What Does It Mean to Be at Rest Relative to the CMB?

[cbetanco]

When one says they are at rest relative to the cosmic microwave background, does this mean that they are in a frame where the same frequency is measureed in all directions? Because, I could imagine if I boosted in one direction, then the spectrum behind me would be redshifted, and the spectrum in front of me would be blue shifted. So to be at rest with respect to the CMB I would need to be in the frame where there is no shift in either direction. Is this right? Or do I have it all wrong?

 

[bahamagreen]

I think that's right - you adjust until the CMB Doppler shift approaches uniformity in all directions.

"The Milky Way is moving at around 552 km/s with respect to the photons of the CMB, toward 10.5 right ascension, −24° declination (J2000 epoch, near the center of Hydra)" (Wikipedia)...

I suspect that this frame ends up being local because of the universal expansion, so this frame it is not "invariant", if that's the right word?

 

[PatrickPowers]

When one says they are at rest relative to the cosmic microwave background, does this mean that they are in a frame where the same frequency is measureed in all directions? Because, I could imagine if I boosted in one direction, then the spectrum behind me would be redshifted, and the spectrum in front of me would be blue shifted. So to be at rest with respect to the CMB I would need to be in the frame where there is no shift in either direction. Is this right? Or do I have it all wrong?

That is correct. The actual data is corrected for the motion of the Earth, Sun, and galaxy.

 

[cbetanco]

I suspect that this frame ends up being local because of the universal expansion, so this frame it is not "invariant", if that's the right word?

But locally, we can define a universal rest frame, that of the CMB? Does this also mean that if there were such a preferred frame, that Lorentz invariance would be violated locally? But now, if you could define such a frame, and Lorentz invariance was locally violated, if I go somewhere else in the universe, then because of this universal expansion, I would have to define a different frame where I was at rest relative to CMB. Would this imply momentum conservation was violated globally, since the preferred rest frame is not translationally invariant?

 

[PatrickPowers]

But locally, we can define a universal rest frame, that of the CMB? Does this also mean that if there were such a preferred frame, that Lorentz invariance would be violated locally? But now, if you could define such a frame, and Lorentz invariance was locally violated, if I go somewhere else in the universe, then because of this universal expansion, I would have to define a different frame where I was at rest relative to CMB. Would this imply momentum conservation was violated globally, since the preferred rest frame is not translationally invariant?

The rest frame with respect to the CMB has nothing to do with the non-existent "preferred frame." Experiment shows us that there is no such preferred frame as far as the laws of physics go. The CMB has no bearing on the laws of physics. They work just as well whether something is at rest with respect to the CMB or not.

 

[cbetanco]

Well, if Lorentz invariance was violated (like at the Planck scale), it would be possible to define a preferred frame. The CMB would seem to be the natural choice. But since this frame is local, I would guess different observers living at different parts of the universe would define this frame differently. Also, if we defined the lagrangian to be the lagrangian where we are at rest with the CMB, then different observers would have to define different lagrangians at differnet points in space, which would mean physics is not translationally invariant, and then momentum conservation would be violated (all assuming Lorentz invariance is violated!).

 

[Histspec]

Well, if Lorentz invariance was violated (like at the Planck scale), it would be possible to define a preferred frame.

Preferred frame violations of Lorentz invariance are already excluded to high precision by http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment" experiments.