Lack of Value Definiteness in Quantum Gravity

Abstract: In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are non-commuting ones. By analogy with some recent arguments put forward in the context of non-relativistic quantum mechanics (QM), we shall propose to interpret these physical quantities as ontologically indeterminate -- i.e., indeterminate in a non-epistemic, mind-independent way. This result has two important consequences for current debates in philosophy of physics. First, it shows that ontological indeterminacy may extend well beyond the non-relativistic case, thereby also suggesting a conceptual continuity between QM and QG. Second, when applied to QG, the notion of indeterminacy may provide a unified philosophical framework for understanding very distinct approaches that are usually considered incompatible.