A tight constraint on some varying speed of light theories

TL;DR

This paper constrains theories where the speed of light varies by showing that differences in electromagnetic and particle velocities would produce observable Cherenkov radiation, which is not seen in high-energy cosmic rays.

Contribution

It provides a very tight upper limit on the difference between the speed of light and the limiting velocity of particles, constraining certain varying speed of light theories.

Findings

V protons from distant sources do not emit Cherenkov radiation

The difference -27 between the speeds is tightly constrained

Supports the constancy of the speed of light in vacuum

Abstract

We argue that if the velocity of electromagnetic waves in vacuum, \cem, is different from the limiting velocity for massive particles, \cst, then, a proton moving with velocity $\cem < v < \cst$ would radiate Cherenkov radiation. Because we have seen protons with energy $\sim 10^{19}$ eV coming from a distance of order more than 1 Mpc, we can put a constraint on $\Delta := (\cst - \cem)/\cst$: $\Delta < 10^{-27}$.