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The Copernican Principle states that Earth is not at a special place in the Universe, and by extension, that there are no "special places" in the Universe (per homogeneity of the universe, aka the cosmological principle). However, the frame in which the CMB is isotropic appears pretty special:

  • There is exactly one reference frame in which the CMB is isotropic
  • It's independent of the observer's motion
  • Every observer agrees which reference frame that is
  • It's not trivial, since it makes the CMB simpler (and the CMB underpins much of modern cosmology)

Does the frame in which the CMB is isotropic violate the Copernican Principle? If so, why do we still believe in the Copernican Principle?

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  • $\begingroup$ The CMB frame is special to any inhabitant of the universe, as far as I can see. The Earth's frame also is, but only to Earthlings. $\endgroup$
    – my2cts
    Jun 4, 2020 at 23:23
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    $\begingroup$ I don't see how that violates the Copernican principle, since the CMB fills the whole universe, it doesn't single out a special place. $\endgroup$
    – PM 2Ring
    Jun 4, 2020 at 23:24
  • $\begingroup$ @PM2Ring hmm, good point. I guess it doesn't violate the Copernican Principle then, although it does still look like a "preferred frame". I will need to think about it. $\endgroup$
    – Allure
    Jun 4, 2020 at 23:30
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    $\begingroup$ GR doesn't rule out the existence of special useful frames. Also note that if you're in a properly sealed lab you cannot determine the CMB rest frame, you have to look outside your lab. $\endgroup$
    – PM 2Ring
    Jun 4, 2020 at 23:35
  • $\begingroup$ @PM2Ring can you detect the CMB in that sealed lab though? If so, you should be able to determine the CMB rest frame. If not, then the sealed lab hardly seems like a workable lab. $\endgroup$
    – Allure
    Jun 4, 2020 at 23:43

1 Answer 1

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CMB frame provides a privileged foliation of spacetime by spacelike hypersurfaces, essentially by defining universal cosmic time via some function $t_c=f(T_\text{CMB})$. A given “slice” $t_c=\mathrm{const}$ could be then interpreted as a space part of a spacetime.

Copernican Principle as stated by OP means that “there are no special places”. Applied to cosmological models we could identify “places” with points of space within a slice $t_c=\mathrm{const}$. And indeed if averaged over sufficiently large scale these slices appear to be homogeneous spaces, every point of it is just like any other point.

We see that cosmological models that assume spatial homogeneity do satisfy Copernican Principle in the sense outlined above.

Note, that the “time” part of spacetime is not homogeneous: every moment (on cosmological timescale) is unique and not like the moments before or after, at the very least they differ by having a specific value of CMB temperature.

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  • $\begingroup$ every point of it is just like any other point wouldn't the point where the CMB is isotropic be special, though? $\endgroup$
    – Allure
    Jun 8, 2020 at 8:00
  • $\begingroup$ One could chose the 4-velocity vector at any point of spacetime so that CMB is isotropic. It would be orthogonal to the slice $t=\mathrm{const}$ at this point. In the language of three-dimensional space it means that we can choose an observer passing through any specific point in space at a given moment in time such that this observer sees CMB as isotropic. $\endgroup$
    – A.V.S.
    Jun 8, 2020 at 8:40

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