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Minkowski's Scalar Invariant Incompatible with any Equation of Motion

Georg Galeczki
Year: 2000
Keywords: Minkowski Invariant, special relativity
Journal of New Energy, Fall 2001 (Proc. Of the 2nd Int. Workshop: Physics as a Science, Galeczki, Marquardt, Wesley Eds.).

The first purely mathematical and irrevocable proof of the incompatibility between "Minkowski space" and particle dynamics is presented. "Special" relativity was a tragic confusion between the independent Eulerian x ; y ; z ; t and Lagrangean x(t) ; y(t) ; z(t) coordinates of a particle moving under the influence of forces. Only continuous, field theories -like Maxwell' s-described by equations with partial derivatives could, if at all, be described by means of Eulerian coordinates. The dynamics of moving bodies, however, as discrete, atomistic theory, is compatible only with ordinary differential equations with the Lagrangean coordinates as solutions. In both types of theories non-invariant initial conditions are an indispensable part. Minkowski's expression (ct)2 - x2 is, therefore, not an invariant, since x-as-a-solution of an equation of motion contains the frame-dependent initial velocity. As "transformations leaving Minkowski's expression invariant", the Lorentz transformation loses is relevance for particle physics, too.