In this paper, we show that there are actually two versions of Maxwell's equations. The new version is mathematically,
but not physically, equivalent to the conventional form. It was missed because of an attempt to give a
mathematical fix for a basic physical problem. This second formulation fixes the clock of the field source for all
inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant
for all observers, but depends on the motion of the source. This approach allows us to account for radiation
reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions
about the structure of the source. This version has a new invariance group which, in general, is a nonlinear and
nonlocal representation of the Lorentz group, and provides a natural (and unique) definition of simultaneity for
all observers.
We briefly review the corresponding particle mechanics. The purpose is to show that there is a (unique) clock
for any closed system of physical bodies. This clock provides a unique definition of simultaneity for all events
associated with the system. We then discuss our view of the photon within this theory.
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