Spurious causality hiding an action at a distance

Details Spurious causality hiding an action at a distance Spurious causality hiding an action at a distance

2010-11-20

arxiv.org/abs/1011.4541v2

Physics

Classical Physics

Expanded to 9 pages

Scientific paper

The Coulomb/Gauss law given in the Maxwell equations describes a spatial relation between the electric field component $E_\parallel({\bf r}, t)$ and its source $\rho({\bf r}, t)$ 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 ${\bf E}$ 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 ${\bf E}_\perp$ part is really causal.

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