  An interesting idea, dating back to Feynman, argues that quantum mechanics
may break down for large masses if one entertains the possibility that gravity
can be "classical", thereby leading to predictions different from conventional
low-energy quantum gravity. Despite the technical difficulty in testing such
deviations, a large number of experimental proposals have been put forward due
to the high level of fundamental interest. Here, we consider the
Schr\"odinger-Newton (SN) theory and the Correlated Worldline (CWL) theory, and
show that they can be distinguished from conventional quantum mechanics, as
well as each other, by performing pulsed optomechanics experiments. For CWL
specifically we develop a framework resembling the commonly used
"Heisenberg-picture" treatment of coupled oscillators, allowing one to perform
simple calculations for such systems without delving into the deeper
path-integral formalism. We find that discriminating between the theories will
be very difficult until experimental control over low frequency quantum
optomechanical systems is pushed much further. However, the predicted
departures of SN and CWL from quantum mechanics occur at the same scale, so
both alternative models could in principle be probed by a single experiment.
