To What Extent Does General Relativity Provide Generalization?

In this paper we discuss whether Einstein’s initial expectations before he developed the theory of general relativity were fulfilled and whether general relativity fully satisfied him in this respect. Einstein employed the equivalence principle as a guiding principle in the development of general relativity. We follow Einstein’s historical reasoning on the equivalence principle by adopting a dynamical approach to relativity and question the theory of general relativity he arrived at in terms of his initial expectations. The key issue here is related to the interpretation of gravitational and inertial “fields” in the equivalence principle. Einstein spoke of the identity of these two notions. This reveals that his intention was to unify gravitation and inertia. In fact, the issue is also related to the extent of generalisation provided by general relativity. Einstein demands a strong generalization in general relativity that requires the equality of all frames, including accelerating frames, in the same way that the relative character of velocity provides in special relativity. However, general relativity does not provide such a strong generalisation as expected from it. Furthermore, in general relativity, the gravitational field is reduced to inertia, but the two are not fully unified. We therefore argue that Einstein’s initial expectations of general relativity were not met and that the theory did not fully satisfy him. Nevertheless, we show that there is a satisfactory way out. On the basis of some heuristic arguments, we demonstrate that if gravitational and non-gravitational interactions are unified into a single elementary interaction at the most fundamental level in nature, then inertia and gravitation are fully unified and the strong generalisation being sought can be obtained. We speculate that Einstein was well aware of this fact and one of his motivations (perhaps the most important one) in his long search for a unified field theory was an attempt to fulfill his initial expectations about general relativity.