Velocity of Light in Dark Matter with Charge

TL;DR

This paper presents a mechanism to reconcile Michelson-Morley experiments with the possibility of light slowing down in charged dark matter, showing that experimental constraints may be less strict than previously thought.

Contribution

It introduces a frequency-dependent index of refraction model for dark matter with charge, deriving how it affects light velocity and local anisotropy in a relativistic context.

Findings

Light speed anisotropy is proportional to second order in the refractive index deviation.

Michelson-Morley experiments do not strongly constrain light slowdown in charged dark matter.

The model allows for dark matter to influence light speed without contradicting experimental results.

Abstract

We propose an interesting mechanism to reconcile the recent experiments of the Michelson-Morley type and slowdown of the velocity of light in dark matter with a fractional electric charge when the index of refraction of dark matter depends on the frequency of a photon. After deriving the formula for the velocity of light in a medium with the index of refraction $n(\omega)$ in a relativistic regime, it is shown that the local anisotropy of the light speed is proportional to the second order in $n(\omega) - 1$. This result implies that the experiments of the Michelson-Morley type do not give rise to a stringent constraint on the slowdown of the velocity of light in dark matter with electric charge.