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The Riemann Foundations of Mechanics and Matter


McAlea, Eamon


Research Papers


Mathematical Physics



Date Published:

December 2, 2011




Riemann, Mechanics, Einstein Hilbert Action, Unified Field, First Order, Higher Order, Fitzgerald Contraction, Time Dilation, Lorentz Invariance


In physics the application of Riemann manifolds and the corresponding analytical apparatus is for the most part identified with the General Theory of Relativity and the light speed preserving space-time coordinate systems which place restrictions on the form of the metric, i.e. only transformations which preserve the speed of light are considered, and the spaces considered are 4D. 3 space and one time. In Non-relativistic theories i.e., classical or Newtonian mechanics, Riemann manifolds are confined to 3 space dimensions and the time is considered separate. The cited reason for this is that in general an arbitrary space time transformation from one coordinate system to another will not preserve the speed of light. This maybe the case, but it should not prevent a non light speed preserving metric from expressing an equation of motion, for what is a geodesic in one coordinate system is also a geodesic in any other coordinate system, even those which do not preserve the speed of light. Realizing this key point allows the full power of the Riemann metric to be exploited. In Relativity Theory the metric is restricted so that the speed of light is always the same, and only transformations between such metrics are allowable. In this paper no such restrictions are imposed, an arbitrary transformation from one reference system to another gives rise to a new metric in which perfectly valid equations of motion are obtained. The requirement of Lorentz invariance is only motivated as t

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