Can the expansion of the universe localize quantum wave functions? How classical behavior may result from Hubble expansion

TL;DR

This paper explores how the universe's Hubble expansion can influence quantum wave functions, potentially causing large-mass objects to behave classically by inducing wave function localization.

Contribution

It introduces a differential equation derived from the Schrödinger equation that predicts wave function localization due to Hubble expansion, linking quantum-classical transition to cosmic expansion effects.

Findings

Large-mass objects have localized wave functions

Small-mass objects exhibit delocalized quantum behavior

A potential quantum-classical boundary related to size and mass

Abstract

We consider an object at rest in space with a universal Hubble expansion taking place away from it. We find that a governing differential equation developed from the Schroedinger equation leads to wave functions which turn out to exhibit pronounced central localization. The extent of concentration of probability depends on the mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses have wave functions that are largely concentrated into much smaller regions. This in turn suggests the possibility that classical behavior is being induced in quantum objects by the presence of the Hubble expansion. If the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, quantum behavior might be expected; whereas classical behavior might be expected for cases in which the region of high probability density is smaller than the size of the object. The resulting quantum-classical boundary due to Hubble expansion may be expressed in terms of a relationship between the size and mass of an object, or may be expressed in terms of a threshold moment of inertia.