these other unknown functions “the potentials.” We will justify this name later. We additionally assume that these potentials vanish sufficiently rapidly at spatial infinity so that the surface integrals containing these potentials vanish at infinity. Our first task will consist in finding the explicit form of these unknown potentials and the equations they satisfy. The causal connection between the expected potentials and their sources $\rho$ and $\textbf{J}$ means that the latter precede in time to the former, i.e., the potentials calculated at the field point $ \textbf{x}$ at the time $t$ are caused by the action of their sources $\rho$ and $\textbf{J}$ a distance $R=|\textbf{x}-\textbf{x}'|$ away at the source point $\textbf{x}'$ at the retarded time $t'\!=\!t -t_0$. It is clear that $t_0\!>\!0$ is the time required for the carrier of the charge-potential connection to travel the distance $R$ between the source point $\textbf{ x}'$ and the point $ \textbf{x}$. Consider now that the carrier of the interaction is the photon which moves in a straight line at the speed of light $c$ in vacuum. This implies $t_0=R/c$ and thus the retarded time takes the form: $t'\!=t -R/c$. Put differently, causality demands that the unknown potentials must be determined by their 