Superposition as a Relativistic Filter

TL;DR

This paper proposes that quantum superposition and wavefunction phases originate from relativistic effects, specifically time dilation, suggesting quantum mechanics fundamentally derives from special relativity.

Contribution

It demonstrates that the Schrödinger equation and superposition principle can be derived from relativistic time dilation effects, unifying quantum mechanics with special relativity.

Findings

Wavefunction phase linked to relativistic time dilation

Superposition acts as a Lorentz filtering process

Quantum mechanics emerges from a relativistic framework

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.