Retarded potentials and the radiative arrow of time

Maxwell's equations admit both retarded and advanced solutions, but only the retarded solutions seem to characterize the radiative phenomena that actually occur in nature. The reason for this, however, is not usually explained in electrodynamics textbooks. We justify the use of the retarded solutions by considering a simple toy model, which allows us to avoid the technical complexities of electrodynamics and focus on the physical concepts. In addition, we explain how the use of the retarded solutions is related to a number of fundamental issues in physics, such as time-reversal invariance and the radiative arrow of time.