Superposition principle and the problem of 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 densities, namely, Riesz formula ⋆T a = 1 2 ⋆ (F θ aF ), which is valid for any electromagnetic field configuration F satisfying Maxwell equation ∂F = 0.

Tailoring the excitation of fundamental flexural guide waves in coated bone by phase-delayed array: Two-dimensional simulations

“…(1) energy conservation between fluctuating kinetic and potential energies and (2) destructive interference elsewhere in the waveform, which cancels the effect of the increase in local energy (Notte-Cuello and Rodrigues, 2008;Matthews, 1985). The phase-delayed array of emitters (N À 1)*t pd increased the total time of flight of the signal compared to a traditional excitation by a single emitter.…”

The effective lorentzian and teleparallel spacetimes generated by a free electromagnetic field

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From the Photon to Maxwell Equation. Ponderations on the Concept of Photon Localizability and Photon Trajectory in a de Broglie-Bohm Interpretation of Quantum Mechanics

“…For that reason, such waves are (equivocated) called by some authors non-diffracting waves, which of course is not the case, because they spread sensibly after travelling a distance greater than the depth of the field. That such spreading necessarily occurs has been rigorously proved in[45] and it is necessary in order to have energy conservation in certain well defined situations.…”