Beyond the speed of light on Finsler spacetimes

TL;DR

This paper demonstrates that scalar fields on Finsler spacetimes can exhibit superluminal propagation due to modified dispersion relations, even with slight deviations from Lorentzian geometry, potentially explaining superluminal neutrino observations.

Contribution

It introduces the study of scalar fields on Finsler spacetimes showing superluminal propagation and compares dispersion relations with metric spacetimes, highlighting new effects from Finsler geometry.

Findings

Particles can propagate faster than light in Finsler spacetimes.

Superluminal effects depend on the ratio of momentum to mass.

Momentum dispersion relations remain consistent with metric spacetimes.

Abstract

As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman-Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.