Almost everyone is familiar with the sentence "accelerated charges radiate em waves". Nevertheless, if you are asked to derive this starting from Maxwell's equations, you might find it difficult. Surely the radiation pattern depends on the history of the motion of the charge. Then, there comes an even harder problem: Consider the quantum-mechanical problem of the em field coupled to a 4-current corresponding to the accelerated motion of the charge. Treat this as a classical source term, without considering the dynamics of the charge. Can we find the differential cross-section of photons with a particular frequency and polarization being radiated in a particular direction? Finally, this cross section is some sort of probability. Suppose a photon is detected. Will this alter the field in some way, similar to the disturbance of quantum particles by measuring their position/momentum, and, if so, how?