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Meaning of Spacetime Foliations

  1. Dec 17, 2011 #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:

     
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  3. Dec 18, 2011 #2
    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. Dec 19, 2011 #3

    haushofer

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    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. Dec 19, 2011 #4
    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. Dec 19, 2011 #5

    ghwellsjr

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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. Dec 19, 2011 #6
    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. Dec 20, 2011 #7

    ghwellsjr

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    Do you agree or disagree with my statement?
     
  9. Dec 20, 2011 #8
    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. Dec 20, 2011 #9

    ghwellsjr

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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. Dec 20, 2011 #10
    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. Dec 21, 2011 #11

    ghwellsjr

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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. Dec 21, 2011 #12
    In BM. Light propagates at c but the wave function propagates instantaneously.
     
    Last edited: Dec 21, 2011
  14. Dec 21, 2011 #13
    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. Dec 21, 2011 #14

    ghwellsjr

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    Are you saying that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame?
     
  16. Dec 21, 2011 #15
    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. Dec 21, 2011 #16

    ghwellsjr

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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. Dec 21, 2011 #17
    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. Dec 22, 2011 #18
    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. Dec 22, 2011 #19
    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. Dec 22, 2011 #20

    ghwellsjr

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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.
     
  22. Dec 22, 2011 #21

    ghwellsjr

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    Or to put it another way--let's suppose that instead of Michelson and Morley proposing MMX to detect aether wind, they proposed an experiment to detect the rest state of the aether by seeing if the speed of light was the same in all directions. It would be exactly the same experiment but with a different stated goal. Then, the very first time they performed their experiment they would have declared success--they had found the absolute rest state of the aether.

    So whatever experiment Bohmian Mechanics wants to propose to detect the absolute preferred rest state of the aether will yield a positive result the first time it is performed.
     
    Last edited: Dec 23, 2011
  23. Dec 22, 2011 #22
    What if the rest state is "C" and mass is a reduction of "c"?
     
  24. Dec 23, 2011 #23
    Yes - obviously that would break the symmetry of the phenomena! :smile:
     
  25. Dec 23, 2011 #24
    Before we get to very complicated spacetime diagrams. Let's first review some basic.

    In SR between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the travelling twin light mirror lightspeed as travelling at c all the time, right.

    In LET between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the travelling twin light mirror lightspeed as varying depending on the motion with respect to each other, right?

    But according to ghwellsjr "I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame"... how do you apply this to the above? In the Twin Paradox, what is the aether frame?
     
  26. Dec 23, 2011 #25
    There can be no difference between [1] and [2]: the exact same measurements are performed, and no model to explain the measurements can affect those measurements.

    According to SR it is not possible to track our motion relatively to such a frame, if it exists; and it is not part of the theory. According to Langevin, his thought experiment therefore merely detects the existence of such an ether frame. Here's his summary statement preceding that thought experiment:
    - p.47 of http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

    That I understand; however, as is the topic here, now Maudlin suggests something like that as well as two(?) other possible explanations. Is there anyone here who understands those other ones? :uhh:
     
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