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

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.

Consistency of Lorentz-invariance violation neutrino scenarios in time delay analyses

“…This deformation prevents the decay of massless superluminal particles. In addition, however, the description of time delays is much more involved than in the LIV case and they might even not exist at all [33][34][35][36]. Other scenarios that can also evade the mentioned constraints are some based on string theory, such as the D-brane foam model considered in [37], which leads to a modification of the kinematics of superluminal particle decays.…”

A new perspective on Doubly Special Relativity

“…If one changes the choice of energy-momentum variables, one will have a different energy dependence of the velocity of propagation; in fact, one can always choose energy-momentum variables to make the velocity of propagation energy independent. In this case, however, translations generated by these variables act nontrivially in spacetime and, when one compares two observers separated by astrophysical distances, one finds once more the amplification of the effects of DSR [32].…”

“…In this case, even if the modification in the velocity of propagation of a particle with respect to SR is proportional to the ratio of the energy of the particle and the energy scale of DSR, there is an amplification effect, proportional to the long distance that astroparticles travel from the source to our detectors in Earth, which could be measured by current experiments. Therefore, a lot of papers were devoted to this possible effect in the context of DSR [32,[39][40][41][42][43][44][45].…”

“…In the perspective of DSR discussed in this work, since the dispersion relation is the one of SR, time delays are absent [32,42]. This means that the strong constraints on the high-energy scale based on the possibility of time delays [46][47][48][49][50][51][52] do not apply in our scheme.…”

Theoretical and experimental challenges in quantum gravity phenomenology

“…DSR was formulated twenty years ago [9]. It does not exist at present a well-defined dynamic framework leading to DSR kinematics, and it presents some controversial issues, not only in its theoretical interpretation (soccer-ball and spectator problems), but also with respect to some of its predictions, such as time delays [35,36]. However, it is a very attractive theoretical scenario (in contrast to LIV, it maintains a relativity principle, as in other revolutions in physics), it may solve fine-tuning problems of the LIV scenario, and may be the key of the interesting phenomenological scenario of an energy scale orders of magnitude below the Planck mass, without the constraints from time delay experiments.…”