  Several recent papers have proposed schemes by which a dispersion measure,
and hence electron column, could be obtained from a time-steady, incoherent
radio source at a cosmological distance (such as an active galactic nucleus).
If correct, this would open a new window on the distribution of intergalactic
baryons. These schemes are based on the statistical properties of the received
radiation, such as the 2- or 4-point correlation function of the received
electric field, and in one case on the quantum nature of the electromagnetic
field. We show, on the basis of general principles, that these schemes are not
sensitive to dispersion measure (or have an extremely small signal-to-noise
ratio), because (i) the classical 2-point correlation function is unaffected by
dispersion; (ii) for a source with a large number of incoherently emitting
electrons, the central limit theorem obliterates additional information in
higher-order functions; and (iii) such an emitter produces a radiation density
matrix that is equivalent to a statistical distribution of coherent states,
which contains no information that is not already in the statistics of the
classical waveforms. Why the proposed observables do not depend on dispersion
measure (or have extremely tiny dependences) is discussed in detail.
