Scattering in spatiotemporal media

Wave scattering is the process according to which a wave is forced to deviate from its trajectory. In Minkowski space, an electromagnetic wave propagating in a homogeneous medium follows a light-like trajectory (world line). Here, we explore electromagnetic wave scattering at general discontinuities in Minkowski space, corresponding to change in the medium parameters in spacetime. The analysis reveals similarities and differences in wave scattering between spatial and temporal discontinuities. In both cases, a frequency shift (spatial and temporal, respectively) takes place, while in a medium with temporal discontinuities multiple reflections do not occur due to causality.