Proper-Time Formulation of Classical Electrodynamics

We show that Maxwell’s equations have a generalization associated with the proper-time of the source and a new invariance group which leaves this variable fixed for all observers. We show that the second postulate (of Einstein) depends on the anthropocentric view that the only clock to use is the proper-clock of the observer. Our work is motivated by the results of Fushchych and Shtelen (F-S), who showed that the free Maxwell equations have an additional invariance group which is Galilean. This work makes it clear that our group is distinct from but closely related to the Lorentz group, and is not Galilean. Since our present (constructive) approach requires a source, it does not apply to the free field case. In an earlier paper, we showed that the F-S transformation is an element of the proper-time (canonical) group which includes the group constructed here. This work is also related to the work of Wegener who showed that use of the proper time allows the construction of Galilean transformations from Lorentz transformations. © 1997 Taylor & Francis Group, LLC.