A generalisation of Weyl's theory of the electromagnetic and gravitational fields

Source abstract

Abstract 1. In the non-Euclidean geometry of Riemann, the metric is defined by certain quantities, gμν, which are identified by Einstein with the potentials of the gravitational field. H. Weyl has shown that, on removing a rather artificial restriction in Riemann’s geometry, the expression for the metric includes also terms which are identified with the four potentials of the electromagnetic field. I believe that Weyl’s geometry, far-reaching though it is, yet suffers from an unnecessary and harmful restriction; and it is the object of this paper to develop a still more general theory. In passing beyond Euclidean geometry, gravitation makes its appearance; in passing beyond Riemannian geometry, electromagnetic force appears; what remains to be gained by further generalisation? Clearly, the non-Maxwellian binding-forces which hold together an electron. But the problem of the electron must be difficult, and I cannot say whether the present generalisation succeeds in providing the materials for its solution. The present paper does not seek these unknown laws, but aims at consolidating the known laws. I hope to show that, in freeing Weyl’s geometry from its limitation, the whole scheme becomes simplified, and new light is thrown on the origin of the fundamental laws of physics.