# Phonon Lorentz invariant?

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1. Jan 18, 2016

### philton

It is said phonon(not photon) in superfluid experiments could also produce similar upper-limit speed effect which I'm not sure if that's also Lorentz invariant.

Another problem is that I can't dig out those paper that demonstrates this kind of effect. Anyone ever seen any of this paper? Thanks..

2. Jan 18, 2016

### Staff: Mentor

Where? Is this something in the paper you can't dig out?

Bear in mind that, without a reference, it's going to be very difficult to answer your question.

3. Jan 19, 2016

### philton

Oops, thanks for the remind:
ACOUSTICS IN BOSE–EINSTEIN CONDENSATES AS AN EXAMPLE OF BROKEN LORENTZ SYMMETRY
http://arxiv.org/pdf/hep-th/0109033v1.pdf

Last edited: Jan 19, 2016
4. Jan 19, 2016

### Staff: Mentor

Ok. Note that they put "Lorentz invariance" in quotes; the "invariance" is in terms of the speed of sound in the material, not the speed of light, and it only applies for phonons of sufficiently low momentum. The speed of sound in a material is not Lorentz invariant (in the usual sense of invariance in terms of the speed of light); it will be different in a frame in which the material is moving than it is in a frame in which the material is at rest. So the phonon behavior discussed in this paper is not Lorentz invariant in the usual sense; the paper appears to be writing down all its equations in the rest frame of the material.

The interest of this model is not that phonons are actually Lorentz invariant; it is that the equations in the low momentum limit have the same form as Lorentz invariant equations in quantum field theory, so that the form of the equations for the breaking of the "Lorentz invariance" of phonons as you go to higher momentum might give suggestions for how a hypothesized breaking of actual Lorentz invariance at or near the Planck scale could work.