If electromagnetism is to be ascribed to some property of spacetime rather than merely embedded in it, additional geometric degrees of freedom are needed.

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 th