Gravitationally induced inhibitions of dispersion according to the Schr\"odinger-Newton Equation

TL;DR

This paper investigates the Schr"odinger-Newton equation to understand gravitational effects on quantum wave packet dispersion, finding that significant inhibitions occur at much higher masses than previously reported, impacting experimental prospects.

Contribution

The study numerically locates the onset of gravitationally induced inhibition of dispersion at much higher masses, refining previous estimates and challenging experimental feasibility.

Findings

Inhibition occurs at about 10^{10} u mass

Results align better with analytical estimates

Experimental realization appears more difficult than previously thought

Abstract

We re-consider the time dependent Schr\"odinger-Newton equation as a model for the self-gravitational interaction of a quantum system. We numerically locate the onset of gravitationally induced inhibitions of dispersion of Gaussian wave packets and find them to occur at mass values more than 6 orders of magnitude higher than reported by Salzman and Carlip (2006, 2008), namely at about $10^{10}\,\mathrm{u}$. This fits much better to simple analytical estimates but unfortunately also questions the experimental realisability of the proposed laboratory test of quantum gravity in the foreseeable future, not just because of large masses, but also because of the need to provide sufficiently long coherence times.