Energy gravitates. QM tells us systems can be in superposition of energy eigenstates, and we'd like to know what happens to the gravitational field in such case

Energy gravitates. QM tells us systems can be in superposition of energy eigenstates, and we'd like to know what happens to the gravitational field in such cases. For that, we need a quantum theory of gravity. We have some recipes to go from a classical to a quantum field theory, but they fail for general relativity. For example, GR is not perturbatively renormalizable: For electromagnetism, we only need to determine a finite number of parameters experimentally to (presumably) fix the theory at all energy scales. That doesn't work for general relativity for technical reasons, and we'd have to measure an infinite number of parameters. Then, there are a couple of conceptual problems, such as GR doing away with a fixed background spacetime, or the so-called problem of time. Different approaches to quantum gravity approach this in different ways (as far as I'm aware, the background normally gets fixed asymptotically in string theory - though don't quote me on that one - whereas loop quantum gravity tackles the issue head on).