Does the CMB reference frame violate the Cosmological Principle?

[smithpa9]

TL;DR Summary

Studies of the Cosmic Microwave Background shows that the Earth is moving roughly 380 km/s with respect to it towards the constellation Leo I think. Yet the Cosmological Principle and the Michelson-Morely experiments suggest there is no preferred reference frame in the universe -- i.e., no center of the galaxy. How can we reconcile these things?

Studies of the Cosmic Microwave Background shows that the Earth is moving roughly 380 km/s with respect to it towards the constellation Leo I think. Yet (I think) the Cosmological Principle and the Michelson-Morely experiments suggest there is no preferred reference frame in the universe -- i.e., no center of the galaxy. How can we reconcile these things? Or do they not need reconciling?

It seems that if we can identify the actual reference frame of the CMB, then that would be the "real" reference frame of the universe, and somehow more special than any other reference frame.

If so, does that violate the Cosmological Principle? And if not, what is the significance of the finding that there is a special reference frame for the universe? Will that help us identify a center?

 

[Orodruin]

No. The cosmological principle does not state what you think it does. It states that the Universe is homogeneous and isotropic. This does single out a particular reference frame - what we call "comoving" reference frames and that corresponds to the CMB rest frame.

The Michelson-Morely results are more related to the local speed of light being the same in all reference frames. This is not violated by the CMB either.

 

[Ibix]

Summary:: Studies of the Cosmic Microwave Background shows that the Earth is moving roughly 380 km/s with respect to it towards the constellation Leo I think. Yet the Cosmological Principle and the Michelson-Morely experiments suggest there is no preferred reference frame in the universe -- i.e., no center of the galaxy. How can we reconcile these things?

It seems that if we can identify the actual reference frame of the CMB, then that would be the "real" reference frame of the universe, and somehow more special than any other reference frame.

The frame where the CMB is isotropic is analogous to the local rest frame of the Earth in our everyday experience. There is nothing special about physical laws in that frame, but it's clearly a hugely important one because of all the matter that is at rest in that frame.

More generally, most situations have a preferred frame that's picked out by the matter under consideration. As always you can work in any frame, but it's usually more convenient to work in acframe that is adapted to the scenario.

 

[smithpa9]

Thanks, Ibix! When you say that frame is hugely important because of all the matter that is at rest in that frame, what matter are you referring to? It's not clear to me that any particular galaxy, star, or planetary system need necessarily move exactly in sync with that reference frame. Are there some you know of? More generally, what are the implications of there being such a "hugely important" reference frame? It seem like that would be very important and meaningful, but I'm struggling to figure out exactly what the important implications are.

 

[smithpa9]

No. The cosmological principle does not state what you think it does. It states that the Universe is homogeneous and isotropic. This does single out a particular reference frame - what we call "comoving" reference frames and that corresponds to the CMB rest frame.

The Michelson-Morely results are more related to the local speed of light being the same in all reference frames. This is not violated by the CMB either. No.

Thanks! So, I guess my question is more generally, what are the implications of there being such a reference frame that is tied to the origin of the universe? It seems like that would be very important and meaningful, but I'm struggling to figure out exactly what the important implications are.

 

[Orodruin]

Locally, there are not many implications. On a small scale, it also does not hold. In general it does not mean much more than there being a particular set of symmetries for the spacetime with the corresponding conserved quantities.

 

[Bandersnatch]

It's unlikely that any single galaxy would find itself exactly at rest with the CMB frame. But, as the name suggests, the matter which was at rest in this frame was the primordial plasma which at one point emitted the CMB. As that initially homogeneous plasma contracted under gravity towards locally forming overdensities, while simultaneously cooling down due to universal expansion, galaxies started to form. So all matter in the galaxies 'started off' from the CMB rest frame, and all galactic velocities relative to this frame are what they have later gained due to mutual gravitational interactions.

The importance of this frame for describing the universe is that it allows us to use the assumption of homogeneity and isotropy.
In any other frame the temperature of the CMB doesn't look the same (on average, disregarding local variations due to already undergoing evolution of overdensities). In particular, moving w/r to that frame introduces a dipole in the CMB spectrum - half of the sky is redshifted away from the direction of motion, the other half is blueshifted.
And since all matter has started from rest in this frame, the large-scale statistical spread of galactic velocities in this frame will be zero, unlike in any other frame.
Furthermore, different observers moving w/r to this frame will each calculate the age of the universe differently, but all will conclude it being less than what would be calculated in the CMB rest frame. So, if you wanted all observers to agree on one description of how old the universe is, you could tell them to use the one frame of reference where the age is maximal - the CMB rest frame.

Once you have picked a frame for which the cosmological principle holds, you can make some simplifying assumptions for the equations of general relativity that let you obtain a relatively simple model of the universe. So whenever you see any conclusions drawn from the cosmological models, it is implied that the CMB rest frame of reference (the comoving frame) is used.
There's no a priori reason preventing you from using any other frame for describing the universe. But without the simplifying assumptions the task would be immensely daunting. Much like you could in principle, but won't ever, use some random frame of reference moving at 99.99% of c w/r to the Moon to launch a lunar lander.

 

[JimJCW]

It seems that if we can identify the actual reference frame of the CMB, then that would be the "real" reference frame of the universe, and somehow more special than any other reference frame.

. . ., what is the significance of the finding that there is a special reference frame for the universe?

According to the Big Bang model, photons freed during the recombination era filled the universe with a blackbody photon gas at a temperature of about 3000 K. The expansion of space stretches the wavelengths of the photons and dilutes their density such that the blackbody nature is maintained but with the temperature reduced, for example, to 2.725 K now (See Sec. 2.1 Expectations and discovery of the microwave background, Steven Weinberg’s 2008 book, Cosmology). As a result, according to the model, the CMB rest frame is special in the sense that in any other frame, such as the earth, having a velocity relative to it will see a redshift/blueshift dipole in the observed CMB spectrum.

The question, what is the significance of this, is interesting but has no easy answers. Similar questions are also discussed elsewhere, for example, Is the CMB rest frame special? Where does it come from?.