Group theory and its applications

Erhard Scholz

pp. 271-314

in: Erhard Scholz (ed), Hermann Weyl's "Raum — Zeit — Materie" and a general introduction to his scientific work, Basel, Birkhäuser, 2001

Abstract

That spacetime is equipped with a (pseudo) Riemannian metric is a fundamental postulate of the General Theory of Relativity. Since the Riemannian type of metric is only one of a rich variety of conceivable metric forms, it is reasonable to ask what the fundamental characteristics of the Riemannian form are that single it out. As discussed in subsections 4.5, 4.6 and 4.7, Weyl analyzed this problem of space, the Raumproblem, in a series of articles (Weyl, 1922a, 1922b, 1923f). Weyl (1949b, p. 400) himself noted that his interest in the philosophical foundations of the General Theory of Relativity motivated his analysis of the representations and invariants of the continuous groups, "I can say that the wish to understand what really is the mathematical substance behind the formal apparatus of relativity theory led me to the study of representations and invariants of groups; and my experience in this regard is probably not unique".