  The Schr\"odinger-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 Schr\"odinger-Newton equation, and we show that it can be realized
with existing technology.
