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Thread: Is the standard cosmic model frame dependent?

  1. #1
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    Is the standard cosmic model frame dependent?

    I was considering a rebuttal to this ATM idea, and realized that the argument appears to apply just as well to the standard cosmological model.

    The crux of my question is how to resolve the apparent conflict between the following three principles:

    1) Space-time is isotropic in space.
    2) Space-time is evolving in time.
    3) There is no preferred frame of reference.

    Essentially, the evolution of space allows the photon density to form a local clock at each point in space. If this clock is isotropic in some reference frame, then the photon density age of the universe forms a global clock in this frame.

    If an observer is moving relative to this isotropic frame, however, there would now be a gradient in the photon density along the direction of the boost. But this means the new frame is not isotropic, meaning that the original frame is a preferred frame of reference.

    Where is my mistake in reasoning? Is this the CMBR frame?

  2. #2
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    There is no direct mistake in your reasoning, however i think the confusion stems from the non-qualified use of "no preferred frame of reference". What you have is indeed simply the frame in which the CMBR is isotropic, or rather the family of frames in which it is isotropic. So you can say that you have some "special" frame of reference, however that is not what the principle of "no preferred frame of reference" means. It just means that the laws of physics take the same form in every frame of reference, not that you can not find some frame of reference with an interesting unique "property".

    But also a couple of nitpicks. Space is isotropic, spacetime is explicitly not (the past looks different than the future). Likewise space is evolving in time, not spacetime. If you want the nitpicks to be fully rigorous add "there exist natural coordinates in which..." before those two statements.

  3. #3
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    Another way to look at it - the frame in which the CMBR is isotropic (essentially a comoving frame) is special with regard to a particular physical system, not the laws of physics. In his fairly massive book Cosmological Physics John Peacock notes that this means that it affords something suspiciously like a uniform cosmic timescale.

  4. #4
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    Thank you, both for the confirmation and clarification. I think I understand.

    Physics has no preferred frame, but the Big Bang theory produces a time-like 4-vector, identifying the CMBR frame, that is nearly constant due to the flatness of space.

  5. #5
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    Quote Originally Posted by utesfan100 View Post
    Thank you, both for the confirmation and clarification. I think I understand.

    Physics has no preferred frame, but the Big Bang theory produces a time-like 4-vector, identifying the CMBR frame, that is nearly constant due to the flatness of space.
    Yes, though it doesn't really have much to do with the flatness of space per se. If you look at the FLRW metric, you'll see the metric doesn't depend on the spatial coordinates, there's only a scale factor depending on time. You can "add" the scale factor in to get comoving coordinates (and get something that looks a lot like minkowski). In those coordinates, staying at a fixed place means the metric is the same as staying in any other fixed place, and looks the same in every direction. So staying at a fixed location in those coordinates gives you some "special" property, homogeneity and isotropy. We call these frames that are stationary in comoving coordinates "moving with the hubble flow", or "where the CMBR is isotropic". And since these all share the same time coordinate, it allows us a notion of cosmological time as ngc3314 remarked.

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