Neo-Hertzian Wave Equation and Aberration

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Scientific Paper
Title Neo-Hertzian Wave Equation and Aberration
Author(s) Thomas E Phipps
Keywords Maxwell's equations, time derivatives, covariant
Published 1994
Journal Galilean Electrodynamics
Volume 5
Number 3
Pages 46-54

Abstract

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.