Solutions that break the Lorentz invariance...?

• I
• Suekdccia
In summary, the physicists discussing Lorentz invariance violations in cosmology mentioned that we can imagine a Lorentz-violating solution to the cosmological equations. They also said that we don't need a theory which violates the Lorentz invariance to have solutions that are not Lorentz invariant.
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

*(https://books.google.com/books?id=W...age&q=inhomogeneities violate lorentz&f=false)

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
That claim is often made even in scientific papers and textbooks. Of course, a special-relativistic theory is Poincare invariant (and thus also Lorentz invariant). Your example of the cosmic microwave background is of course also Poincare invariant. It's simply electromagnetic radiation in thermal equilibrium at a temperature of about 2.725K. Now sometimes it's claimed that QFT at finite temperature "breaks Lorentz invariance", but that's of course not true. Of course, there is a special (in GR local) inertial frame distinguished by the physical situation, i.e., the rest frame of the CMBR, but this doesn't imply that somehow Poincare invariance is broken. You can formulate it manifestly covariant. You only have to take into account all "elements" you need for its description. We need temperature, which is a Lorentz scalar and the four-velocity ##u^{\mu}## of the observer relative to the (local) rest frame of the CMBR. Then the statistical operator can be written in manifestly covariant form,
$$\hat{R}=\frac{1}{Z} \exp[-u \cdot \hat{p}/(k_{\text{B}} T)], \quad Z=\mathrm{Tr} \exp[-u \cdot \hat{p}/(k_{\text{B}} T)].$$

Klystron

What is Lorentz invariance?

Lorentz invariance is a fundamental symmetry in the laws of physics, particularly in the theory of relativity, which states that the laws of physics are the same for all observers regardless of their constant velocity. It implies that physical phenomena are invariant under Lorentz transformations, which include rotations and boosts (changes in velocity).

Why are solutions that break Lorentz invariance significant?

Solutions that break Lorentz invariance are significant because they challenge the foundational principles of modern physics, particularly the theory of relativity. They can provide insights into new physics beyond the Standard Model and help explore potential quantum gravity theories or other high-energy physics phenomena.

What are some theoretical frameworks that allow for Lorentz invariance violation?

Some theoretical frameworks that allow for Lorentz invariance violation include certain models of quantum gravity, string theory, and various extensions of the Standard Model, such as the Standard Model Extension (SME). These frameworks propose mechanisms by which Lorentz symmetry could be violated at very high energies or small scales.

How can Lorentz invariance violation be detected experimentally?

Lorentz invariance violation can be detected experimentally through high-precision tests in various domains, such as astrophysical observations, particle physics experiments, and atomic clock comparisons. Deviations from expected results in these experiments could indicate possible violations of Lorentz invariance.

What are the potential implications if Lorentz invariance is found to be violated?

If Lorentz invariance is found to be violated, it would have profound implications for our understanding of fundamental physics. It could lead to the development of new theories that better describe the nature of space-time, potentially unifying quantum mechanics and general relativity, and providing deeper insights into the workings of the universe.

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