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.

14 pages

References in corpus (23)

• Lorentz-violation-induced arrival delays of cosmological particles
• Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944
• Light speed variation from gamma-ray bursts
• Bounds on Lorentz invariance violation from MAGIC observation of GRB 190114C
• The 2014 TeV Gamma-ray Flare of Mrk 501 Seen with H.E.S.S.: Temporal and Spectral Constraints on Lorentz Invariance Violation
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• A new method to study energy-dependent arrival delays on photons from astrophysical sources
• Relativistic kinematics beyond Special Relativity
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Reaching the Planck scale with muon lifetime measurements
• Ultrahigh-energy photons from LHAASO as probes of Lorentz symmetry violations
• Lorentz Invariance Violation Limits from the Spectral Lag Transition of GRB~190114C
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Exploring Special Relative Locality with deSitter momentum-space
• A bound on Planck-scale deformations of CPT from muon lifetime
• Constraints on the deformation scale of a geometry in the cotangent bundle
• Curved momentum space, locality, and generalized space-time
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Spacetime and deformations of special relativistic kinematics
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
• Doubly Special Relativity and Relative Locality

Cited by in corpus (4)

• A new perspective on Doubly Special Relativity
• Consistency of Lorentz-invariance violation neutrino scenarios in time delay analyses
• Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation
• Time Delay in $\kappa$-Anti-de Sitter Spacetime