Mathematical Concepts in Physics

Abstract The purpose of this paper show how mathematical concepts not designed for physics can muddle understanding and/or prevent progress. We provide the following examples to justify our position: 1. A proof that Minkowski’s (third) postulate is incompatible with Einstein’s first postulate for two or more particles. 2. A proof that the Dirac equation is not physically equivalent to the square root equation but is related by a unitary transformation. 3. The design of a Hilbert space for Feynman’s path integral formulation of quantum theory KS 2 [ℝ n ], which is not physically equivalent to L 2 [ℝ n ], the Hilbert space for the Schödinger formulation, but is related by a unitary transformation. A major contribution of this paper is that mathematical equivalence is not the same as physical equivalence and that unbiased physical analysis and justification of mathematical concepts should be required before acceptance into physical theory.