Nonlocal interferences induced by the phase of the wavefunction for a particle in a cavity with moving boundaries

TL;DR

This paper explores how the phase of a particle's wavefunction in a moving-boundary cavity exhibits nonlocal effects, potentially allowing signaling within non-relativistic quantum mechanics, with implications for understanding quantum nonlocality.

Contribution

It demonstrates that wavefunction phase in a moving cavity depends on boundary motion and discusses potential nonlocal signaling effects within the Schrödinger framework.

Findings

Wavefunction phase depends on wall motion for certain initial states

Nonlocal interference effects could enable signaling in non-relativistic quantum mechanics

High-energy state contributions are negligible in the adiabatic approximation

Abstract

We investigate the dynamics of a particle in a confined periodic system---a time-dependent oscillator confined by infinitely high and moving walls---and focus on the evolution of the phase of the wavefunction. It is shown that, for some specific initial states in this potential, the phase of the wavefunction throughout the cavity depends on the walls motion. We further elaborate a thought experiment based on interferences devised to detect this form of single-particle nonlocality from a relative phase. We point out that, within the non-relativistic formalism based on the Schr\"odinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.