1 Vortex theory of electromagnetism and its non-Euclidean character

By examining the theory of relativity, as originally proposed by Lorentz and Poincaré, the fundamental relationship between space-time and matter is discovered, thus completing the theory of relativity and electrodynamics. As a result, the four-dimensional theory of general motion and the four-dimensional vortex theory of interaction are developed. It is seen that the electromagnetic four-vector potential and strength fields are the four-dimensional velocity and vorticity fields, respectively. Furthermore, the four-vector electric current density is proportional to the four-dimensional mean curvature of the four-vector potential field. This is the fundamental geometrical theory of electromagnetism, which determines the origin of electromagnetic interaction and clarifies some of the existing ambiguities. Interestingly, the governing geometry of motion and interaction is non-Euclidean