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.
Abstract Ontology is integral to the two most fundamental scientific theories of the twentieth century: quantum theory and the special and general theories of relativity. Issues that drove the development of quantum theory include the reality of quanta, the simultaneous wave- and particle-like nature of matter and energy, determinism, probability and randomness, Schrodinger’s wave equation, and Heisenberg’s uncertainty principle. So did the reality of the predictions about space, time, matter, energy, and the universe itself that were deduced from the special and general theories of relativity. Dirac’s prediction of antimatter based solely on the mathematics of his theory of the electron and Pauli’s prediction of the neutrino based on his belief in quantum mechanics are cases in point. Ontological interpretations of the uncertainty principle, of quantum vacuum energy fields, and of Schrodinger’s probability waves in the form of multiple universe theories further illustrate this point.
“For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory...” J. S. Bell (2004, p. 171) The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. Although various primitive ontologies (including Bohmian pilot wave, spontaneous collapse, and objective collapse theories) along with wave function realism ontologies, many-worlds interpretations, and multi-field theories address the tension between special relativity and quantum mechanics, none has successfully resolved it. This analysis addresses the problem by positing an ontic, mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”). 4D spacetime’s three spatial dimensions and the N dimensions of Planck Space are composed of two substructures: discrete, three-dimensional, quantized units of space ("Planck Spheres") and an ontic State of Absolute Nothingness (the "SOAN") whose sole physical characteristic is onticness. Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete 4D spacetime and 2) mathematical 3N configuration spaces with a physical (3 x N) Planck Space. Moreover, structurally and dynamically, the Dual Ontology is predicated on the one-to-one mapping and identity between the Planck Spheres that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity physically and theoretically support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply. Keywords: Quantum Cosmology; Special Relativity; Quantum Mechanics, Wave Function Collapse; Mixed Ontology; Dual Ontology; (3 x N) Planck Space; Planck Identity; Bell Identity