be measured at x and what will be measured at y. No mystery at all.
    EPR situations are more subtle.

    cheers,
    patrick.
     
  9. May 10, 2005 #8
    Yes, EPR tells us more. I only mean that the causality prinpicle in QFT does not conflict with QM. That is enough for the question i raised in the begining.

    regards
    wangyi
     
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