Optomechanical test of the Schrödinger-Newton equation

The Schrodinger-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 Schrodinger-Newton equation, and we show that it can be realized with existing technology.