Does a deformation of special relativity imply energy dependent photon time delays?

Abstract

Theoretical arguments in favor of energy dependent photon time delays from a modification of special relativity (SR) have met with recent gamma ray observations that put severe constraints on the scale of such deviations. We review the case of the generality of this theoretical prediction in the case of a deformation of SR and find that, at least in the simple model based on the analysis of photon worldlines which is commonly considered, there are many scenarios compatible with a relativity principle which do not contain a photon time delay. This will be the situation for any modified dispersion relation which reduces to E = | p| for photons, independently of the quantum structure of spacetime. This fact opens up the possibility of a phenomenologically consistent relativistic generalization of SR with a new mass scale many orders of magnitude below the Planck mass.

Does a deformation of special relativity imply energy dependent photon time delays?

“…3 we will see the main results obtained in Ref. [17] referring to two models very much studied in the literature, κ-Minkowski and Snyder spacetimes, checking that previous works (Refs. [14,15,16]) are particular cases of this model and give specific conditions for the absence of energy-dependent photon time delays.…”

“…In Ref. [17] two models of noncommutativity are studied, one where the modification starts at first order in the high energy scale whilst the second one starts at second order. The first one is κ-Minkowski spacetime, which has been very much studied in relation with DSR theories.…”

“…The worldlines of a particle x µ (τ), with τ an arbitrary parameter that flows along the worldline, can be obtained by applying the variational principle (as it is done in Ref. [17]), obtaining…”

Observers and Their Notion of Spacetime beyond Special Relativity

“…In this work, we will review a recently proposed [9] model for the nontrivial spacetime structure that arises in the description of physical measurements made by translated observers in DSR theories, and in view of this result, we will update the time delay calculation presented in Ref. [10], giving a new perspective on the problem.…”

“…However, we have seen that it is possible to implement the locality condition Eq. (10) in such a way that the function ϕ µ ν for one of the particles depends only on its own momentum p (this choice gave the relationship between the MCL and the one-particle noncommutative spacetime Eq. (12)).…”