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Meaning of Spacetime Foliations

  1. We know that we didn't go from Galilian Invariance to Lorentz Invariance by just adding lenght contraction and time dilation. We also added the speed limit of light as c. So Lorentz Spacetime is a completely new foundation than Galilian Spacetime. And Spacetime foliation as I understood it being a slice of different nows and lengths giving rise to relativity of simultaneity. However, I can't understand what Tim Maudlin was talking about in the article "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done" when he tried to make compatible Bohmian mechanics non-local nature by adding a new "Spacetime Foliation". Maudlin said:

    How does it differs to the normal Spacetime foliations in Lorentz Spacetime? Is Mauldin describing about adding Spacetime foliations to Newtonian absolute space and time. Or is it adding additional structure to Lorentz Spacetime? But why did he refer to it as spacetime foliations (which has generic meaning in SR as slicing of spacetime in relativity of simultaneity)? Also wouldn't this end up the same as Lorentz Spacetime? I just can't imagine how the two differs and want to know how their spacetime diagrams differ.

    The following is prior to the above paragraph to give the context of what Maudlin was describing:

     
  2. jcsd
  3. To those familiar with Mauldlin article. Is he talking about putting a preferred frame in SR to define the Bohmian frame of absolute simultaneity? If not. What is he talking about?
     
  4. haushofer

    haushofer 974
    Science Advisor

    I don't understand

    If you have a 1-dim spacetime foliation (a vector indicating the "time" direction and a 3-dim. spatial metric on the hypersurface), an absolute time will prevent you from constructing the "total metric" from these ingredients; there is no 4-dim. invariant spacetime interval. I would say there is no "Lorentz metric" to start with.
     
  5. Say, are all preferred frames in SR automatically aether frame? If not. What are the preferred frames that don't use aether in SR? Bohmian mechanics are one of the intensively researched interpretations in Arxiv more than Many world Interpretation. And back to back with it is search for spacetime structure that can allow non-locality with beables.
     
  6. ghwellsjr

    ghwellsjr 5,062
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    Any inertial frame in SR will be exactly like the presumed single aether rest state of LET. Any and all characteristics attributable to aether will also be applicable to any other inertial frame moving with respect to the aether that you want to choose. Can you think of any characteristic of the aether rest state for which this is not true?

    What do you mean by "preferred frames in SR"? There is only one "preferred frame" and it's in LET, not SR, and nobody knows how to identify it.
     
  7. In Bohmian mechanics, the wave function is sensitive to all configuration changes instantaneously throughout the universe. Any idea how to model this nonlocality in Special Relativity? I mentioned BM because in Copenhagen, since the wave function is not physical but just in the equations. There's nothing there to be non-local. But in BM, non-locality is its middle name. Let's avoid LET for now.
     
  8. ghwellsjr

    ghwellsjr 5,062
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    Do you agree or disagree with my statement?
     
  9. I agree but in Bohmian Mechanics, somehow the wave function can use the preferred frame, that is undetectable by us. So how does it do it?
     
  10. ghwellsjr

    ghwellsjr 5,062
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    It does it the same way light propagates at c only in the aether frame and yet it also propagates at c in any other inertial frame moving with respect to the aether that you want to choose. Since you said you ageed with my statement, why are you asking about other specific examples?
     
  11. It can't just propagate at c. This is because in Bohmian Mechanics, the wave function is sensitive to any configuration changes throughout the universe instantaneously. For example. The wave function of any object on earth can feel the configuration of any object say 20 billion light years away and instantaneously. So how does it do it?
     
  12. ghwellsjr

    ghwellsjr 5,062
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    Are you saying that in Bohmian Mechanics, light does not propagate at c in the aether frame but rather instantaneously?
     
  13. In BM. Light propagates at c but the wave function propagates instantaneously.
     
    Last edited: Dec 21, 2011
  14. Interesting!
    I didn't know that article (although I now had a quick look at it); but I do have (and read) his book "Quantum Non-Locality and Relativity". One of the possible options that he mentions in view of Bell's theorem (which he takes for granted) and relating to Bohm's explanation is the existence of what he calls a "preferred frame", with which he obviously does not really mean a preferred but an "absolute" frame - just as Bell did before him.

    So, perhaps he means with "further space-time structure" simply the addition of a Lorentz-Einstein ether, in which, as he mentions, "absolute simultaneity" exists although we cannot detect it ("not empirically accessible"). However, he calls such an interpretation of relativity not "completely relativistic" and presents another interpretation by Tumulka which he does hold to be completely relativistic - but which I do not understand (and neither do I understand the one by Ghirardi).
    Anyone else?

    Harald
     
  15. ghwellsjr

    ghwellsjr 5,062
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    Are you saying that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame?
     
  16. They used different languages like foliating spacetime specially such that absolute simultaneity can be arranged. I'm still reading on Maudlin book. But for the purpose of this message. Yup. One can say (for purpose of discussion) that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame. What's the problem with that?
     
  17. ghwellsjr

    ghwellsjr 5,062
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    I'm not saying it's a problem. I'm just saying that if it's true in the aether frame then it is also true in any other inertial frame moving with respect to the aether frame. What's the problem with that?
     
  18. I was thinking that only FTL with aether can avoid causality problem by the BM wave function always in instantaneous speed in the aether frame. So you are saying we can use plain SR and FTL and no causality problem by making the FTL true in every inertial frame?? Hmm....
     
  19. To hold that an influence can also be instantaneous in any other inertial frame creates a self contradiction: except for one specific direction, an instantaneous influence in one standard inertial reference system (the "ether frame") is determined (or defined) as an influence forward or backward in time in other such systems that are in uniform motion relative to the first one.

    PS: But certainly you know that, so I guess that you meant something else than what you appeared to say. :smile:
     
    Last edited: Dec 22, 2011
  20. I think one significative property such a frame has is that it seems a way (the only one I know) of reconciling Quantum nonlocality and local realism. Something that is usually considered as impossible. Then again we don't seem to have empirical evidence of such frame (though this is debatable), and it is also apparently incompatible with GR cosmological models (also a moot point IMO).
     
  21. ghwellsjr

    ghwellsjr 5,062
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    I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame, otherwise, we would have a way to identify the rest state of the aether and that would make headlines and since it hasn't made any headlines, it must not be the case.
     
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