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

TL;DR

This paper rigorously proves that the energies and momenta of superposed free Maxwell fields are additive, confirming compatibility between superposition and energy-momentum conservation using Clifford bundle formalism and Riesz formula.

Contribution

It provides a rigorous mathematical proof that superposition of electromagnetic fields preserves energy-momentum additivity, resolving recent claims of incompatibility.

Findings

Energies and momenta of superposed Maxwell fields are additive.

The proof uses Clifford bundle formalism and Riesz formula.

No incompatibility between superposition and energy-momentum conservation.

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.