Modifications to Lorentz invariant dispersion in relatively boosted frames

TL;DR

This paper explores how energy-dependent photon speeds, predicted by some quantum gravity theories, transform under Lorentz boosts, revealing potential violations of Lorentz invariance and implications for spacetime geometry.

Contribution

It provides a detailed analysis of Lorentz invariance violations in quantum gravity scenarios from boosted frames, highlighting the need for non-classical spacetime features.

Findings

Consistency conditions for photon burst measurements in boosted frames

Characterization of Lorentz violation effects on quantum-gravity scale

Insights into non-classical spacetime geometry requirements

Abstract

We investigate the implications of energy-dependence of the speed of photons, one of the candidate effects of quantum-gravity theories that has been most studied recently, from the perspective of observations in different reference frames. We examine how a simultaneous burst of photons would be measured by two observers with a relative velocity, establishing some associated conditions for the consistency of theories. For scenarios where the Lorentz transformations remain valid these consistency conditions allow us to characterize the violations of Lorentz symmetry through an explicit description of the modification of the quantum-gravity scale in boosted frames with respect to its definition in a preferred frame. When applied to relativistic scenarios with a deformation of Lorentz invariance that preserves the equivalence of inertial observers, we find an insightful characterization of the necessity to adopt in such frameworks non-classical features of spacetime geometry, e.g. events that are at the same spacetime point for one observer cannot be considered at the same spacetime point for other observers. Our findings also suggest that, at least in principle (and perhaps one day even in practice), measurements of the dispersion of photons in relatively boosted frames can be particularly valuable for the purpose of testing these scenarios.