Topology and the non-existence of magnetic monopoles

Abstract

Most of the work being done to unify General Relativity and Quantum Mechanics tries to represent General Relativity in the Quantum Mechanics language. We propose here an approach to represent Quantum Mechanics in the language of Relativity. In order to introduce discretness into the language of Relativity we consider the classical  invarients of homolopy theory, in particular the index of a vector field. We insist that these invariants be treated as physical quantities, independent of choices of observers and conventions. Following this prescription we found an argument that pseudovectorfields should have zero index. Hence magnetic monopoles should not exist. We give extended philosophical arguments that the index should play an important role in Mathematics, and hence Physics, based on a novel definition of Mathematics and the meaning of the underlying unity of Mathematics.