A modification of the conventional Maxwell theory of electrodynamics is constructed by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional formulation. The change induces a new symmetry group that is distinct from, but closely related to, the Lorentz group and fixes the clock of the source for all observers. The new wave equation contains an additional dissipative term that arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a charge on itself, but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass, so that classical radiation has both a massless and a massive part. Hence, at the local level, the theory is one of particles and fields, but there exists no self-energy divergence (nor any of the other problems with which the conventional theory is afflicted). It is also shown that, for any closed system of particles, there exists, for each observer, a global inertial frame and a unique invariant global proper-time from which the system may be observed. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this global clock is the historical clock, discussed by Horwitz and Piron (1973) and Fanchi (1993a and 1993b). The theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy. The present theory is analogous to theirs, but we do not use advanced fields.

Einstein used three-dimensional notation, but Poincarè (1905) noted that the transformations of Lorentz could be treated as rotations if time is made an imaginary coordinate. He also introduced the metric now attributed to Minkowski (1909), who recognized the importance of proper-time and showed that it is the only unique variable associated with the source and available to all observers. Carrying Poincarè’s idea further, he proposed that space and time should not be treated separately, but should be unified in the now well-known fashion leading to Minkowski space. It was natural for him to think along these lines because of his geometrical number theory. Once he accepted this approach, it was natural to assume that the proper-time of the source be used to parameterize the motion, acting as the metric for the underlying geometrization of the special theory of relativity, thus implicitly requiring that another postulate be added.

The resulting four geometry was very popular at that time (and ever since), but some investigators (e.g., Einstein, Lorentz, Poincarè, and Ritz) regarded it as a mathematical abstraction, lacking physical content. Many physicists felt that an alternative approach should be possible which preserves some remnant of an absolute time variable (true time) while still allowing for the constancy of the speed of light. Apparently Lorentz believed in this ‘true time’ until he died, as well as in a Euclidean Newtonian spacetime, and in absolute simultaneity.

Interpretational problems that are not well-known exist with the Minkowski approach. First, note that the conventional use of the words coordinate time tends to obscure the fact that this is the proper-time of the observer. This makes physical interpretation complicated and strange, because one is required to refer back to the proper-time of the source (or the postulated clock of a co-moving observer) to completely interpret and analyze experiments. Dirac (1963) was critical of the use of Minkowski geometry as a fundamental concept. He observed, “... the picture with four dimensional symmetry does not give us the whole situation.... Quantum theory has taught us that we must take a three-dimensional section of what appears to our consciousness at one time (an observation), and relate it to another three-dimensional section at another time”. Dirac further questioned the fundamental nature of the four-dimensional requirement in physics and noted that, in some cases, physical descriptions are simplified when one departs from it. From our point of view, the important question is: What does one replace it with that solves the outstanding problems and has some contact with known physics?

Physics Journal, Relativistic Invariance, Generalized Maxwell Theory, Special Relativity, Radiation Reaction, Quantum Theory, Euclidean Newtonian Spacetime, Electron, Electromagnetic Waves, Optical Doppler Effect, Quantization, Lorentz Transformations, Electrodynamics.