Is There a Preferred Lorentz Frame in the CMB?

[DavidK]

Consider two farmes of reference moving relative each other. In one of the frames the CMD is fully isotropic, i.e., it looks the same in all directions. In the other frame however, the CMD should be red shifted in one direction and blue shifted in the other direction. Thus, the first frame can be considered to be at rest relative the CMD, and therefore, in some sence, constitute a preferred lorenz frame.

How can this be?

 

[marcus]

Consider two frames of reference moving relative each other. In one of the frames the CMB is fully isotropic, i.e., it looks the same in all directions. In the other frame however, the CMB should be red shifted in one direction and blue shifted in the other direction. Thus, the first frame can be considered to be at rest relative the CMB, and therefore, in some sense, constitutes a preferred Lorentz frame.

That is perfectly correct.

It is not forbidden to have preferred frames in that sense.

How can this be?

One way to think about why it can be is to say this to yourself:

special relativity says that the LAWS of physics must be Lor. inv.
So we expect the EQUATIONS like the Maxwell eqns. to be Lor. inv.

But we do not expect particular SOLUTIONS of those equations to have this same symmetry.

So, well, the universe is a particular solution to the Einstein General Relativity equation. This solution is approximately the Friedman solution (called various things, Friedman-Lemaitre, FRW metric, various names...)

this particular solution, call it Friedman solution or whatever you like, is NOT Lorentz invariant. It has a concept of being at REST which was already discovered by Hubble back in 1930s (if I remember history right) long before people knew about CMB!

One can be at rest with respect to the expansion------sometimes they call it being at rest with respet to the "Hubble flow". So that the recession speed of distant galaxies looks the same in all directions.

That idea of being at rest turns out to be the SAME as being at rest with respect to the CMB, as you described.

If you are not at rest then it will look to you as if the galaxies in one direction are receding FASTER from you than the galaxies the same distance away in the opposite direction.

If you adjust your velocity so the Hubble expansion looks the same in all directions, then you will also find that the CMB looks on average the same in all directions (I mean has no dipole, it still can have small irregularities but think of them as averaged out).

 

[DavidK]

Thanks for the very informative answer. A natural follow up question is: why is the Earth at rest relative the CMB? Is it something one should expect?

 

[marcus]

Thanks for the very informative answer. A natural follow up question is: why is the Earth at rest relative the CMB? Is it something one should expect?

It is not at rest. If I remember, the solarsystem is moving some 370 km/second with respect CMB.

the direction we are going is in the direction of the constellation Leo.

this motion w.r.t. CMB has to be deducted and compensated when people analyse the data.

The orbital motion of WMAP satellite, which is roughly similar to Earth's motion, also has to be deducted but that is only about 30 km/sec and varies seasonally. The main motion thing they need to get rid of is the overall motion of the solar system w.r.t. CMB.
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Here is a paper about measuring the speed and direction of sun relative CMB

http://arxiv.org/astro-ph/9601151

Sep 1996 The Dipole Observed in the COBE DMR Four-YearData
C. H. Lineweaver et al

"The largest anisotropy in the cosmic microwave background (CMB) is the ~3mK dipole assumed to be due to our velocity with respect to the CMB. ..."

this will give the coordinates of the direction and the speed (in case i have forgotten the speed)

 

[DavidK]

Ahhh...now it all makes sense again .

 

[Chronos]

I prefer to think of the CMB as a convenient reference frame, not absolute. The danger of that assumption is buried in Maxwell's equations.