  This paper is a review of the canonical proper-time approach to relativistic
mechanics and classical electrodynamics. The purpose is to provide a physically
complete classical background for a new approach to relativistic quantum
theory. Here, we first show that there are two versions of Maxwell's equations.
The new version 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. The theory provides a new
invariance group which, in general, is a nonlinear and nonlocal representation
of the Lorentz group. This approach also provides a natural (and unique)
definition of simultaneity for all observers. The corresponding particle theory
is independent of particle number, noninvariant under time reversal (arrow of
time), compatible with quantum mechanics and has a corresponding positive
definite canonical Hamiltonian associated with the clock of the source.
  We also provide a brief review of our work on the foundational aspects of the
corresponding relativistic quantum theory. Here, we show that the standard
square-root and the Dirac equations are actually two distinct
spin-$\tfrac{1}{2}$ particle equations.
