Three little paradoxes: making sense of semiclassical gravity

I review the arguments most often raised against a fundamental coupling of classical spacetime to quantum matter. I show that an experiment by Page and Geilker does not exclude such a semiclassical theory but mandates an inclusion of an objective mechanism for wave function collapse. In this regard, I present a classification of semiclassical models defined by the way in which the wave function collapse is introduced. Two related types of paradoxes that have been discussed in the context of the necessity to quantize the gravitational field can be shown to not constrain the possibility of a semiclassical coupling. A third paradox, the possibility to signal faster than light via semiclassical gravity, is demonstrably avoided if certain conditions are met by the associated wave function collapse mechanism. In conclusion, all currently discussed models of semiclassical gravity can be made consistent with observation. Their internal theoretical consistency remains an open question.