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Are singularities part of the manifold?

  1. Aug 10, 2013 #1
    Mod note: Posts split off from https://www.physicsforums.com/showthread.php?p=4468795

    Hi, WN, might the OP be referring to GR instead of SR, more specifically to the expanding FRW universe in which it is impossible to even consider the notion of exansion without agreeing about an "everywhere at once" notion?, after all the current opinion in physics is that our universe is globally described by GR (which implies locally by SR of course) rather than by Minkowski flat spacetime where relativity of simultaneity truly belongs.
     
    Last edited by a moderator: Aug 10, 2013
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  3. Aug 10, 2013 #2

    Nugatory

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    He might be, but so what? The answer is the same either way: "at the same time" is observer-dependent.
     
  4. Aug 10, 2013 #3
    You mean expansion is observer-dependent?
    I mean if you apply the relativity of simultaneity strictly to extended objects like the universe there is no possible BB model.
     
  5. Aug 10, 2013 #4

    Nugatory

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    Einstein's equivalence principle is about acceleration not motion; you'd have to replace the word "moved" with "accelerated" to make what you said above correct.
     
  6. Aug 10, 2013 #5

    WannabeNewton

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    For the FLRW universes, everything is described in terms of the observers comoving with the Hubble flow. The global simultaneity slices are with respect to the congruence defined by these observers so again the global simultaneity is only for said family of observers. A different family of observers in the same space-time that define a congruence with non-vanishing twist won't even have global simultaneity slices.
     
  7. Aug 10, 2013 #6
    Certainly, but the relativity of simultaneity argument you guys are using to answer the OP forbids the existence of such family of observers when strictly applied (and even more something physical like a last scattering surface and the CMBR everyone in the universe, any family of observers must agree about). This was my point when making the distinction SR/GR.
     
  8. Aug 10, 2013 #7
    That family of observers is free to define congruences as they see fit, but the mainstream theory says they should still observe the CMB and be able to relate the doppler shift they observe it with to the family of observers that define global simultaneity slices (global "now instants") and that allow the notion of a homogeneous universe at each instant and a density change with respect to those instants (spatial expansion).
     
  9. Aug 10, 2013 #8

    Dale

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    There is no absolute simultaneity implied by GR either. You can take the FLRW spacetime, do a coordinate transform with a different global simultaneity convention, and still be able to correctly describe all physics. The GR vs SR distinction doesn't make a difference here. Simultaneity is relative either way.
     
    Last edited: Aug 10, 2013
  10. Aug 10, 2013 #9
    DaleSpam: If you're referring to my post, I agree with you completely on the relativity of simultaneity. My qualifier was on my statement that there always exists a global synchronization procedure. I don't feel comfortable generalizing this to GR (does it simply depend on whether the manifold admits a global coordinate system?).
     
  11. Aug 10, 2013 #10
    You woul need to define what you mean by "absolute" here, I don't think it is a scientific term.
    Also I'm not sure what you mean by a coordinate transformation with global simultaneity convention, what global convention? you surely know there is no global coordinates in GR.
    And exactly relative to what, is the simultaneity of the CMB?
     
  12. Aug 10, 2013 #11

    PeterDonis

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    This is not correct; the expansion of the congruence of "comoving" observers in FRW spacetime is independent of coordinates and independent of any choice of simultaneity convention.

    No. See above.

    Sure there is; the spacetime geometry described by the BB model is independent of coordinates and independent of any choice of simultaneity convention, just like any spacetime geometry in GR.

    No, it doesn't. The "last scattering" surface is independent of coordinates and independent of any choice of simultaneity convention. So is the CMBR.

    What you should be saying is that there is only one set of coordinates and one simultaneity convention in which the last scattering surface is a surface of constant coordinate time, and in which the isotropy of the CMBR is manifest in the coordinates. But that statement doesn't justify the other claims you're making.

    And all of this is indeed what such a family of observers will be able to do. Why do you think it wouldn't be?
     
  13. Aug 10, 2013 #12

    Dale

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    You are correct. By "absolute simultaneity" I simply mean the converse of "relative simultaneity" where simultaneity is a matter of convention and different conventions lead to different notions of simultaneity.


    That isn't true, in general. Many space times do admit global coordinates. However, to make my statement applicable to general space times you can weaken it to "non-local" rather than "global".


    The CMB doesn't have an intrinsic simultaneity. You will have to explain what you mean by simultaneity of the CMB.
     
  14. Aug 10, 2013 #13
    Peter, you are making Exactly the same point I am, I don't know how you manage to make it look like you are arguing with me. ;)
     
  15. Aug 10, 2013 #14
    No, not in general, I said in GR so I was referring to curved spacetimes.
    Sure I mean the relativity of simultaneity of observers very far apart but at rest with the CMB.
     
  16. Aug 10, 2013 #15

    PeterDonis

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    Because it seems like you're saying the opposite. This has happened before. :wink:
     
  17. Aug 10, 2013 #16

    Dale

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    It seems to me that you are making opposing points.
     
  18. Aug 10, 2013 #17

    PeterDonis

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    Relativity of simultaneity according to what simultaneity convention? Remember that the global simultaneity convention of the "comoving" FRW chart (in which each surface of constant coordinate time is a surface of simultaneity for each "comoving" observer) "lines up" with the local simultaneity convention of each "comoving" observer--i.e., within the local inertial frame of each "comoving" observer, events which are simultaneous with respect to the global FRW coordinates are also simultaneous with respect to the LIF.
     
  19. Aug 10, 2013 #18

    Dale

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    Me too, specifically I was referring to the FLRW spacetime.

    The FLRW spacetime admits a traditional coordinate chart which defines the simultaneity convention you are focused on, but it also admits many other coordinate charts. The notion of simultaneity defined by those alternate coordinate charts is every bit as "global" as the notion of simultaneity on the traditional chart, although they disagree. All of the physics of the FLRW chart is the same regardless of the simultaneity convention adopted. Therefore, simultaneity is relative in the FLRW spacetime also, the CMB notwithstanding.
     
  20. Aug 10, 2013 #19
    My only point has been that relativity of simultaneity is a local notion, how is this making opposing points?
     
  21. Aug 10, 2013 #20
    I guess we are referring to different things when talking about global coordinates, I mean the standard sense in which global means covering the whole manifold. I'm sure now you will agree with me. ;-)
     
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