  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.
