Linear response laws and causality in electrodynamics

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear response laws and causality in the time and frequency domains with the aim of pedagogical clarity. We will show that it is easy to violate causality in the frequency domain by making a vanishing absorption approximation. Furthermore, we will show that there can be subtle differences between Fourier transforming Maxwell equations and using a monochromatic source function. We discuss how these concepts can be obscured and offer some suggestions to improve the situation.