  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.
