Abstract

Einstein spent his life trying to develop a system of dynamics independent of reference frame. But this lofty goal demands a hard look at the very meaning of reference frame, a starting point for this paper. Einstein's fruitless attempts were based on his own observer-based theory of relativity, in turn based on Lorentzian covariant paradigms. Covariant mathematics admits transformations between coordinate systems and reference frames, but does not suggest a path towards invariance. However, the del operator provides a means of expressing spatial derivatives independent of coordinate system. Likewise, if time is independent of space, as this paper suggests, the total time derivative operator, d/dt, is also independent of reference frame. Therefore, physical equations that can be expressed with the del operator and the total time derivative, as opposed to reference-frame dependent partial derivatives, are naturally independent of reference frame. In particular, Maxwell's equations can be correct only if expressible by the del and d/dt operators, as proposed by Hertz and more recently advocated by Phipps. From fluid dynamics, developed by Bernoulli, Euler, Langrange, and many others, over a hundred years before Maxwell, we have the convective or Lagrangian time derivative d/dt = d/dt + v * del. Both sides of this equality are independent of observer, but the two right-hand terms differ in weight depending on how an observer moves with respect to the quantity being differentiated. One observer might see a buildup of material, while another sees an altered flow; one observer might see a changing field, another an acceleration. But the total change, the sum, remains invariant. With the convective derivative, we can readily derive Maxwell's famous "source current" term in Ampere's Law and clear up mysteries surrounding Faraday's Law, particularily relating to unipolar induction and the Sagnac experiment. Invariant Hertzian dynamics provides a means to finally get off Einstein's covariant train.