Correlated random walks caused by dynamical wavefunction collapse

TL;DR

This paper predicts that in the CSL wavefunction collapse model, nearby particles exhibit correlated random motions, and proposes an experiment to detect this effect, which could constrain the model's parameters.

Contribution

It demonstrates that the CSL collapse mechanism causes positive correlations in particle diffusions and proposes an experimental test to observe this, constraining the model's length scale.

Findings

Nearby particles show correlated diffusions under CSL.

Proposed experiment can detect correlations at low temperature and pressure.

Results can bound the CSL length scale.

Abstract

Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model---one of the most well developed collapse models---the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale.