system
Given the following post, respond as if you're commenting on Reddit:
human
How can we can have motion relative to the CMB if it is observed from all directions?

I just got put in my place by trying to call bullshit on someone who was saying we can measure our velocity relative to the cosmic microwave background. Apparently this is an actual thing. Can someone explain this please? How can the CMB rest frame exist if CMB photons are observed from all directions?
gpt
CMB photons are observed from all directions but not all with the same energy.

To be more precise: there exist, well, at least one frame where the CMB is seen as an isotropic blackbody spectrum (meaning the temperature does not depend on the direction). That's obvious or calling the CMBR "isotropic" would not make sense. Your claim is that an observer moving relative to this frame does not see anything different, and is unable to determine his motion wrt this preferential frame.

This is wrong because the relative speed between you and the CMB frame implies the photons coming straight ahead get blueshifted, the ones behind redshifted. (You can explicity see this as the effect of the Lorentz transformation on the photon's 4-momentum). There is this cute property about the Planckian / blackbody spectrum: if you multiply all the frequencies by a constant, it is still a blackbody spectrum, but at a different temperature. So the CMB ahead of you is warmer and behind you colder. In detail you have a **dipole** anisotropy due exclusively to your relative motion to the "CMB frame".

It's a pretty small effect unless you're moving at relativistic speed. Earth's speed is around 400 km/s plus an annual term. This gives a smallish (order of the mK) but very measurable dipole anisotropy in the CMBR that allows us to measure the above speed and direction.

Finally, when people talk about the anisotropies of the CMBR, they mean the remaining anisotropy after subtracting this mK dipole; the remaining fluctuations are of the order of the μK and have cosmological relevance.