Pinhole interference in three-dimensional fuzzy space

TL;DR

This paper explores how quantum interference naturally diminishes in a three-dimensional fuzzy sphere model, providing insights into the quantum-to-classical transition without external environments, and improves upon previous two-dimensional models.

Contribution

It extends the analysis of quantum decoherence in non-commutative spaces from 2D to 3D, addressing symmetry and transition limitations of earlier models.

Findings

Suppression of interference at high energies or particle numbers.

Fuzzy sphere model restores expected symmetry in interference patterns.

Quantum-to-classical transition occurs at realistic conditions.

Abstract

We investigate a quantum-to-classical transition which arises naturally within the fuzzy sphere formalism for three-dimensional non-commutative quantum mechanics. This transition may be understood as the mechanism of decoherence, but without requiring an additional external heat bath. We focus on treating a two-pinhole interference configuration within this formalism, as it provides an illustrative toy model for which this transition is readily observed and quantified. Specifically, we demonstrate a suppression of the quantum interference effects for objects passing through the pinholes with sufficiently-high energies or numbers of constituent particles. Our work extends a similar treatment of the double slit experiment by Pittaway and Scholtz (2021) within the two-dimensional Moyal plane, only it addresses two key shortcomings that arise in that context. These are, firstly that the interference pattern in the Moyal plane lacks the expected reflection symmetry present in the pinhole setup, and secondly that the quantum-to-classical transition manifested in the Moyal plane occurs only at unrealistically high velocities and/or particle numbers. Both of these issues are solved in the fuzzy sphere framework.