Global ontologies for relativistic quantum systems and quantum field theory

Epistemic models of nature prove to be problematic in many settings, particularly in those in which measurement procedures are ill-defined. By contrast, in ontological models of nature, measurement results are independent of the procedure used to obtain them. Quantum mechanics, as a model of nature, is notoriously ambiguous in this regard. If we assume that all measurement results can be expressed in terms of pointer readings, then any useful ontology would need to unambiguously specify the positions of things. But the positions of pointers are ill-defined in many relativistic and cosmological settings. One potential solution to this problem presents itself in the solutions to the Wheeler-DeWitt equation as developed by Hartle and Hawking. In this article we introduce such a model in which these solutions to the Wheeler-DeWitt equation serve as the ontology of the model. We then show that, for any model that admits these solutions as beables, the global preservation of Lorentz invariance is incompatible with global determinism. However, we also show that an Everett-like interpretation that allows for all possible mappings of the matter field to the geometry and for all possible foliations of these mappings as being equally real, might solve this problem.