I am having a lot of trouble understanding this concept. It seems to be the intersection of many theories: electrodynamics, special relativity, and quantum theory. Classical electrodynamics and quantum theory apparently have two different conceptions of what an EM wave is; in classical electrodynamics, an EM wave is a continuous change in the continuous EM field surrounding an electron undergoing continuous acceleration. In quantum theory, the EM wave is a photon. But a photon has to have a certain frequency, but a classical EM wave could be a complex, possibly non-periodic wave-form, having a whole spectrum of frequencies. A photon doesn't have a whole spectrum of frequencies, so if quantum theory is right, does this mean there is a whole spectrum of photons being emanated from the accelerating electron, with probability of finding a photon of a particular frequency equivalent to the amplitude of that frequency according to the Fourier decomposition of the EM field of the electron? But if each photon comes in a discrete amount, does this mean that according to quantum theory, there is no such thing as smooth acceleration? It is said that EM energy is transmitted by photon particles, but I don't understand this if the only thing that approximates a photon with a particular frequency in classical EM is the electric field of a uniformly oscillating charged particle, and the particle does not necessarily have to follow such a path. The more I think about this, the less I understand.