A Derivation of the Quantum Phase

Abstract

The quantum phase has profound effects on quantum mechanics but its physical origin is currently unexplained. This paper derives its general form from two physical axioms: 1) in the limit in which space goes to zero, spacetime reduces to a constant quantity of areatime, and 2) the proper time dimensions of areatime and of spacetime are orthogonal but can be compared to each other according to what will here be called an angular dual bilateral symmetry. The mathematical derivation and the explanation of the physical origin of the quantum phase from these two axioms is straightforward and implies that the quantum phase is intimately related to the quantization of spacetime.