  Shortly after the completion of the general theory of relativity in  1915, Einstein, Weyl, and others began to work on a unified field  theory. It was natural to assume at that   time[44]  that this task would only involve the unification of gravity and  electromagnetism. In Einstein’s geometrization of gravity, the  Newtonian gravitational potential, and the Newtonian gravitational  force, are respectively replaced by the components of the metric  tensor \(g_{ij}(x)\), and the components of  the symmetric linear connection \(\Gamma^{i}_{jk}(x)\). In the general  theory of relativity the gravitational field is thus accounted for in terms of the curvature of spacetime, but the electromagnetic field  remains completely unrelated to the spacetime geometry. Einstein’s  mathematical formulation of his theory of general relativity does  not, however, provide room for the geometrization of the other long  range force field, the electromagnetic   field.[45]  It was therefore natural to ask whether nature’s only two long range  fields of force have a common origin. Consequently, it was quite  natural to suggest that the electromagnetic field might also be  ascribed to some property of spacetime, instead of being merely  something embedded in spacetime. Since, however, the components  \(g_{ij}(x)\) of the metric tensor are  already sufficiently determined by Einstein’s field equations, this  would require setting up a more general differential geometry than  the one which underlies Einstein’s theory, in order to make room for  incorporating electromagnetism into spacetime geometry. Such a  generalized differential geometry would describe both long range  forces, and a new theory based on this geometry would constitute a  unified field theory of electromagnetism and gravitation. 