  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.
