Acoustics in Bose--Einstein condensates as an example of Lorentz symmetry breaking

TL;DR

This paper explores how phonon behavior in Bose--Einstein condensates can serve as a physical model illustrating the potential breakdown of Lorentz invariance at high energies, providing insights into quantum gravity effects.

Contribution

It presents a concrete physical model using Bose--Einstein condensates to demonstrate Lorentz symmetry breaking, bridging condensed matter physics and quantum gravity phenomenology.

Findings

Low-momentum phonons exhibit relativistic dispersion relations.

High-momentum phonons deviate from relativistic behavior, indicating Lorentz violation.

The model avoids causality issues by being physically realizable.

Abstract

To help focus ideas regarding possible routes to the breakdown of Lorentz invariance, it is extremely useful to explore concrete physical models that exhibit similar phenomena. In particular, acoustics in Bose--Einstein condensates has the interesting property that at low-momentum the phonon dispersion relation can be written in a ``relativistic'' form exhibiting an approximate ``Lorentz invariance''. Indeed all of low-momentum phonon physics in this system can be reformulated in terms of relativistic curved-space quantum field theory. In contrast, high-momentum phonon physics probes regions where the dispersion relation departs from the relativistic form and thus violates Lorentz invariance. This model provides a road-map of at least one route to broken Lorentz invariance. Since the underlying theory is manifestly physical this type of breaking automatically avoids unphysical features such as causality violations. This model hints at the type of dispersion relation that might be expected at ultra-high energies, close to the Planck scale, where quantum gravity effects are suspected to possibly break ordinary Lorentz invariance.