Loop quantum gravity and light propagation

TL;DR

The paper investigates observable consequences of loop quantum gravity on light propagation by deriving an effective Maxwell theory in flat spacetime through Thiemann regularization and a would-be semiclassical weave state. The resulting dispersion relations include a helicity-dependent Planck-scale term consistent with Gambini–Pullin and, for a specific scaling parameter Υ, a correction akin to Ellis et al., plus nonlinear magnetic terms controlled by the same formalism. The authors derive the modified Maxwell equations, obtaining ω = c k [ 1 + θ_7 (ℓ_P/ℒ)^{2+2Υ} − 2 θ_3 (k ℓ_P)^2 ± 2 θ_8 (k ℓ_P) ], which implies a Planck-scale deviation of the photon speed and possible time delays for cosmological sources; these effects are Lorentz-violating and helicity-dependent at leading order. The work further identifies new nonlinear magnetic terms with distinct polarization signatures and discusses how Gamma Ray Bursts could probe such corrections, while highlighting avenues for future semiclassical-state refinements and broader quantum-gravity phenomenology.

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.