Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity

TL;DR

This paper explores how quantum gravitational effects within a Newtonian approximation can cause decoherence in macroscopic closed systems, linking gravitational entanglement to thermodynamical behavior and entropy increase.

Contribution

It provides a novel Newtonian approximation-based formula predicting gravitationally induced decoherence in macroscopic quantum superpositions and many-body systems.

Findings

Decoherence occurs when superpositions involve mass distributions separated by small fractions of the radius.

Gravitational effects induce decoherence between configurations differing in particle cluster positions.

Entropy tends to increase with matter-clumping, suggesting a link to cosmological entropy growth.

Abstract

A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary, framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter-gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a single classically well describable ball of uniform mass density in empty space. Estimating the quantum gravitational effects on this system within a simple Newtonian approximation, we obtain formulae which predict e.g. that as long as the mass of the ball is considerably larger than the Planck mass, such a would-be-coherent static superposition will actually be decohered whenever the separation of the centres of mass of the two ball-states excedes a small fraction (which decreases as the mass of the ball increases) of the ball radius. We then obtain a formula for the quantum gravitational correction to the would-be-pure density matrix of a non-relativistic many-body Schroedinger wave function and argue that this formula predicts decoherence between configurations which differ (at least) in the "relocation" of a cluster of particles of Planck mass. We estimate the entropy of some simple model closed systems, finding a tendency for it to increase with "matter-clumping" suggestive of a link with existing phenomenological discussions of cosmological entropy increase.