Lorentz symmetry violation due to interactions of photons with the graviton background

TL;DR

This paper investigates how interactions between photons and a graviton background could cause Lorentz symmetry violations, analyzing different models of virtual photon lifetime and their implications for photon time delays.

Contribution

The study introduces a model of low-energy quantum gravity that predicts photon time delays due to graviton interactions, considering two approaches to virtual photon lifetime and including graviton pairing effects.

Findings

Lorentz violation is negligible in the uncertainty-based model (~10^{-28})

Time delay depends on photon energies and is proportional to their energy differences in the conjectured model

Higher energy photons are predicted to arrive later due to graviton interactions

Abstract

The average time delay of photons due to multiple interactions with gravitons of the background is computed in a frame of the model of low-energy quantum gravity by the author. The two variants of evaluation of the lifetime of a virtual photon are considered: 1$)$ on a basis of the uncertainties relation (it is a common place in physics of particles) and 2$)$ using a conjecture about constancy of the proper lifetime of a virtual photon. It is shown that in the first case Lorentz violation is negligible: the ratio of the average time delay of photons to their propagation time is equal approximately to $10^{-28}$; in the second one (with a new free parameter of the model), the time-lag is proportional to the difference $\sqrt{E_{01}}-\sqrt{E_{02}}$, where $E_{01}, E_{02}$ are initial energies of photons, and more energetic photons should arrive later, also as in the first case. The effect of graviton pairing is taken into account, too.