Time delays, choice of energy-momentum variables and relative locality in doubly special relativity

TL;DR

This paper investigates the conditions under which doubly special relativity predicts photon time delays, clarifies the role of energy-momentum variables, and connects these findings to noncommutative spacetime models.

Contribution

It generalizes a model for photon time delays in DSR, clarifies the dependence on energy-momentum variable choices, and links results to noncommutative spacetime frameworks.

Findings

Photon time delays are not guaranteed in DSR scenarios.

The choice of energy-momentum variables does not affect the time delay results.

Time delay results are consistent with noncommutative spacetime models.

Abstract

Doubly Special Relativity (DSR) theories consider (quantum-gravity motivated) deformations of the symmetries of special relativity compatible with a relativity principle. The existence of time delays for massless particles, one of their proposed phenomenological consequences, is a delicate question, since, contrary to what happens with Lorentz Invariance Violation (LIV) scenarios, they are not simply determined by the modification in the particle dispersion relation. While some studies of DSR assert the existence of photon time delays, in this paper we generalize a recently proposed model for time delay studies in DSR and show that the existence of photon time delays does not necessarily follow from a DSR scenario, determining in which cases this is so. Moreover, we clarify long-standing questions about the arbitrariness in the choice of the energy-momentum labels and the independence of the time delay on this choice, as well as on the consistency of its calculation with the relative locality paradigm of DSR theories. Finally, we show that the result for time delays is reproduced in models that consider propagation in a noncommutative spacetime.