Probability amplitude waves described by quantum mechanics are globally coherent relativistically space-like space-time structures, having no internal causal links. In this sense these non-classical structures are anticipated by the classical ontology of special relativity, which also delineates (in a completely different way) space-like non-causal intervals in space-time. I discuss and distinguish two broad classes of globally coherent relativistically space-like space-time structure, and suggest a parsimonious extension of the core ontology of physics to include both (rather than only one as at present), as a way of resolving some puzzles in the interpretation of quantum mechanics, and motivating its formalism. This ontological extension yields well known formal features usually postulated ad-hoc, such as separability of the wave function, and explains the puzzling absolute nature of time in quantum mechanics. The curious fact that the ontologies of both special relativity and quantum mechanics delineate (in strikingly different ways) strictly non-causal intervals in space-time suggests the existence of an explanatory “last common ancestor” ontology, at a higher level of abstraction than the ontologies of either. I briefly sketch such an ontology, consisting of world self-mappings, in terms of which there are two distinct concepts of time, intrinsic and extrinsic, which together play an abstract identity role in the world, and which suggests part of the meaning of both special relativity and quantum mechanics, and of the non-causal coherence of non-classical space-time structures, concerns extrinsic abstract structure, in particular extrinsic time.