  One can interpret the Dirac equation either as giving the dynamics for a
classical field or a quantum wave function. Here I examine whether Maxwell's
equations, which are standardly interpreted as giving the dynamics for the
classical electromagnetic field, can alternatively be interpreted as giving the
dynamics for the photon's quantum wave function. I explain why this quantum
interpretation would only be viable if the electromagnetic field were
sufficiently weak, then motivate a particular approach to introducing a wave
function for the photon (following Good, 1957). This wave function ultimately
turns out to be unsatisfactory because the probabilities derived from it do not
always transform properly under Lorentz transformations. The fact that such a
quantum interpretation of Maxwell's equations is unsatisfactory suggests that
the electromagnetic field is more fundamental than the photon.
