CMB and prefered lorentz frames

In summary: If you take the equations as they are written, without imposing any special symmetry, you get a set of equations that include the speed of light in terms of the other constants. So the equations are Lorentz invariant, in the sense that the same solutions always give the same results, no matter what the frame of reference is. But that's not what we usually want: we usually want the results to depend on the frame of reference, so that different frames will give different results. So we have to impose a symmetry on the equations, which is what special relativity does.
  • #1
DavidK
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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?
 
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  • #2
DavidK said:
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).
 
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  • #3
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?
 
  • #4
DavidK said:
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 [Broken]

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)
 
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  • #5
Ahhh...now it all makes sense again :approve: .
 
  • #6
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.
 

1. What is CMB and why is it important in physics?

CMB stands for Cosmic Microwave Background, which is a faint radiation leftover from the Big Bang. It is important in physics because it provides evidence for the Big Bang theory and helps us understand the structure and evolution of the universe.

2. How does CMB support the theory of relativity?

CMB supports the theory of relativity by exhibiting the same properties in all directions, regardless of an observer's frame of reference. This is known as isotropy and is a fundamental principle of relativity.

3. What is a preferred Lorentz frame and how does it relate to CMB?

A preferred Lorentz frame is a hypothetical frame of reference in which the laws of physics take on simpler forms. CMB is important in determining a preferred frame because it is the only known reference frame that has a true isotropic distribution of radiation, making it a natural choice for a preferred frame.

4. How has the study of CMB helped us understand the expansion of the universe?

By analyzing the temperature fluctuations in the CMB, scientists have been able to measure the rate of expansion of the universe and provide evidence for the theory of cosmic inflation. This has helped us understand the history and future of the universe.

5. Can CMB be used to study dark matter and dark energy?

Yes, CMB can be used to study dark matter and dark energy. The fluctuations in the CMB can reveal information about the distribution of matter and energy in the universe, including the presence of dark matter and dark energy. This helps us understand the composition and dynamics of the universe on a large scale.

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