Constructing consistent hybrid quantum-classical models,with applications to gravity

While we do not know if gravity is quantum in Nature, the quantization route has
often been favored on the ground that semiclassical approaches were necessarily
inconsistent. It is natural to think so based on early examples, but it is not true. In
fact, in the past decade, it has been understood that there is no obstacle in
constructing well behaved hybrid classical-quantum theories. There are even many
seemingly different proposals for how to do so. My main objective is to explain what
their philosophy is, why they escape the usual problems, and how they are in fact all
mathematically equivalent. At least under reasonable constraints, there is just one
way to construct consistent quantum-classical dynamics. Finally, I will explain what
the empirical consequences of these models are, and relate them to the recent
proposals to experimentally witness the ability of gravity to entangle.