4.2 The link to particle physics

In the context of particle physics, a recent paper by Straumann (1987) illustrates the role of Weyl in introducing gauge theory into cosmology. Weyl (1918) discusses the then only known other interaction besides gravity, the electromagnetic interaction, in the frame of cosmology.

``A true near-geometry, however, may know only one principle of transferring a length from one Point to an infinitely neighbouring one, and then one has as little reason to assume that the problem of transferring a length from one point to another at finite distance is integrable, as the problem of transferring directions is found to be integrable. In removing this said inconsequence, one obtains a geometry which, surprisingly, applied to the world, explains not only the effects of gravity, but also those of the electromagnetic field. According to the theory thus formulated, both come from the same source, even more, in general one cannot separate in an arbitrary way gravity and electricity. In this theory all physical properties have a world geometrical meaning; in particular, the quantity of action appears from first principles as a pure number. It leads to an essentially uniquely defined World Law; it even permits in a certain sense to understand why the world is four-dimensional. . .
The occurring formulae must correspondingly show a double invariance: 1. they must be invariant with respect to arbitrary continuous coordinate transformations, 2. they must remain unchanged, when the gik are substituted by gik, where is an arbitrary continuous function of position. The appearance of a second invariance property is characteristic for our theory...
. . . . in the same way as according to investigations by Hilbert, Lorentz, Einstein, Klein and the author the four conservation laws of matter (of the energy-momentum-vector) are connected to the invariance of action, which contains four arbitrary functions, against coordinate transformations, is the here newly appearing `gauge invariance' [Maßstab-Invarianz], which introduces an arbitrary fifth function, connected with the conservation of electricity.''