Does light from steady sources bear any observable imprint of the dispersive intergalactic medium?

TL;DR

This paper investigates whether light from steady sources shows observable effects of the dispersive intergalactic medium, concluding that classical pulses are necessary for dispersion detection and proposing phase measurement as a promising method.

Contribution

It clarifies the conditions under which dispersive effects can be observed in incoherent light and introduces phase measurement techniques for detecting intergalactic dispersion signatures.

Findings

Classical pulses are required for dispersive broadening detection.

Quantum treatment shows individual photons are not susceptible to dispersion.

Phase measurement of radio waves can reveal dispersion signatures.

Abstract

There has recently been some interest in the prospect of detecting ionized intergalactic baryons by examining the properties of incoherent light from background cosmological sources, namely quasars. Although the paper by \cite{lieu13} proposed a way forward, it was refuted by the later theoretical work of \cite{hir14} and observational study of \cite{hal16}. In this paper we investigated in detail the manner in which incoherent radiation passes through a dispersive medium both from the frameworks of classical and quantum electrodynamics, which led us to conclude that the premise of \cite{lieu13} would only work if the pulses involved are genuinely classical ones involving many photons per pulse, but unfortunately each photon must not be treated as a pulse that is susceptible to dispersive broadening. We are nevertheless able to change the tone of the paper at this juncture, by pointing out that because current technology allows one to measure the phase of individual modes of radio waves from a distant source, the most reliable way of obtaining irrefutable evidence of dispersion, namely via the detection of its unique signature of a quadratic spectral phase, may well be already accessible. We demonstrate how this technique is only applied to measure the column density of the ionized intergalactic medium.