Neo-Hertzian Wave Equation and Aberration
Year: 1994
Keywords: Maxwell's equations, time derivatives, covariant
Heinrich Hertz developed a covering theory of Maxwell's equations that was Galilean invariant - i.e., first-order invariant, not covariant. This was accomplished by replacing Maxwell's partial time derivatives with total (complete) time derivatives, while leaving the spatial partial derivatives unaltered. To proceed to high-order approximations, frame time is replaced by field detector proper time. The resulting "neo-Hertzian" wave equation is solved in three dimensions by the method of d'Alembert. The solution is shown to give an account of aberration, based on a 3-vector invariance, that is simpler and less beset with equivocations than that offered by the established 4-vector covariant formalism. The 4-vectors seem to be fighting the physics every step of the way - and, were it not for their friends, losing.