Electrodynamics without Lorentz force

TL;DR

This paper critically examines the foundational assumptions of Electrodynamics, questioning the physical validity of the Lorentz force and proposing a covariant formulation that decouples electric and magnetic fields from relativistic transformations.

Contribution

It introduces a covariant formulation of electromagnetic fields using differential forms, challenging the traditional Lorentz force rule's physical necessity and its derivation from special relativity.

Findings

Lorentz force is physically untenable but empirically successful.

Electromagnetic fields can be modeled covariantly without entanglement under Lorentz transformations.

Induced electric fields in moving charges are half the Lorentz force, explaining experimental observations.

Abstract

This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century, led to the notion of Lorentz force, still today ubiquitous in literature on Electrodynamics. Is this a noteworthy instance of a rule which, generated by an improper simplification of Maxwell-JJ Thomson formulation, is in fact physically untenable but, this notwithstanding, highly successful. Modelling of electromagnetic fields and fluxes in spacetime respectively as even and odd spatial differential forms and the formulation of induction laws by means of exterior and Lie derivatives, make their covariance manifest under any smooth spacetime transformations, contrary to the usual affirmation in literature which confines this property to relativistic frame-changes. A remarkable consequence is that there is no entanglement between electric and magnetic fields and fluxes under special relativity transformations. In particular, relativistic support to Lorentz force rule is thus deactivated. For translational motions of charged bodies immersed in a uniform and constant magnetic field, the induced electric field in such a frame, is equal to one half the Lorentz force term. The qualitative successful application of the Lorentz force rule to experimental evidence of special observers is therefore explained.