Quantum gravity without vacuum dispersion

TL;DR

This paper investigates how quantum gravity models, specifically causal dynamical triangulation, can reconcile a scale-dependent speed of light with experimental constraints that rule out vacuum dispersion, by proposing a scale-dependent time interval.

Contribution

It introduces a scale-dependent transformation of geodesic distance and time intervals that explains the observed scale-dependent speed of light without violating experimental bounds on vacuum dispersion.

Findings

Scale-dependent geodesic distance accounts for the observed speed of light variations.

A specific functional form implies a discrete equidistant area spectrum.

A scale-dependent time interval maintains invariant light speed despite quantum effects.

Abstract

A generic prediction of quantum gravity is the vacuum dispersion of light, and hence that a photon's speed depends on its energy. We present further numerical evidence for a scale dependent speed of light in the causal dynamical triangulation (CDT) approach to quantum gravity. We show that the observed scale dependent speed of light in CDT can be accounted for by a scale dependent transformation of geodesic distance, whose specific functional form implies a discrete equidistant area spectrum. We make two non-trivial tests of the proposed scale transformation: a comparison with the leading order quantum correction to the gravitational potential and a comparison with the generalised uncertainty principle. In both cases, we obtain the same functional form. However, contrary to the widespread prediction of vacuum dispersion in quantum gravity, numerous experiments have now definitively ruled out linear vacuum dispersion beyond Planckian energy scales, and have now even constrained quadratic dispersion. Motivated by these experimental constraints we seek to reconcile quantum gravity with the absence of vacuum dispersion. We point out that given a scale dependent geodesic distance, a scale dependent time interval becomes essential to maintaining an invariant speed of light. We show how a particular scale dependent time interval allows a photon's speed to remain independent of its energy.