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Non-locality, the poll

  1. Bell's theorem proves non-locality, therefore special relativity must be wrong.

  2. Special relativity strongly suggests locality, therefore Bell's theorem must be flawed.

  3. Bell's inequality is valid, but it disproves something besides locality.

  4. There is no conflict between special relativity and Bell's theorem.

  5. Other. (briefly (or thoroughly) describe)

  1. Aug 14, 2005 #1
    In this thread, I got a lot of different replies on exactly how to interpret Bell's theorem. Some suggested relativity must be wrong; others suggested Bell's inequality might not disprove locality, but some other assumption Bell made (such as an assumption based on the existence of a reality); still others suggested that there is no conflict between special relativity and Bell's theorem. So I'd like to know what the majority opinion is around here. If you'd like, leave a comment explaining why you take your position (for example, if you say relativity and Bell's theorem don't conflict, you might be thinking along the lines of Everett's many-worlds interpretation).
    Last edited: Aug 14, 2005
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  3. Aug 14, 2005 #2


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    I voted the Bell's inequality is valid, but disproves something other than locality. What it disproves is realism; that objects have properties all the time, rather than as in the Copenhagen interpretation of QM, only when observed. Without realism there is no possibility for one unobserved particle to affect the (nonexistent) properties of the other.
  4. Aug 14, 2005 #3


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    I've already made my views clear on that other thread, but I have to point out the sheer preposterousness of this suggestion. Surely the concept of "locality" presupposes the concept of "reality." If there's no reality, what in the world (no pun intended) could it even *mean* to say that causal interactions between objects respect relativity's prohibition on superluminal causation? Without "realism" there is simply no such *issue* as locality vs. non-locality (not to mention, nothing for physicists to study or think about!). So to say that Bell's Theorem refutes "realism" but permits us still to believe in "locality" is literal nonsense.
  5. Aug 14, 2005 #4
    No, it shows the critical importance of why "philosophy" must always preceed "physics" (or any attempt at scientific thinking, or any type of thinking at all for that matter)--a basic fact that many fail to appreciate. Thus, if one holds as an axiom of metaphysical philosophy the position that the "primacy-of-consciousness" takes priority over the "primacy-of-existence" then it makes perfect sense to conclude that Bell's Theorem refutes realism but allows "locality".
  6. Aug 14, 2005 #5


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    To be fair, I think every permutation of the situation is equally preposterous and that is what makes the debate so interesting. :rofl:
  7. Aug 14, 2005 #6


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    I agree with the sentiment, but I dont' think it's true that all the possible views here are *equally* preposterous. Surely regarding relativity as less fundamental than we all previously thought, is surprising -- but not preposterous the way denying the exsitence of an external reality is. Denying realism leaves no such science as physics; denying the fundamentality of relativity (ie, the truth of the principle of relativity) just leaves some interesting questions for how physics ought to proceed.
  8. Aug 14, 2005 #7


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    Realism is not the postulate that there is an external reality: it's a postulate about how that reality behaves.

    Specifically, I think it's the postulate that there are quantities out there from which one can, in principle, determine the result of any measurement.
  9. Aug 14, 2005 #8


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    No, that postulate is called "determinism".
  10. Aug 15, 2005 #9
    Bell's theorem is valid. It's a *theorem* after all. Bell inequalities
    are valid insofar as they're correctly constructed.

    Experimental violations of Bell inequalities show that formulations
    of the nonlocal observational context which employ Bell's locality condition
    are incorrect. They're incorrect because Bell's locality condition doesn't
    apply in the nonlocal observational contexts.

    Events at A and B, in the global context, are related, but not
    to each other via signalling across spacelike separations. They're
    related to each other due to a relationship imparted at emission, which
    can be regarded as a hidden global constant, which is captured in
    the experiments by time-correlating the results -- and
    they're related to each other via a global instrumental variable. It's
    the global instrumental variable which actually determines the
    variable (A,B) results.

    Bell treated the hidden global parameter, due to emission, as a
    determining variable in the global context, which doesn't work.
    Treating the hidden global parameter as a constant in the
    global observational context does work.

    So, it's not reality, or 'realistic' descriptions, or locality, or nonlocality,
    or ftl or instantaneous signalling that are in question here. It's simply
    a matter of inappropriately applying a certain sort of description to
    a certain observational context.

    Qm is compatible with lhv descriptions wrt certain contexts and not
    others. Some observational contexts are local and some are nonlocal.
    Lhv descriptions apply to some contexts, and ghc descriptions apply
    to others. Relativity isn't affected by any of this. Nature is local
    and nonlocal, depending on how/what you're looking at. And, finally,
    whether or not ftl signalling is a fact of nature is an open question.
    However, ftl signalling isn't necessary for a conceptual understanding
    of the results of Bell tests and violations of Bell inequalities.
  11. Aug 15, 2005 #10
    there is still something to discover

    If the physical world is made up of "quantum pieces",
    If these pieces build the physical space up to its classical scale,
    Then, don't the "quantum pieces" still have some "right" to escape the classical locality?

    We still need to understand deeper how classical physics emerges and interacts with the quantum.
  12. Aug 15, 2005 #11


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    Your pet phrase "nonlocal observational context" seems to be merely a euphemism for: there's non-locality going on, the situation is non-local, what's happening violates Bell Locality. But that shows the inanity of your overall statement: Bell's locality condition doesn't apply in situations where Bell Locality is violated. Well duh. =b

    No, this is precisely what Bell's Theorem shows is impossible. You can't attribute hidden variables to the pairs at emission such that the correlations are explained. That's no doubt what Einstein thought -- that physicists should look for a local hidden variable theory of this kind was precisely the conclusion of the EPR paper. But we now know it isn't possible. Bell proved that *no* Bell Local hidden variable theory can reproduce the QM predictions. So a common cause explanation like you are arguing for above is ruled out, period.

    Listen to what you're saying: a global instrumental variable (which I gather means "theta", the difference angle between the settings on the two sides) determines the results A and B. OK, so in particular, the result A is due (at least in part) to the setting over by B, and vice versa. That's nonlocality -- it violates Bell Locality. Throwing a bunch of confusing and ill-defined terms (like "observational context") at the problem isn't going to make that fact go away.

    Right, it doesn't work -- i.e., if you assume there is no Bell Locality, your theory doesn't work, it doesn't match the correct QM predictions. That's Bell's Theorem. You talk as if the very content of the theorem is somehow a proof that the theorem is invalid!

    Of course it works. Orthodox QM (with its nonlocal wave function collapses) also works. Bohmian Mechanics (with its nonlocal dynamics) also works. Lots of theories with different sorts of nonlocality in them "work."

    Bell proved that *only* such (nonlocal) theories "work." Are you disagreeing with that claim? It's hard to tell since you say at once that his argument is inapplicable, and that your alternative is nonlocal.

    Translation: the issue isn't locality vs nonlocality; it's simply a matter of having a nonlocal theory.

    In other words, there are certain experiments which can be explained by a local hidden variable theory, and some others that can't. That's true. But this only means that, in general, the local hidden variable theories cannot be right. A single inexplicable fact means the theory which can't explain it is wrong.

    Oh I see. So the people who are bothered that the nonlocal parts of nature contradict relativity should just look at something else... then the contradiction goes away. (Pass the beer!)
  13. Aug 15, 2005 #12
    Bell's inequality is flawed. In the Bell's inequality is absent the geometrical property of the curved space. Let's to consider the real space with the static classical gravitational fields. In curved space the Bell's inequality must coincide with experimental results. The geometrical property of the curved space is non-local. Reference
    1.About geometrical Hidden Variables and the Nature of Quantum Statistics// Journal of Russian Laser Research, 2001, v. 22, ¹ 5, p. 475-479.
    2. quant-ph/0212139
    Last edited: Aug 15, 2005
  14. Aug 16, 2005 #13
    Duh indeed. :-)

    Using an lhv formulation to describe a global observational context
    is sort of like using a 1/2 inch wrench to turn a 1 inch nut. Is
    it a big deal to discover that you can't do that?

    Bell locality is 'violated' due to an incorrect interpretation
    of the physical meaning of the qm method for calculating
    joint probabilities. The probability of individual detection at
    either end is always .5, and it's actually the joint probability
    that you're calculating after detection at one end or the
    other and then projection.

    If you reread what I wrote, you'll see that I'm not attributing hidden
    variables to the pairs at emission. I'm attributing a hidden relationship
    (call it the entanglement at the submicroscopic level) that doesn't vary from
    pair to pair. A hidden constant.

    A common cause hidden variable accounting is ruled out -- but not a
    common cause hidden constant. The variable that actually determines
    the joint results isn't hidden.

    What you're calling a fact isn't, in fact, a fact.
    The results at A aren't (even in part) due to the setting at B, and vice versa.
    If you vary the setting at A you'll see no corresponding change in the rate of detection at B, and vice versa. You can do anything you want at one
    end (turn it upside down, pour beer on it, play rap music to it, etc.) and it
    will in no way affect the rate of detection at the other end.

    But, you *will* have altered the *joint* results (perhaps irreparably). :-)
    A and B are correlated via timing (which is designed to ensure that paired results are
    associated with disturbances produced by the same interaction or emission event).
    Then (A,B) is correlated to Theta.

    The mathematical theorem itself is valid. Interpretations of it
    which say that it shows that there must be superluminal signalling,
    or that it shows that there can't be real physical disturbances with
    real physical characteristics moving between emitter and detector,
    or that it shows that local hidden variable theories are impossible
    are invalid.

    The experimental violation of Bell inequalities does have an
    important use however. It can be used as an indicator of the
    presence of entanglement.

    Bell's argument is that lhv descriptions of global contexts are
    incompatible with qm descriptions and experimental results
    of those contexts. Ok. So what does that mean? It means he's using
    the wrong 'wrench'. It doesn't mean that lhv's aren't relevant in *any*
    context -- of course they're relevant in some contexts.. It doesn't mean
    that there's nothing real happening between emitters and
    polarizers -- of course there is. It doesn't mean that there are no local
    hidden variables -- of course there are, they just aren't relevant to the
    results in the global context. It doesn't mean that we need to start thinking
    about what sort of superluminal signals might be propagating between
    A and B, because it doesn't rule out an emission-produced global
    hidden *constant*.

    No, it means that some experimental results are determined by local
    hidden variables and some aren't. A good general theory makes the
    contextual requirements clear -- so that you don't use the wrong tool
    for a particular job.

    System-dependent behavior doesn't contradict relativity. Global observational
    contexts involving correlations of global variables don't contradict relativity.
    People who are "bothered that the nonlocal parts of nature contradict
    relativity" have incorrectly interpreted the physical meaning of experimental
    violations of Bell inequalities. Perhaps these people, along with the guy
    who hypothesizes a new force of nature to account for his picking the wrong
    wrench and the people who are bothered by the color scheme of the new
    phone books should indeed look at something else for a while, or at least
    cut down on the beer. :-)
  15. Aug 16, 2005 #14


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    Yes, I voted the same. As repeated ad nauseam here, I think there are - as Dr Chinese points out - only a few alternatives, which are each by themselves ridiculous :grumpy:

    1) Pure epistemology - there's no reality, or at least, our theories and measurements don't describe reality.

    2) QM and/or relativity are, in the end, not strictly correct (that is: there is true non-locality (bye SR-GR) and the wave function stuff is in the end, not the state of the world but just a statistical description of it ; true classical physics emerges, a la Copenhagen, but this time with a precise transition)

    3) QM and relativity are strictly correct and describe reality: that's a MWI scenario. Note that there is absolutely no problem with reconciling Bell with QM in such a view (see my journal) ; if MWI weren't so weird and didn't have other problems, it would make the riddle go away. I think that, only for that reason, MWI has its merits, in the same way as Bohmian mechanics has: it is a counterexample to a claim that something cannot be done.

    I think it is silly to state that Bell's theorem could be "not correct". It is a theorem ! Also, QM respects certain kinds of locality (information locality for instance) nevertheless, QM doesn't obey Bell's theorem.
    So Bell's theorem is correct, and it certainly does not disprove locality in certain respects (as in QM, for instance), so it must indicate something else. It COULD disprove locality if we made another hypothesis, such as determinism, for instance. Bell's theorem just states:

    (locality) AND (underlying determinism) <==> Bell locality ==> Bell's inequality

    So, NOT(Bell's inequality) ==> (NOT locality) OR (NOT underlying determinism)

    Bell locality is also equivalent to the factorisation hypothesis, that correlations are only due to two possibilities: direct causal relation OR common cause.

    Locality above is a condition which can only say things when CHOICES can be made voluntarily concerning boundary conditions - otherwise locality doesn't mean anything (if no choices can be made, everything is fixed since the very beginning and "locality" and "causality" loose their meaning). In this case, locality means that the description of the situation at an event can only depend on the choices made within its past light cone, and that choices affecting only things outside of this past lightcone do not change the description at that event ; description which determines the outcomes statistically at that event. I called that kind of locality "information locality" because it is the necessary and sufficient condition for not having a communication channel coming in from outside the past light cone (indeed, if you CAN affect the probabilitic description, you CAN have information transfer, and if you cannot affect the probabilistic description, you CAN'T have information transfer).
  16. Aug 16, 2005 #15


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    I agree fully with you here :approve: I have great difficulties with pure epistemology.
    Of course, where we disagree is on HOW FAR we can stretch the notion of "external reality". You stick to what you measure is what *IS* there, I simply say that what I measure must be derivable from what is there. Not that I like that, but I think the option must be left open, and that all we *currently* know points in that direction (namely that QM and relativity are somehow correct). Even though I hope that a turn will be taken at some point (after we've ran out of oil, fought WWIII and the ants took over :uhh: )
  17. Aug 16, 2005 #16


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    After so many posts in the last couple days, I'm starting to share the feeling of nausea. But there are a few points that need to be made about your post here. (Welcome back, by the way!)

    Relativity theory makes certain claims about the structure of space-time, yes? So if there is really no such thing, isn't relativity false?

    My point is: this "pure epistemology" view isn't any kind of *alternative* to rejecting relativity in the face of quantum non-locality. It's actually the most severe possible way of rejecting relativity (and a whole bunch else besides).

    "by SR-GR" is ambiguous. Yes, you might have to throw away the "Principle of Relativity" (i.e., confess that there is some preferred foliation or absolute simultaneity) but it's not like you have to throw the Lorentz transformation equations (and all the positive roles they've played in motivating and organizing other physics) into the trash. It'd be just like when people discovered that air wasn't a fundamental fluid, but was, rather, made of molecules, so that things like sound waves weren't fundamental but were, rather, reducible to the motions of massive particles obeying Newton's laws. But none of this meant you had to scrap your knowledge of acoustics.

    A second point about this option #2 of yours: when you say "the wf stuff is ... not the state of the world but just a statistical description of it" do you mean that a hidden variable theory turns out to be right? It's of course true that such a hv theory would have to conflict with the Principle of Relativity or whatever. But your wording suggests that the same is not true for Copenhagen. But it is. If you think hv theories conflict with relativity (because, as Bell proved, they have to violate Bell Locality in order to agree with experiment), then so does OQM. It too violates Bell Locality. (I know, I'm a freaking broken record on this point...)

    Doesn't this just reduce to #1? When you say MWI is "weird", isn't that just a vague way of confessing that it doesn't provide any picture whatsoever of physical objects/fields evolving in space and time? And isn't that just a fancy way of saying that it completely pulls the rug out from under relativity?

    Maybe you want to say that the souped-up Schroedinger equation that governs the wf evolution in some full universal MWI theory is Lorentz invariant, so that it is consistent with relativity. But I find that silly. Having Lorentz invariant equations is not the only test of consistency with relativity. You have to actually respect the fundamental principles that gave rise to the Lorentz transformations (etc) in the first place -- in particular the principle of relativity. Do you think MWI (which I think you think entails solipsism) is really consistent with a statement like "the laws of physics are the same for all inertial observers" or "there is no structure to spacetime beyond that contained in the Minkowski metric"?

    Technically, you should say "QM doesn't obey Bell locality". Bell's theorem is that Bell Local hidden variable theories obey a certain inequality that QM predicts (and experiment confirms) is violated. But OQM isn't a hidden variable theory, so Bell's theorem doesn't even apply to it. But no need: you can just look at how OQM works and see that it, too, violates Bell Locality.

    I thought I dissuaded you of that on the other thread. It's true that any stochastic theory can be made into a deterministic theory by adding hidden variables. This is true for both Bell Local and Bell Nonlocal theories. So all this means is that the whole distinction of stochastic vs deterministic is completely decoupled from any discussion of locality. The only relevance of this point is in assessing the extent to which Bohr was a dumbass (for claiming it was impossible to make OQM into a deterministic theory by adding hidden variables, i.e., for claiming QM was complete).

    No, no, no! Bell's Theorem is that

    (Bell Locality) and (hidden variables) ==> (Bell's inequality)

    This can be derived with or without a determinism assumption. Also, Bell Locality is not equivalent to "locality" and "underlying determinism". That's what I pointed out yesterday in the resurrected thread.

    Finally, according to your last formulation, since Bell's Inequality is not satisfied we have to give up either locality or determinism. That means there should be non-local deterministic theories that predict violations of Bell's inequality, and also local non-deterministic theories that predict violations of Bell's inequalities. There are no doubt theories in the first category: Bohm is non-local and deterministic. But I challenge you to produce a theory that is local and non-deterministic.

    Of course, maybe here by "local" you mean only "signal locality", not Bell Locality. Is that right? But then your statement is *clearly* flawed, for Bohm's theory is *both* "signal local" and deterministic.

    The real point of Bell's theorem (supplemented with EPR's argument) is that no Bell Local theory can predict the right answers. That's it. It proves nothing about determinism and nothing about "signal locality".

    What else might cause correlations?? I'm sure scientists in other fields will be excited to hear that there is another option here.

    Are you saying that "parameter independence" is necessary and sufficient for "signal locality"? That's not true, actually. You also need the assumption that it's possible to *prepare* a system in a chosen state K. In fact, this is how Bohm's theory works: it violates PI, but according to the theory you cannot control the initial positions of the particles in the wf (there is "absolute uncertainty" or "quantum equilibrium") and this initial uncertainty washes out the ability to send a signal with the non-locality.
  18. Aug 16, 2005 #17


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    I don't think so. Not special relativity anyway. Minlowski introduced spacetime to clarify relativity, but it isn't essential to it.
  19. Aug 16, 2005 #18


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    So, just to be clear, a version of Bohmian Mechanics in which, say, the ether picks out a preferred frame (to give meaning to the instantaneous action at a distance in the guidance formula) is consistent with special relativity? After all, we can still have all the equations of relativity -- the ether just adds some structure to space-time that can't be accounted for by the Minkowski metric.

    At some point this becomes semantics, but I'll simply register that this particular candidate for a "relativistic theory" looks funny indeed!
  20. Aug 16, 2005 #19


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    My feeling is that if you give up on a reality, anything goes. We're looking at a video tape in our non-existing heads. I don't see why there should be any principle in that case that governs our "knowledge". Whatever will play on the tape will do. That's why I don't like it. Of course it is a strictly fail-safe attitude :-)

    I agree. It rejects everything. The author of the tape (call her god) can do whatever she pleases.

    It is my secret hope :-)

    Yes, you're sounding like a broken record, and yes, Copenhagen is even uglier. Doesn't make much sense even, to me.

    Yup, that's it.

    Not a very strong argument :-)

    Well, I think for one that it is sufficient. And I even would add: necessary. I know, we disagree on that. Matter of esthetics.

    I reduce it indeed to a perfect symmetry in the laws of nature: all expressions have to be geometrical quantities independent of their parametrisation in a certain coordinate mapping. Or at least be able to be formulated that way, even if it is not the most practical way to actually calculate things.


    You tried, but I think you failed. I'm still convinced that the difference between information locality and Bell locality is underlying determinism. By underlying, I mean: even if formulated stochastically, it CAN be reduced in principle to a deterministic model, by adding hidden variables.

    Yes, but a Bell Nonlocal theory, which is information local, cannot be made deterministic, without violating locality IN PRINCIPLE (even though it will not be observable). The INNER WORKINGS allow in principle for non-local information transfer (even though it will not be possible to exploit it). You do not accept that viewpoint, but I do. It doesn't allow you to express all the quantities as geometric objects, independent of a coordinate representation. Even if that aspect will not be observable in the lab.

    For instance, you cannot define Bohmian mechanics in a geometrical way in Minkowski space. The trajectories are not well-defined world lines, independent of the choice of the coordinate system ; hence they are not geometric objects defined on the manifold. THAT is the underlying principle of relativity: all objects in the theory are to be geometrical objects on the 4-manifold.

    I agree with you, Bohr was a dumbass. Too bad nobody else recognizes our superior intelligence :biggrin: They are ALL dumbasses :grumpy:

  21. Aug 16, 2005 #20


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    That's right. Exactly what I tried to point out. I thought (can be wrong) that the deeper idea behind relativity was that all objects to which we want to assign an ontology in our theory have to be geometrical objects defined on the 4-manifold.
    Once you've done "ether-like" things, even if it is unobservable because of some blurryness which forbids you to see things that way, you've made it impossible to define your ontology on a 4-manifold, and you're stuck to a particular coordinate system (or, with objects whose aspect CHANGES depending on which coordinate system you prefer to use). So this means that there are essential objects in your theory to which you want to assign an ontology which are not geometrical objects on the 4-manifold, and I thought that that was bad bad bad in relativity.
  22. Aug 16, 2005 #21


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    Yes, that's exactly my take too. And for the benefit of all the others reading this (I know Patrick has heard me say it about a bazillion times) orthodox QM violates the above characterization of "fundamental relativity" just like Bohmian Mechanics does. The collapse postulate (which of course is formulated using words like "instantaneously") is the same as the ether, as far as the above perspective is concerned.
  23. Aug 16, 2005 #22


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    What do you mean exactly by "violating locality IN PRINCIPLE"? Surely a Bell Nonlocal but signal local stochastic theory can be made deterministic by adding hidden variables. That's trivial. Will it still be Bell Nonlocal? Yes (assuming it's going to agree with the QM predictions). So if Bell Locality is what you mean by "locality IN PRINCIPLE" then your statement is true, but the part pertaining to determinism is superfluous. No Bell Local theory can agree with the QM predictions regardless of whether or not it's deterministic.

    Or maybe what you meant by "locality IN PRINCIPLE" is signal locality. But then the claim is just false. Bohmian Mechanics adds hidden variables to OQM, restores determinism, and yet there is still no violation of signal locality.

    I don't think we disagree about the viewpoint. I just insist on a clear and non-changing definition of "in principle." When you say the "inner workings allow in principle for non-local information transfer", what principle exactly does "in principle" refer to? If it refers to the principles of the theory you're trying to assess the signal locality *of*, then it's just *false* to claim that, for example, Bohmian Mechanics is non-local. In principle (meaning, according to the principles of Bohmian Mechanics), non-local information transfer is *not* allowed.

    Maybe what you mean is that if you were god, then you could see that there is nonlocality (because god would know what we don't know: the exact locations of the particles). But then god would probably know the wave function, too, which collapses instantaneously according to OQM.

    So I still fail to see any relevant and meaningful definition of "locality" other than "signal locality" and "Bell Locality". If you have some third definition in mind when you speak of "locality IN PRINCIPLE" you better define what you mean, because it's not clear.

    But don't you see? There is no theory which allows that. Not OQM, not Bohm, not MWI, not anything.

    Well, you're wrong about several things... but not this! :smile:
  24. Aug 16, 2005 #23


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    Actually, this discussion helped me making this intuitive notion clear in my mind. It means: only using geometrical objects in 4-dim geometry. Being able to formulate the theory in such a way, that the mathematical objects which have an ontological meaning (I think we both agree that in order to do physics, you have to postulate an ontology in the first place) are geometrical objects, and do not depend on a particular slicing up of the 4-manifold (= reference frame).
    For instance, the quantum fields (as long as they evolve unitarily) ARE such geometrical objects (although very complicated! I think they must be a cross section of a fibre bundle over Minkowski space, and the fiber is the set of Hermitean operators over Hilbert space) - as far as I understand this.
    If we associate an ontological reality to the quantum fields, this is then allowed because it is a geometrical object.
    However, as both you and I agree, the projection postulate screws this up dearly.

    Well, your insistance upon this gutfeeling and its unequal application to Bohm and the others helped me make it clear now - at least I think. So I repeat: the theory must be able to be formulated with only geometrical objects over the 4-dim manifold, then it is "in principle" local.

    This is indeed what I intended to, thanks for making this clear :-)
    And, we both agree that OQM with the projection postulate is just as ugly - it is a small mistery why so many people working in highbrow QFT and string theory simply don't know this !

    I think you helped me make this clear for myself (the god stuff was indeed what I intended, but it sounds of course ridiculous).

    I think that MWI allows this, in contrast with Bohm and OQM ; as long as you accept that the unitary evolution is "local in principle" (geometrical) - at least if the Lagrangian is a Lorentz-scalar, then the object describing "reality" is the wavefunction which is, and remains, a geometrical object, and is never projected.
    The second thing you need are world lines of consciousnesses. I never worked this out in complete detail, but I'd think that the world line defines a local reference frame for each conscious observer and as such this reference frame has a geometrical meaning (the vierbein associated with the world line). In this reference frame, it hops from branch to branch in the wavefunction, according to its own local Born rule. As you point out correctly, MWI people have a great difficulty DERIVING this Born rule, so I just postulate it, that's easier. I don't think it violates this geometrical definition of locality, because choices are only to be made when the local body associated with the consiousness entangles, which is determined purely by local interactions.
    So a "quantum experience" is the universal wavefunction (a geometrical object) and a world line of a consciousness (I think it can be made a geometrical object too). It observes an aspect of the universal wave function.
  25. Aug 16, 2005 #24


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    What's 'going on' we don't (yet) understand.

    That there is something 'deeper' (or maybe 'wider') that can encompass both the Bell theorem and SR, is a hope (but, as of today, little more).

    How could we decide? What experiments can we do (in principle) that would help us decide between preposterous alternatives (granted, there is no 'equality of preposterousness'; but then, since when has the 'merits' of a particular kind of preposterous been an important factor in determining whether 'the universe' plays by that particular set of counter-intuitivity?)?

    And if there are no experiments we could do, then have we encountered a 'hard limit' to physics?
  26. Aug 16, 2005 #25
    I agree. What if Newton had said, oh well, the planets just do what they do; they don't have to make sense. Of course, when it's all said and done there's no guarantee that we'll have a complete set of self-consistent physical laws, but if nature can't be described with mathematics, she sure has been playing a clever joke on us for the past 4 centuries.
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