Particle scattering in a sonic analogue of special relativity

TL;DR

This paper models particle scattering within a sonic analogue of special relativity, demonstrating how external particles appear Lorentz-violating to in-universe observers and how their motion relative to the medium can be inferred through sonic Compton scattering.

Contribution

It introduces a toy model of particle scattering in an analogue gravity system, highlighting Lorentz symmetry for phonons and how external particles can be analyzed through sonic experiments.

Findings

External particles appear Lorentz-violating to in-universe observers.

Sonic Compton scattering can reveal the observer's velocity relative to the medium.

The dispersion relation of external particles can be determined through sonic measurements.

Abstract

We investigate a simple toy model of particle scattering in the flat spacetime limit of an analogue-gravity model. The analogue-gravity medium is treated as a scalar field of phonons that obeys the Klein-Gordon equation and thus admits a Lorentz symmetry with respect to $c_\mathrm{s}$, the speed of sound in the medium. The particle from which the phonons are scattered is external to the system and does not obey the sonic Lorentz symmetry that the phonon field obeys. In-universe observers who use the exchange of sound to operationally measure distance and duration find that the external particle appears to be a sonically Lorentz-violating particle. By performing a sonic analogue to Compton scattering, in-universe observers can determine if they are in motion with respect to their medium. If in-universe observers were then to correctly postulate the dispersion relation of the external particle, their velocity with respect to the medium could be found.