Classical unified field theories since antisymmetry seemed essential for electromagnetism, the symmetry requirement was relaxed for one or both fields. Einstein's proposed unified-field equations (fundamental laws of physics) were generally derived from a variational principle expressed in terms of the Riemann curvature tensor for the presumed space-time manifold. In field theories of this kind, particles appear as limited regions in space-time in which the field strength or the energy density are particularly high. Einstein and coworker Leopold Infeld managed to demonstrate that, in Einstein's final theory of the unified field, true singularities of the field did have trajectories resembling point particles. However, singularities are
Classical unified field theories some aspect of the free-space field equations. He also shared the hope that an improved fundamental theory would explain why the two elementary particles then known (proton and electron) have quite different masses. The Dirac equation for the relativistic quantum electron caused Eddington to rethink his previous conviction that fundamental physical theory had to be based on tensors. He subsequently devoted his efforts into development of a "Fundamental Theory" based largely on algebraic notions (which he called "E-frames"). Unfortunately his descriptions of this theory were sketchy and difficult to understand, so very few physicists followed up on his work. When