Earth's velocity wrt CMB gives the centre of the universe?

[Happiness]

Alan Guth mentioned in his lectures that to get the accurate linear relationship of Hubble's law, we need to subtract the velocity of the Earth with respect to the cosmic microwave background (CMB) when calculating the velocity of galaxies.

Question 1:
If space is expanding uniformly throughout, why does the Earth move with respect to CMB?

Question 2:
If the Earth is moving at a velocity with respect to CMB, then doesn't this mean there is a special point that we can consider the centre of the universe? Divide the Earth's velocity by the Hubble's parameter, we will get a displacement vector, which is the vector that points from the centre of the universe to the Earth. Doesn't this contradict the assumption that the universe has no centre?

Guth's lecture:

 

[Orodruin]

If space is expanding uniformly throughout, why does the Earth move with respect to CMB?

Because Earth is not at rest with respect to the comoving coordinates. There is going to be local variations just as there are local variations of velocities in a fluid.

If the Earth is moving at a velocity with respect to CMB, then doesn't this mean there is a special point that we can consider the centre of the universe?

No. Definitely not. There is simply no logic in this statement.

 

[wabbit]

If you are moving with respect to an isotropic backround, you see something very specific, a blue shift in one direction and red shift in the opposite one, and once you correct for this (assuming this is due to proper motion), you recover the isotropic background - nothing of the sort will show up if the background isn't isotropic.
So the CMB observations provide both a measure of Earth's motion relative to the background, and the evidence that this background is isotropic.

And large scale homogeneity with no center is the simplest assumption that explains this isotropy.

 

[Drakkith]

If the Earth is moving at a velocity with respect to CMB, then doesn't this mean there is a special point that we can consider the centre of the universe?

No, because those galaxies that are receding from us at huge redshifts also see themselves as barely moving with respect to the CMB, just as we see ourselves barely moving with respect to the CMB. By 'barely' I mean that our velocities are a tiny fraction of c relative to a nearby frame that is considered stationary with respect to the CMB. In other words, those galaxies receding from us do NOT measure a huge difference in the CMB between different parts of the sky.