Could deformed special relativity naturally arise from the semiclassical limit of quantum gravity?

TL;DR

This paper argues that deformed special relativity can naturally emerge from the semiclassical limit of a quantum gravity theory, leading to energy-dependent modifications of the metric without breaking Lorentz invariance.

Contribution

It demonstrates how quantum gravity effects can produce energy-dependent metric deformations consistent with special relativity in the semiclassical limit.

Findings

Deformed metric terms linear in energies can arise from quantum gravity.

Such effects are compatible with the absence of preferred frames.

Potential experimental signatures in high-energy astrophysical observations.

Abstract

A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the assumption that a Hamiltonian constraint is imposed. We study circumstances in which Lambda, G and hbar all may be separately neglected, but there may arise terms in the ratio of particle energies to the Planck mass which are small but measurable. Such cases include probes of an energy dependent speed of light such as are possible in experiments such as MAGIC and GLAST. We show that in such cases the leading order effect of quantum gravity will, if certain scaling relations are satisfied, be to deform the metric in the effective Hamiltonian of the matter quantum field theory by terms linear in energies. As the Hamiltonian constraint has been imposed there can be no preferred time coordinate or frame of reference, hence this is a modification rather than a breaking of special relativity.