Transformations of systems of relativistic particle mechanics

Abstract

An attempt is made to present a complete set of axioms for relativistic particle mechanics in the sense of the special theory of relativity. Under a certain weak hypothesis, the set of transformations is determined which always carry systems of relativistic particle mechanics into systems of relativistic particle mechanics. Although this set of transformations is not a group (under the usual operation), it is shown to be essentially a Brandt groupoid. The results seem to represent an improvement of those of MacColl (Trans. Amer. Math. Soc. 46:328-347, 1939) in that (1) the work is within an explicit axiomatic framework; (2) transformations are considered of the units of mass and force as well as position and time; and (3) tranformations are considered from one value of the velocity of light to another.