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Abstract

One of the most interesting aspects of the Special Theory of Relativity is its intimate connection with geometry by way of Minkowski's four dimensional space-time world. In this thesis we examine that connection from various points of view. On the one hand we consider Minkowskt space as an axiomatic system built on certain postulates in the style of Peano and Hilbert, an avenue of development which began with Robb prior to 1914 and continues still with the work of Schutz in 1973 and 1979. On the other hand certain groups arid group geometries are given prominence; this avenue of development began with Lorentz and Larmor before 1905, continued with Bateman and Cunningham in 1909 and received a boost recently with the work of Zeeman in 1964. The unifying theme of this part of our development concerns the way of making manifest, in the various group geometries associated with Minkowski space, key matters of physical experience and intuition, collectively known as the principle of causality. The procedures by which causal issues are treated in the Minkowski space model are subjected to critical review and the thesis contains original and/or simpler proofs of the theorems associated with the local and global causal groups. In addition, we present a systematic mathematical development of a procedure for dealing with the class of uniformly accelerated frames within the theory of Special Relativity, without the necessity of dealing with the curved space-time of General Relativity. The problems of physical interpretation that arise regarding the preservation of local and global causality and the restrictions on the use of the allowable transformations are also discussed and critically evaluated.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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