Abstract

Owing to the principle of relativity, the present state of knowledge explicitly allows Maxwell's equations to be solved not only in the rest frame of an electromagnetic transmitter but also directly in the rest frame of the receiver without use of the Lorentz transformation and the Lorentz force. Recently, such a calculation was first performed for the Hertzian dipole. The analysis of the resulting formula breaks new scientific ground and indicates that Maxwell's equations predict that electromagnetic waves in vacuum propagate at the speed of light, notably for each receiver, even when these receivers have relative velocities with respect to each other. Although this paradoxical phenomenon was expected, the finding that Maxwell's equations nevertheless predict a classical Doppler effect was unexpected and indicates inconsistent or not yet fully understood aspects of canonical Lorentz-Einstein electrodynamics consisting of Maxwell's equations, Lorentz force and Lorentz transformation.