# Velocity-dependent deformations of the energy spectrum of a quantum cavity from Lorentz symmetry violations

## TL;DR

This paper investigates how Lorentz symmetry violations at high energies affect the energy spectrum of a quantum cavity, revealing velocity-dependent deformations and potential instabilities that could allow measuring an observer’s velocity relative to a preferred frame.

## Contribution

It introduces a model of a quantum cavity with Lorentz-violating dispersion relations, showing how energy levels depend on cavity velocity and can indicate a preferred frame, violating relativity principles.

## Key findings

- Energy levels depend non-trivially on cavity velocity v.
- Instability occurs when wall speed exceeds phase velocity.
- Energy levels diverge as velocity approaches light speed.

## Abstract

Several approaches to quantum gravity suggest that Lorentz invariance will be broken at high energy. This can lead to modified dispersion relations for wave propagation, which can be concretely realized in effective field theories where the equation of motion involves higher order spatial derivatives in a preferred frame. We consider such a model in the presence of a finite cavity whose walls follow parallel inertial trajectories of speed $v$ with respect to the preferred frame. We find evidence that when the cavity wall speed exceeds the phase velocity, the system becomes classically unstable. For dispersion relations that do not lead to an instability, the energy levels of the cavity are non-trivial functions of $v$. In other words, an observer could in principle measure their velocity with respect to the preferred frame by studying the energy spectra of a quantum cavity, which is a stark violation of the principle of relativity. We also find that the energy levels of the cavity become infinitely large as its velocity approaches light speed.