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I have read this question:

The existence of a CMB frame asserts that there exists a global frame in which the universe is (approximately) space-translationally and rotationally invariant (though not time-translationally- or boost-invariant) - a completely logically independent statement.

What frame of reference in the universe is (most) rotation-neutral?

A rotating universe must have a certain axis of rotation, so it must have a particular type of anisotropy that picks out a certain preferred direction. We can therefore look at the cosmic microwave background and see whether its anisotropy contains a preferred axis.[Collins 1973] Such observations impose a limit that is tighter than provided by solar-system measurements (perhaps 10^-9 rad/yr[Su 2009] or 10^-15 rad/yr[Barrow 1985]), but such limits are model-dependent. Because all of the present observation are consistent with zero rotational velocity, it is not possible to attribute any prominent cosmological role to rotation.

What if the universe is rotating as a whole?

Anglular momentum is conserved, so any tiny initial rotation that a the original ball of gas had becomes faster as the gas collapses down into a star and disk of planets.

How do the Planets and Sun get their initial spin?

As far as I understand, all answers on this site explain the angular momentum of celestial bodies by the original angular momentum that the particles had that build them up, for example, the Milky Way is rotating because the original gas and dust clouds had angular momentum. Based on the first answer, the CMB does not show rotation as a whole (as viewed from our frame), but every single object in the universe does possess angular momentum (the Earth, the Sun, the Solar system, the Milky Way, other galaxies, even galaxy clusters and superclusters), may that object be a quantum particle (quantum spin), or a composite object, like a proton, or whole galaxies. What they all have in common, is that they all possess angular momentum.

Now if all these composite objects possess angular momentum, and this originates to the original angular momentum that the particles (gas and dust) had that built them up, and the CMB was created at the time of decoupling from the same matter particles, then how is it possible that the CMB's frame does not inherit this angular momentum?

Question:

  1. Why is the CMB's frame not rotating?
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    $\begingroup$ The composite objects' angular momentum need not add up to a net angular momentum. $\endgroup$
    – Sebastian Riese
    Commented Dec 13, 2021 at 23:34
  • $\begingroup$ This is not an answer, but it may help. Is it possible something in the universe is not orbiting anything? $\endgroup$
    – mmesser314
    Commented Dec 14, 2021 at 2:56
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    $\begingroup$ Just to be clear, you understand that angular momentum is a vector quantity which can cancel out, right? Just because a bunch of individual components of a system have angular momentum doesn't imply that the system as a whole will have a particularly large angular momentum. $\endgroup$
    – Emilio Pisanty
    Commented Dec 14, 2021 at 9:22
  • $\begingroup$ @EmilioPisanty thank you, this could be an explanation, the question could be then, why does this cancel out with the CMB photons, but does not cancel out with any other object in the universe? $\endgroup$
    – Árpád Szendrei
    Commented Dec 14, 2021 at 16:25
  • $\begingroup$ Why the downvote? $\endgroup$
    – Árpád Szendrei
    Commented Dec 17, 2021 at 2:47

2 Answers 2

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Imagine a box with some particles inside and you observe the box from a frame where it has no linear momentum.

If you increase the temperature, the particles inside the box will move. They will individually have linear momentum that was not derived in any way from the momentum of the box. Instead object can gain momentum through interactions below the scale of the entire system. (It so happens that we can sum the momenta of all the particles inside and will find that it comes to nearly zero).

The same can happen in an angular sense. We can have a collection of particles whose net angular momentum is indistinguishable from zero. But can partition it into subcollections, each with a non-zero angular momentum. As in the first example, we would expect that the sum of all such angular momenta approaches that of the collection.

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  • $\begingroup$ Thank you so much! $\endgroup$
    – Árpád Szendrei
    Commented Dec 14, 2021 at 6:58
  • $\begingroup$ You could extend the analogy by rotating the box, which would create currents in the particle and the rotation would be detectable for a detector in the box (the CMB in this question) $\endgroup$
    – anna v
    Commented Dec 14, 2021 at 7:02
  • $\begingroup$ @annav can you please tell me what is wrong with my question? $\endgroup$
    – Árpád Szendrei
    Commented Dec 18, 2021 at 19:03
  • $\begingroup$ @ÁrpádSzendrei I think it is an ultimate question that hits on the experimental observation that the data do not show such a rotation. an ultimate "why" question that hits on "that is what has been observed" , and our cosmological model has developed consistently with this obervation. $\endgroup$
    – anna v
    Commented Dec 18, 2021 at 20:00
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If the universe has an axis about which there is rotation, the GR assumption that the universe on a large scale is homogeneous and isotropic would be false.

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