Quantum gravity without vacuum dispersion

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.

Version published in International Journal of Modern Physics D. 13 pages, 3 figures

References in corpus (8)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• Diffusion on $\kappa$-Minkowski space
• Testing Lorentz Invariance with Ultra High Energy Cosmic Ray Spectrum
• Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations
• New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations
• Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole
• Hypothesis on the Nature of Time

Cited by in corpus (12)

• Dimension and Dimensional Reduction in Quantum Gravity
• Lorentz symmetry is relevant
• Imprint of quantum gravity in the dimension and fabric of spacetime
• Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime
• Raychaudhuri equation with zero point length
• Quantum metric for null separated events and spacetime atoms
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Asymptotically Weyl-Invariant Gravity
• Renormalizing Spacetime
• Is Asymptotically Weyl-Invariant Gravity Viable?
• New constraints on quantum foam models from X-ray and gamma-ray observations of distant quasars
• A Falsifiable Alternative to General Relativity