On Felix Klein's Geometric Model of Electromagnetism

Abstract

In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm and geometrical modeling of physical phenomena. He was aiming at a physical foundation for non Euclidean geometry. However, the letters he wrote to Einstein had no sequel. We think that F. Klein's ideas still deserve some attention, as they can be useful for modeling Maxwell's equations with a radically different approach than resorting to field theories. One reason for looking for alternatives is that current field theories use geometry exclusively as a formal technique thereby inhibiting human intuition from grasping the physical world. This article collects cues that we deem relevant for a model of electromagnetic received signals. In the first two chapters we highlight a few features of classical physics, namely the trajectories of mass points, and the differences in treating rotations between statics and dynamics. In the third chapter, we finally review F. Klein's approach toward geometrical modeling of electromagnetism and special relativity.