The Schrödinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrödinger-Newton equation, and we show that it can be realized with existing technology.

13 pages, 4 figures, 1 table, 1 page of supplemental material