Weyl and geometrization of physics (Q2928243)

Hermann Weyl was at the forefront of mathematical physics in the early years of both general relativity and quantum mechanics. His own development, as the author shows, was from a markedly a priori position in which a pre-established harmony between mathematics and physics allows mathematics to prescribe much of physics to a more empirical one. It led to interesting differences with Hilbert in the early years and to disagreements with Einstein later on that are the subject of this paper.NEWLINENEWLINEThe so-called Weyl geometries and Weyl's first gauge principle are products of the first phase. As the author shows, the philosophies of Weyl and Hilbert, and even some of their mathematical methods, were very similar, but Hilbert nonetheless criticised Weyl's approach as ``Hegelian physics'', meaning that it gave too much weight to strictly mathematical considerations. The author shows that Hilbert would better have attributed Weyl's philosophical background to Fichte and Husserl, and his pungent remark shows his own affinity with a Kantian approach to mathematical physics. As is well known, Weyl's first gauge theory, which he advocated as a way to unify the theories of gravitation and electro-magnetism, was criticised by Einstein, and Weyl eventually withdrew it. In the 1920s, Einstein moved towards a more prescriptive unifying theory and now it was Weyl's turn to charge him with implausible physics, in this case by drawing on insights from the new quantum physics.NEWLINENEWLINEThe paper draws carefully on existing work by Scholz and others, but it is also a fresh account attentive to both philosophical and contextual, historical, issues.