Quantum mechanics on spacetime I: spacetime state realism

What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function real-ism. We elaborate the sense in which wave-function realism does provide an ontological picture; and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatis-fied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state re-alism; a view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, al-though, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature; even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden