Phonons mimicking doubly special relativity kinematics

TL;DR

This paper demonstrates how phonons in certain fluid models can mimic doubly special relativity kinematics, with the analogue Planck scale arising from high-energy non-Newtonian effects, bridging fluid dynamics and relativistic physics.

Contribution

The authors explicitly construct hydrodynamic models where phonons obey doubly special relativistic kinematics, linking fluid interactions to quantum gravity phenomenology.

Findings

Elastic storage approximates Amelino-Camelia's scenario

Elastic restoring forces lead to Magueijo-Smolin model

Analogue Planck scale emerges from non-Newtonian high-energy behaviour

Abstract

Collective excitations (phonons) in barotropic, irrotational, inviscid fluids exhibit an effective Lorentz invariance, where the sound speed plays the role of the invariant speed of light in special relativity. By carefully selecting the interaction potentials, we explicitly construct two hydrodynamic models in which phonons obey doubly special relativistic kinematics, with the analogue Planck scale emerging from non-Newtonian behaviour at high energies. Specifically, we demonstrate that elastic storage leads to an approximate realization of Amelino-Camelia's scenario, while the Magueijo-Smolin model naturally emerges in the presence of elastic restoring forces.