Ontological indeterminacy is when we don’t have a way to map our conceptual understanding of existence onto actual existence. Or, as Allen Ginsburg defined it: “Ontological indeterminacy (OI) involves incompatible conceptual systems being applicable to a domain with equal empirical adequacy”. But what happens when we don’t have empirical adequacy, such as with quantum field theory and chaos theory?
Quantum field theory is, to put it in simplistic terms, the idea that quantum particles are fluctuations in different fields: a single electron is a fluctuation in an electron field that spans the entire universe, a photon is a fluctuation in the electromagnetic field that spans the entire universe, and so on for every elementary particle. These fields, as I said, span the entire universe – the exist even when they have a value of zero. In a sense, we might say that where there is no electron, there is still an existing non-existence of an electron: a potential electron, if you will.
What is the nature of this existing non-existence? It exists as a mathematical construct, as all fields do, but mathematical constructs are ontologically indeterminate: you are just as correct saying that no electron exists where the electron field is zero as saying that something called the electron field exists there, but which of these notions is true, insofar as they describe how reality actually is? When we consider mereological sums, do they take the zero-values of the field into consideration, or just the parts of the field that have values (i.e. where there are fluctuations in the fundamental fields)?
It is also the case that, due to the indeterminacy of quantum fields, there is also an indeterminacy in the phase space of fundamental particles: what can we say of an initial condition that has zero actual value but some potential value? This is possibly where the Navier–Stokes existence and smoothness problems arise.
My reason for pointing out these issues is that any ontological realism must be ontologically determinate, and therefore must have some accounting for these (potential) indeterminacies. My own views are somewhat more anti-realist, which might accept that there is no ontological fact of the matter about quantum fields and that they are simply just a way for humans to conceptualize quantum phenomena. They may be real in a sense that they provide information: the concept of quantum fields allow us to make predictions (reduce uncertainty) about quantum phenomena, and therefore exist as information, but then we still have to decide whether information itself has ontological determinacy or whether it exists in any primal sense (i.e. it is an actual extensional existence independent of our concepts).