Electrical communications as well as physics are strongly based on infinitely extended periodic sinusoidal functions. Neither the causality law nor the conservation law of energy have any meaning for waves represented by such functions. Information theory demands that any physical process starts at a finite time and ends at a finite time since we can neither observe negative or positive infinite times. A corresponding statement holds for space intervals. Maxwell's equation do generally not have solutions that start at a finite time and thus permit to represent the causality law. Hence, they represent generally steady state solutions rather than transient or signal solutions. The problem with Maxwell's equations is overcome by permitting magnetic dipole currents that are produced by rotating magnetic dipoles. The modified Maxwell equations make it possible to study the propagation of heavily distorted signals in seawater. When we further replace infinite times and distances by arbitrarily large but finite ones, we avoid the problem of the infinite 'zero-point energy' in quantum electrodynamics and eliminate the need for renormalization. Finally, if we observe that infinitesimal intervals dx, dt are no more observable than infinite ones, we find that differential calculus should be replaced in relativistic quantum physics with the calculus of finite differences using arbitrarily small but finite intervals Δx, Δt.