How can we recover the classical spacetime from within quantum mechanics?

The world is fundamentally quantum mechanical. That means that our minimal ontological commitment relies only on having a Hilbert space, a quantum state, and an evolution equation (Schroedinger's equation) together with a Hamiltonian.

Yet, most of our understanding of quantum systems, including gravitational ones, are plagued by classical notions, including the notion of space. For the past century, we have been focusing on quantizing systems, starting from the classical realm towards the quantum. So, perhaps it's not surprising that we cannot shake off all the classical notions that come with it. Meanwhile, physicists still puzzle over how to reconcile gravity with quantum mechanics. I will argue that these problems are related and that an alternative strategy is to focus on recovering classical spacetime from quantum mechanics instead of "quantizing gravity". This approach hints that gravity might be completely emergent from structures contained within the Hilbert space.