Gravitational quantum collapse in dilute systems

TL;DR

This paper investigates a gravitationally induced quantum collapse model in dilute systems, showing how it reproduces measurement outcomes and modifies Newtonian forces due to collapse effects, consistent with relativistic constraints.

Contribution

It applies the GBC model to dilute quantum systems, demonstrating collapse dynamics during measurement and spontaneous effects on gravitational interactions.

Findings

Collapse reproduces von Neumann postulate during measurement

Spontaneous collapse modifies Newtonian forces

Model remains compatible with relativistic no-signaling

Abstract

Penrose has suggested that large fluctuations of the gravitational energy of quantum systems, resulting from fluctuations of its density in space, may induce a quantum collapse mechanism \cite{Penrose-1996}, but he did not propose a precise dynamics for this process. We use the GBC (Gravitational Bohmian Collapse) model \cite{GBC}, which provides such a dynamics. The effects of collapse in dilute quantum systems are investigated, both in ordinary 3D space and in configuration space. We first discuss how a single result appears during a quantum measurement. The GBC model predicts a continuous but very fast evolution of the state vector that, at the end of the measurement, reproduces the von Neumann projection postulate. This ensures that the model remains compatible with the relativistic nosignaling constraint. In the absence of any measurement, we study the spontaneous effects of the GBC process, which depend on the quantum correlation function of observables with the spatial density operator. If the selected observable is the local current of the density fluid, we show that the collapse term leads to modifications of the Newton force, in a scalar or tensor form.