Relative-locality effects in Snyder spacetime

TL;DR

This paper investigates the implications of relative locality in Snyder spacetime, concluding that unlike other noncommutative models, it does not predict energy-dependent delays for massless particles due to preserved Lorentz invariance.

Contribution

It demonstrates that Snyder spacetime does not exhibit relative locality effects for massless particles, contrasting with other noncommutative geometries, and aligns with doubly special relativity.

Findings

No delay in arrival times for massless particles in Snyder spacetime

Distant observers can measure different flight times for massive particles

Lorentz invariance remains undeformed in Snyder spacetime

Abstract

When applied to some models of noncommutative geometry, the formalism of relative locality predicts the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. This conclusion is in accordance with the findings of doubly special relativity. Distant observers may however measure different times of flight for massive particle.