Macroscopic Quantum Mechanics in a Classical Spacetime

TL;DR

This paper explores the application of the many-particle Schrödinger-Newton equation to macroscopic objects, revealing observable differences in quantum uncertainty evolution and implications for gravity-mediated quantum interactions.

Contribution

It derives an effective Schrödinger-Newton equation for macroscopic centers of mass and predicts measurable deviations in quantum uncertainty evolution.

Findings

Quantum uncertainty frequency differs from classical eigenfrequency.

Gravity does not transfer quantum uncertainty between objects.

Predictions align with semiclassical Newtonian physics for multiple objects.

Abstract

We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we found that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr\"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet they do not allow quantum uncertainty to be transferred from one object to another through gravity.