  The paper shows how the Bohmian approach to quantum physics can be applied to
develop a clear and coherent ontology of non-perturbative quantum gravity. We
suggest retaining discrete objects as the primitive ontology also when it comes
to a quantum theory of space-time and therefore focus on loop quantum gravity.
We conceive atoms of space, represented in terms of nodes linked by edges in a
graph, as the primitive ontology of the theory and show how a non-local law in
which a universal and stationary wave-function figures can provide an order of
configurations of such atoms of space such that the classical space-time of
general relativity is approximated. Although there is as yet no fully worked
out physical theory of quantum gravity, we regard the Bohmian approach as
setting up a standard that proposals for a serious ontology in this field
should meet and as opening up a route for fruitful physical and mathematical
investigations.
