Localization of quantum objects in an expanding universe and cosmologically induced classicality

TL;DR

This paper investigates how the expansion of the universe influences quantum object localization, proposing a size-based criterion for when objects behave classically versus quantum mechanically, with implications for cosmological quantum-classical transition.

Contribution

It introduces a cosmological model incorporating universe expansion into quantum equations, deriving a size threshold for classicality that aligns with existing uncertainty-based criteria.

Findings

Localized wave functions depend on object mass and universe expansion

Large mass objects tend to be more localized and classical

The size threshold for classicality matches previous uncertainty relation results

Abstract

Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on 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 are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, then quantum behavior could be expected; whereas if the region of high probability density for the location of the center of mass is smaller than the size of the object, the object would behave in a more classical manner. The resultant size threshold for classicality accords with results of other studies examining these issues based on uncertainty relations and wave packets. This size threshold is informative for the case of compact extended objects and, as the constraint applies to the center of mass of the system, does not lead to inconsistencies for quantum correlations between distant entangled quantum objects. While local decoherence may lead to classicality under a variety of conditions, cosmologically induced classicality would appear to cause fundamental limitations on quantum behavior in our universe.