The Dispersion Relation of Massive Photons in Plasma: A Comment on "Bounding the Photon Mass with Ultrawide Bandwidth Pulsar Timing Data and Dedispersed Pulses of Fast Radio Bursts"

TL;DR

This paper clarifies the dispersion relation for massive photons in plasma, arguing that the classical relation remains valid and challenging recent claims of a revised relation based on Proca equations.

Contribution

It provides a theoretical analysis showing the classical dispersion relation for massive photons in plasma is correct, countering recent proposals of a modified relation.

Findings

The classical dispersion relation ($ u^{-2}$) remains valid for massive photons in plasma.

The proposed $ u^{-4}$ dispersion relation by Wang et al. is not supported by the derivation from Proca equations.

The paper clarifies the theoretical basis for photon mass constraints using plasma dispersion measurements.

Abstract

The dispersion measures of fast radio bursts have been identified as a powerful tool for testing the zero-mass hypothesis of the photon. The classical approach treats the massive photon-induced and plasma-induced time delays as two separate phenomena. Recently, Wang et al. (2024) suggested that the joint influence of the nonzero photon mass and plasma effects should be considered, and proposed a revised time delay for massive photons propagating in a plasma medium, denoted as $\Delta t'_{m_{\gamma}} \propto \nu^{-4}$, which departures from the classical dispersion relation ($\propto \nu^{-2}$). Here we discuss the derivation presented by Wang et al. (2024) and show that the classical dispersion relation remains valid based on Proca equations.