Causality in Maxwell’s Equations and the Creation of Electromagnetic Fields

Abstract

Peter M. Enders, Asemgul A. Kisabekova and Aisha Anafina

As well known, Maxwell’s equations in a vacuum can be transformed into two wave equations, the solutions of which are the electric and magnetic fields as a functional of arbitrary charge and current densities and first derivatives of them. Accordingly, Jefimenko and others have argued that the true sources of the electromagnetic field are the charge and current densities, while the electric and magnetic fields are independent of each other. On the contrary, Maxwell, Weyl, and others interpret Maxwell’s equations such that, in charge- and current-free regions, the electric and magnetic fields induce each other. As a matter of fact, Jefimenko’s arguing, (i), discards the advanced solutions (describing incoming fields), (ii), implies action at a distance, and, (iii), is derived from non-fundamental equations. In contrast, the mutual creation of electric and magnetic fields emerges from fundamental equations and is free of that artifacts.

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