Signature of the Planck scale

TL;DR

This paper explores how a fundamental Planck scale induces noncommutative spacetime, modifies Lorentz symmetry, and unifies approaches involving quantum gravity effects and photon mass in high-energy astrophysics.

Contribution

It demonstrates that the small photon mass hypothesis naturally follows from Planck scale physics, unifying two different Lorentz symmetry violation mechanisms.

Findings

Planck scale leads to noncommutative spacetime and modified dispersion relations.

Photon mass within experimental limits implies Lorentz violation observable in gamma rays.

The photon mass mechanism is derived from quantum gravity considerations.

Abstract

A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This latter consideration has also been used by some scholars though based on purely phenomenological models that have been suggested by the observation of Ultra High Energy Cosmic Rays. On the other hand a parallel development has been the proposal of a small but non zero photon mass by some scholars including the author, such a mass being within experimentally allowable limits. This too leads to a small violation of Lorentz symmetry observable in principle in very high energy gamma rays, as in fact is claimed. We show in this paper that the latter mechanism in fact follows from the former, thus unifying two apparently different approaches.