The cancellation of the surface terms on the right-hand side of the Lorentz reciprocity theorem, for an integration over all space, is not entirely obvious but can be derived in a number of ways. A rigorous treatment of the surface integral takes into account the causality of interacting wave field states: The surface-integral contribution at infinity vanishes for the time-convolution interaction of two causal wave fields only (the time-correlation interaction leads to a non-zero contribution).