The Huygens Principle Model of Electro-magnetic Interactions: A Critical Analysis of the Lagrangian Formalism

Abstract

This paper presents a systematic development of the "Huygens principle model" for electromagnetic interactions, extending the analysis initiated in previous works [31–39]. The model offers an alternative to the classical field description by adopting a purely geometric, kinematic approach based on spherical wavefront propagation. The primary objective is to derive interaction forces for arbitrarily moving charges and electric currents directly from the Huygens principle, thereby avoiding the introduction of a distinct magnetic field and the use of differential operators (grad, div, rot). The analysis reveals fundamental limitations of the Lagrangian formalism when applied to systems with retardation and nonlocality. The model successfully reproduces the Ampère force between parallel currents, validating its core assumptions. It further reveals a striking difference between open and closed current configurations: tangential forces appear only for closed loops (such as circular windings or solenoids), a fact that can be linked to the non-inertial nature of rotating electron systems, echoing Feynman's insight on the absoluteness of rotation. Philosophical implications concerning the nature of the ether, the wave-particle duality, and the possibility of detecting absolute motion are discussed.