The emergence of a universal limiting speed

TL;DR

This paper investigates how different fields with initially distinct limiting velocities can evolve to a common speed at low energies through interactions, using renormalization group analysis, with implications for gravitational wave observations.

Contribution

It introduces models demonstrating how velocities converge at low energies, including a power-law running scenario, and discusses experimental constraints and phenomenological implications.

Findings

Velocities tend to unify logarithmically over energy scales.

A power-law running model can achieve faster convergence.

Gravitational wave speed measurements are key tests.

Abstract

We display several examples of how fields with different limiting velocities (the "speed of light") at a high energy scale can nevertheless have a common limiting velocity at low energies due to the effects of interactions. We evaluate the interplay of the velocities through the self-energy diagrams and use the renormalization group to evolve the system to low energy. The differences normally vanish only logarithmically, so that an exponentially large energy trajectory is required in order to satisfy experimental constraints. However, we also display a model in which the running is power-law, which could be more phenomenologically useful. The largest velocity difference should be in system with the weakest interaction, which suggests that the study of the speed of gravitational waves would be the most stringent test of this phenomenon.