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On the role of mass in the mathematical structure of Newtonian and special relativistic mechanics

Gabor Zsolt Toth
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Abstract

We consider five-dimensional real linear spaces with a (otherwise well-known) linear action of the Galilei and the Poincare group on them, describe the geometry of these two spaces, and show, that these geometries comprise the notions of space-time, mass, momentum, force and physical dimensions in a natural way. In this way we geometrize the quantity of mass and integrate it together with space-time into two geometries in a natural way, so that these geometries are perfectly suitable for underlying the Newtonian and special relativistic mechanics of pointlike bodies.

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Gabor Zsolt Toth. 1999-10-29. On the role of mass in the mathematical structure of Newtonian and special relativistic mechanics. https://arxiv.org/abs/math-ph/9910049

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