# Solutions that break the Lorentz invariance...?

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Suekdccia
TL;DR Summary
Solutions that break the Lorentz invariance...?
I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned.

There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify any example of such solutions (a solution which really breaks the Lorentz symmetry)?

They also said that we don't need a theory which violates the Lorentz invariance to have solutions that are not Lorentz invariant. What do they mean by that? Can you specify any example of such solutions (a solution which really breaks the Lorentz symmetry)?

Thank you

Mentor
You have to distinguish two very different things:

(1) The laws of physics are (locally) Lorentz invariant; but

(2) Particular solutions to the equations, in general, are not.

For example, the particular solution that describes our universe is not Lorentz invariant, because it includes lots of matter and radiation, and the matter and radiation has particular states of motion. The simplest example is the CMB, since it's everywhere; at any event in spacetime, the CMB only looks isotropic (the same temperature in all directions) in one particular Lorentz frame. So the CMB is not Lorentz invariant. But the underlying laws that govern the CMB and everything else are Lorentz invariant.

That is what they are talking about in the reference you give.

• malawi_glenn, vanhees71 and topsquark
$$\hat{R}=\frac{1}{Z} \exp[-u \cdot \hat{p}/(k_{\text{B}} T)], \quad Z=\mathrm{Tr} \exp[-u \cdot \hat{p}/(k_{\text{B}} T)].$$
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