Superposition Principle and the Problem of the Additivity of the Energies and Momenta of Distinct Electromagnetic Fields

Abstract

In this paper we prove in a rigorous mathematical way (using the Clifford bundle formalism) that the energies and momenta of two distinct and arbitrary free Maxwell fields (of finite energies and momenta) that are superposed are additive and thus that there is no incompatibility between the principle of superposition of fields and the principle of energy-momentum conservation, contrary to some recent claims. Our proof depends on a noticeable formula for the energy-momentum 1-form fields T^{a},namely Riesz formula, which is valid for any electromagnetic field configuration F satisfying Maxwell equation.