’s. To be sure, this unexpected parallelism between the equations of electromagnetics and the curvatures of a Weyl space might have been attributed to mere chance. But, as must be admitted, the temptation to view matters otherwise was great. Weyl assumed, therefore, that space-time was of the Weylian type and not of the more restricted classical species, as Einstein had supposed. The electric and magnetic field tensor
, which in Einstein’s space-time appeared to be a foreign entity intruding on the continuum, was then in reality none other than the Weylian curvature of this generalised space-time. These views led Weyl to assume that when electromagnetic fields were present, hence when
did not vanish, the Weylian characteristics of space-time manifested themselves, whereas, in regions free of electromagnetic fields, space-time resumed its classical characteristics and became once again the space-time of Einstein’s theory. For similar reasons, the four electromagnetic potentials, i.e., the four
’s were identified with the four
’s of the Weylian structure. In this way, electromagnetic phenomena, to the same extent as gravitational phenomena, appeared to be necessary manifestations of the metrics of the fundamental space-time continuum.
Let us consider the further modifications which these new views will impose. First, we remember that in the classical spaces, hence in Einstein’s space-time, it was possible to build up fundamental or structural tensors (