Mark, Stephen,
In your essay, page 3, you state, "Thus if the wave was travelling really slowly, it would have an incredibly short wavelength, implying that its energy was contained in a very small volume."
I do not understand the quoted statement. What does the velocity of an EM wave have to do with "energy volume?"
I would think the "energy volume" of an electromagnetic (EM) wave would be defined by the wavelength. For equation (6), wavelength and frequency are inversely proportional and this is a linear relationship. When an EM beam enters a material in which it can propagate, that has a different permittivity, it is assumed both the frequency and the wavelength are changed; typically a change in frequency is measured, which implies a change in wavelength. Ask Eckard which came first. Keep in mind that equation (10) is defining energy, an idealized quanta of energy, in relationship to the frequency of an EM wave. The actual "energy content" of an EM wave is a result of the process that creates the wave. And, it is "assumed" that the EM field configuration and the energy content of the EM wave does not result in a nonlinear response in the medium in which it is permitted to propagate.
Equation (6) is somewhat like the equation that represents Ohm's law, V=IR, it represents a linear relationship. EEs recognize that simplistic formula represents idealized conditions, that is, there are no conditions that will cause one of the parameters to become nonlinear. The problem with equation (6) is equivalent, everyone is "assuming" there are no conditions which would result in one of the parameters becoming nonlinear.