Superposition as a Relativistic Filter

Abstract

By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz filtering process, removing paths that are relativistically inequivalent. In a model that includes a stochastic component, the free-particle Schr\"{o}dinger equation emerges from a completely relativistic context in which its origin {\em and function} is known. The result establishes the fact that the phase of wavefunctions in Schr\"{o}dinger's equation and the attendant superposition principle may both be considered remnants of time dilation. This strongly argues that quantum mechanics has its origins in special relativity.