  For every observer, however distant, the electric field of a uniformly moving
charge is always directed away from, or points towards, the instantaneous
present position of the charge and not away from, or towards, the retarded
position at which the observer sees it (due to the finite speed of light). This
fact is a well-established consequence of, among others, the application of the
Li\'enard-Wiechert potentials, and its significance for fundamental physics is
probably not fully appreciated. Here we show how and why this property has
non-negligible consequences for what we take for granted about the relativity
of simultaneity and faster-than-light communication. In particular, if we
consider two opposite electric charges whose distance shrinks to zero at a
constant velocity (shrinking electric dipole), then the cancellation of the
total field seems to be instantaneous everywhere in space and in every inertial
reference frame. A simple variant of the shrinking electric dipole setup
appears to allow a sort of faster-than-light communication of information. Our
results provide simple theoretical support to the conclusions of recent
experiments on the propagation speed of Coulomb and magnetic fields. It would
also be interesting to explore any possible connection between our findings and
quantum non-locality.
