User DZS has directed me to a paper which provides a relativistically covariant ontology for QFT! Consistent histories already had this, but the histories there can be arbitrarily sparsely specified. This ontology, “space-time state realism”, goes to the opposite extreme and it does so very ingeniously. It uses the “Heisenberg picture” of QFT rather than the “Schrodinger picture”. The Schrodinger picture is the usual one in which the state vector evolves in time and the operators do not. The Heisenberg picture is usually described as using a state vector which doesn’t evolve in time and operators which do; but the important fact, for the purposes of interpretation, is that the operators are associated to space-time points and so form a manifold-like set that can be relativistically transformed.
Operators are not yet states, however. What these authors (Wallace and Timpson) do, is to define a Hilbert space for an arbitrary space-time region, and then a way to construct a state in that Hilbert space, using data about how the field operators in that region behave with respect to the unique “initial” state used in the Heisenberg picture. So in their ontology, absolutely every space-time region and subregion (every open set, maybe? haven’t gone over the details) has a quantum state attached, in a way that is consistent across regions. It’s very clever, and it’s just enough overkill to guarantee that the true ontology is almost certainly hiding somewhere in there.
User DZS has directed me to a paper which provides a relativistically covariant ontology for QFT! Consistent histories already had this, but the histories there can be arbitrarily sparsely specified. This ontology, “space-time state realism”, goes to the opposite extreme and it does so very ingeniously. It uses the “Heisenberg picture” of QFT rather than the “Schrodinger picture”. The Schrodinger picture is the usual one in which the state vector evolves in time and the operators do not. The Heisenberg picture is usually described as using a state vector which doesn’t evolve in time and operators which do; but the important fact, for the purposes of interpretation, is that the operators are associated to space-time points and so form a manifold-like set that can be relativistically transformed.
Operators are not yet states, however. What these authors (Wallace and Timpson) do, is to define a Hilbert space for an arbitrary space-time region, and then a way to construct a state in that Hilbert space, using data about how the field operators in that region behave with respect to the unique “initial” state used in the Heisenberg picture. So in their ontology, absolutely every space-time region and subregion (every open set, maybe? haven’t gone over the details) has a quantum state attached, in a way that is consistent across regions. It’s very clever, and it’s just enough overkill to guarantee that the true ontology is almost certainly hiding somewhere in there.