Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light

TL;DR

This paper explores how doubly special relativity, which modifies Lorentz transformations with an energy-dependent speed of light, leads to large-scale violations of locality and translational invariance, challenging conventional notions of spacetime.

Contribution

It demonstrates that an energy-dependent speed of light in doubly special relativity causes macroscopic violations of locality and translational invariance.

Findings

Energy-dependent speed of light implies non-local effects.

Violations of translational invariance on macroscopic scales.

Challenges to conventional spacetime symmetries in doubly special relativity.

Abstract

There are two major alternatives for violating the (usual) Lorentz invariance at large (Planckian) energies or momenta - either not all inertial frames (in the Planck regime) are equivalent (e.g., there is an effectively preferred frame) or the transformations from one frame to another are (non-linearly) deformed (``doubly special relativity''). We demonstrate that the natural (and reasonable) assumption of an energy-dependent speed of light in the latter method goes along with violations of locality/separability (and even translational invariance) on macroscopic scales. PACS: 03.30.+p, 11.30.Cp, 04.60.-m, 04.50.+h.