  What gravitational field is generated by a massive quantum system in a
spatial superposition? This is one of the most important questions in modern
physics, and after decades of intensive theoretical and experimental research,
we still do not know the answer. On the experimental side, the difficulty lies
in the fact that gravity is weak and requires large masses to be detectable.
But for large masses, it becomes increasingly difficult to generate spatial
quantum superpositions, which live sufficiently long to be detected. A delicate
balance between opposite quantum and gravitational demands is needed. Here we
show that this can be achieved in an optomechanics scenario. We propose an
experimental setup, which allows to decide whether the gravitational field
generated by a quantum system in a spatial superposition is the superposition
of the two alternatives, or not. We estimate the magnitude of the effect and
show that it offers good perspectives for observability. Performing the
experiment will mark a breakthrough in our understanding of the relationship
between gravity and quantum theory.
