Macroscopic Quantum Mechanics in a Classical Spacetime

We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle {\it quantum} wave function and a {\it classical} space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\"{o}dinger-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 find 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 it is not allowed that quantum uncertainty to be transferred from one object to another through semiclassical gravity.