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”

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, Y.-B. Wang et al. 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo accent="false">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> , which departures from the classical dispersion relation (∝ ν −2 ). Here we discuss the derivation presented by Y.-B. Wang et al. and show that the classical dispersion relation remains valid based on Proca equations.