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Electron column densities measured from the dispersion of pulsar pulses are a well-established tool for probing the distribution of ionized gas in the interstellar medium. The quest for the missing cosmological baryons has motivated the study of ways to measure electron columns over intergalactic sightlines, but this requires a "backlight" visible at cosmological distances. In this talk, I will discuss the theory behind attempts to obtain a dispersion measure from continuous rather than pulsed sources. Several ideas along these lines have emerged using correlation functions of the electric field received from the source, or using the quantum nature of electromagnetic radiation. In each case, the role of individual pulses emitted by a pulsar is played by a statistical process, or by the discreteness of photons. I will describe why, at least in their simplest version, these methods will not work when applied to a time-steady synchrotron or free-free source, and consider what characteristics are needed for a source to be a candidate for providing cosmological dispersion measures.