Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model

TL;DR

This paper derives a quantum-gravitational vacuum refractive index for photons using a string theory model of space-time foam, explaining energy-dependent photon delays observed in astrophysics.

Contribution

It introduces a novel string-theoretic derivation of vacuum refractive index based on D-particle interactions, linking quantum gravity effects to observable photon delays.

Findings

Refractive index depends linearly on photon energy.

Photon delay increases linearly with energy due to string interactions.

Model aligns with astrophysical observations of high-energy photon propagation.

Abstract

It has been suggested that energetic photons propagating in vacuo should experience a non-trivial refractive index due to the foamy structure of space-time induced by quantum-gravitational fluctuations. The sensitivity of recent astrophysical observations, particularly of AGN Mk501 by the MAGIC Collaboration, approaches the Planck scale for a refractive index depending linearly on the photon energy. We present here a new derivation of this quantum-gravitational vacuum refraction index, based on a stringy analogue of the interaction of a photon with internal degrees of freedom in a conventional medium. We model the space-time foam as a gas of D-particles in the bulk space-time of a higher-dimensional cosmology where the observable Universe is a D3-brane. The interaction of an open string representing a photon with a D-particle stretches and excites the string, which subsequently decays and re-emits the photon with a time delay that increases linearly with the photon energy and is related to stringy uncertainty principles. We relate this derivation to other descriptions of the quantum-gravitational refractive index in vacuo.