How did the CMB Lorentz frame get chosen?

[Sam_Playle]

The cosmic microwave background is anisotropic: the temperature is distributed as a dipole with the temperature at the poles differing by ±0.00335 K from the mean.

This defines a Lorentz frame: we can boost by several hundred km/s to make the dipole vanish, on average. This new frame could be considered the rest frame of the CMB.

The laws of Physics are Lorentz invariant, so this appears to require spontaneous breaking of Lorentz symmetry by the CMB.

My question is: how and when is this breaking supposed to have occurred? Must the frame have been chosen at the start of the Universe, or is it possible for a Lorentz-invariant early Universe to break its symmetry at recombination?

Could there be topological defects that are remnants of recombination when we try to define the CMB frame globally?

 

[marcus]

A curved spacetime, or one with spatial expansion, does not have global poincaré symmetry. So from the start the U did not have the kind of symmetry you are talking about. So it did not need to be broken.

Lorentz frames do not describe things globally, they have no curvature, they do not expand.

Cosmology deals with a GR world, not an SR world. It is very different. Just by boosting you only get a LOCAL Lorentz frame that is at CMB rest--it only approximately fits reality. If you travel very far, or let substantial time elapse, you begin to realize how bad the fit is.

Maybe somebody else can take over and make this clearer, I have to do something else.

The cosmic microwave background is anisotropic: the temperature is distributed as a dipole with the temperature at the poles differing by ±0.00335 K from the mean.

This defines a Lorentz frame: we can boost by several hundred km/s to make the dipole vanish, on average. This new frame could be considered the rest frame of the CMB.

The laws of Physics are Lorentz invariant, so this appears to require spontaneous breaking of Lorentz symmetry by the CMB.

My question is: how and when is this breaking supposed to have occurred? Must the frame have been chosen at the start of the Universe, or is it possible for a Lorentz-invariant early Universe to break its symmetry at recombination?

Could there be topological defects that are remnants of recombination when we try to define the CMB frame globally?

 

[Sam_Playle]

Thanks. My question, then, is why is it this particular frame, and not another one? What is the cosmological origin? The CMB would seem to define (modulo SO(3)) a section of the frame bundle on spacetime; why is it the section that it is, instead of a different one? What is the historical fact leading to it?

A curved spacetime, or one with spatial expansion, does not have global poincaré symmetry. So from the start the U did not have the kind of symmetry you are talking about. So it did not need to be broken.

Lorentz frames do not describe things globally, they have no curvature, they do not expand.

Cosmology deals with a GR world, not an SR world. It is very different. Just by boosting you only get a LOCAL Lorentz frame that is at CMB rest--it only approximately fits reality. If you travel very far, or let substantial time elapse, you begin to realize how bad the fit is.

Maybe somebody else can take over and make this clearer, I have to do something else.

 

[marcus]

Hi Sam, I had to be out this afternoon and just got back. Isn't it true that as soon as you have matter in the picture you have picked out a section of the frame bundle? One in which the local matter, on average, isn't going anywhere?
I'm kind of surprised no one else stepped into answer your question in the past 3 hours.

I'll think a bit more about it and get back to this thead later.

 

[Chronos]

Echoing marcus point, Lorentz invariance, like special relativity, can only be applied to local reference frames. It does not apply to the universe as a whole, which is governed by general relativity. Were this not true we would have universal laws of conservation, which is not supported by observational evidence.

 

[Sam_Playle]

Thanks for your replies. I am convinced that no laws are violated. However, this doesn't sate my curiosity. I want to know how this frame bundle was picked, as opposed to another one, which, a priori, would be equally permissible.

Is the local choice of frame just the rest frame of some matter in the plasma right before recombination? Or does it go back further - does the CMB section of the frame bundle define a Cauchy surface which is, in principle, the time evolution of a special Cauchy surface fixed since the big bang?