General Relativity and Quantum Theory - Ontological Investigations

It is common to note that the two great theoretical frameworks of twentieth-century physics, quantum theory and general relativity, are prima facie incompatible. Within the physics community, the incompatibility is largely discussed on a technical level. In this paper, I would like to frame the problem more conceptually, focussing on the respective ontologies of the two frameworks. When I speak of ontology, I have in mind the idea that theories make use of a formal (often mathematical) language for talking about the world. The ontology of the theory then just consists of the objects and properties to which the names and predicates of the language refer. Although this ontology may vary according to different ways of regimenting the language, there is frequently a common or standard formulation. Thus the ontology of astronomy is roughly understood to be planets, stars and galaxies (the objects), which have their various masses and shapes ("internal" properties) and positions and velocities ("external" properties) . For the most part, fundamental physical theories refer only implicitly to the objects themselves, for it is the properties that are mathematically quantified. The language of Newton's mechanics and his theory of gravitation enables one to refer to any object having a mass, a position, and a velocity. Thus Newton's theory is as much about planets as it is about apples. Maxwell's theory of electromagnetism refers to objects that have the property not only of mass but charge as well. In that respeCt it is not significantly different from Newton's theory. But it also refers to something called the electromagnetic field. The values of the field are properties, but they are properties not of Newtonian objects but of spacetime itself. Historically, Maxwell's theory may be the first theory in which spacetime plays the role of an "object", a bearer of properties. Previously, space and time had simply been thought of as the background in which objects lived. (Of course, one can anachronistically reconstruct, e.g., Newtonian theory from the modern perspective.) As we shall see, general relativity expands on this development, while quantum theory retains a