  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.
