Loop quantum gravity and light propagation

TL;DR

This paper develops an effective Maxwell theory within loop quantum gravity, revealing Planck scale corrections to light propagation that could be tested through cosmological observations like Gamma Ray Bursts.

Contribution

It constructs a coarse-grained approximation for Einstein-Maxwell theory in loop quantum gravity, deriving effective Maxwell equations with quantum gravity corrections.

Findings

Planck scale corrections to light dispersion relations

Recovery of helicity-dependent effects from previous models

Potential observational signatures in Gamma Ray Bursts

Abstract

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized a la Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological Gamma Ray Bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.