Spurious causality hiding an action at a distance

Abstract

The Coulomb/Gauss law given in the Maxwell equations describes a spatial relation between the electric field component $E_{\parallel }(\mathbf{r},t)$ and its source $\rho (\mathbf{r},t)$ that is instantaneous, occurring at the same time $t$. This instantaneous action at a distance can be hidden by writing it formally as the sum of two causal terms. I show here that the causal expression of the total electric field $\mathbf{E}$ suffers from such a spurious causality hiding the action at a distance that is $E_{\parallel }$. In fact, $E_{\parallel }$ remains instantaneous in time even when it is part of a wave equation. Only the ${\mathbf{E}}_{\perp }$ part is really causal.

Expanded to 9 pages

Cited by in corpus (1)

• Lorenz's electromagnetic theory of light