Quantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light

TL;DR

This paper proposes that quantum-gravitational effects cause stochastic fluctuations in the speed of light, leading to photon diffusion and timing uncertainties, which could be tested through astrophysical gamma-ray observations.

Contribution

It introduces a model based on Liouville string theory and D-brane fluctuations to explain quantum-gravitational diffusion of light in vacuum, linking string effects to observable photon velocity fluctuations.

Findings

Quantum-gravitational fluctuations induce stochastic photon velocity variations.

The model predicts frequency-dependent vacuum refractive index effects.

Potential observational constraints via gamma-ray astrophysics.

Abstract

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light ``in vacuo''. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of $D$-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion ``in vacuo'' via $\gamma$-ray observations of distant astrophysical sources.