On the space‐time structure and its relation to quantum mechanics

Abstract

AbstractThe Weyl covariant formulation of Dirac's equation by means of a rest mass the Weyl type of which is — 1, implies the introduction of a Riemann structure in addition to the Weyl structure. The Ehlers‐Pirani‐Schild attempt to specify the space‐time structure and the lowest order of the WKB approximation are compatible with each other. Only the requirement that the connection to which the Dirac field couples minimally is identical to the connection the autoparallels of which are the world lines of structure‐less test particles, leads to a reduction of the Weyl structure to the Riemannian one.