  No experimental evidence exists, to date, whether or not the gravitational
field must be quantised. Theoretical arguments in favour of quantisation are
inconclusive. The most straightforward alternative to quantum gravity, a
coupling between classical gravity and quantum matter according to the
semi-classical Einstein equations, yields a nonlinear modification of the
Schr\"odinger equation. Here, effects of this so-called Schr\"odinger-Newton
equation are discussed, which allow for technologically feasible experimental
tests.
