Whatever is Never and Nowhere is Not: Space, Time, and Ontology in Classical and Quantum Gravity

Dissertation, University of Pittsburgh (1996)

Gordon Belot
University of Michigan, Ann Arbor
Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists working on quantum gravity, who claim that the conceptual problems which they face are intimately related to interpretative questions concerning general relativity . My goal is to show that the physicists are correct--there is a close relationship between the interpretative issues of classical and quantum gravity. ;In the first part of the dissertation I challenge the received view that substantivalism has a commanding advantage over relationalism on grounds internal to GR. I argue that this view is based on a misconception of the relationships between realism and substantivalism, and between empiricism and relationalism. This has led to a narrow conception of relationalism. Once this is relinquished it can be seen that none of the standard arguments in favor of substantivalism are cogent. ;In the second part of the dissertation, I consider the way in which considerations arising out of quantum gravity bear upon the substantival-relational debate. I develop a framework in which to discuss the interpretative problems of gauge theories and place GR in this context. From this perspective, I provide a taxonomy of interpretative options, and show how the hole argument arises naturally as a consequence of gauge freedom. This means that certain substantivalist interpretations of GR render the theory indeterministic. In the final chapter, I argue that, far from being a drawback, this presents an opportunity for substantivalists. Examples from quantum mechanics, quantum field theory, and quantum gravity, are used to demonstrate that the ambiguities inherent in quantization can lead to an interpretative interplay between theories. In the case of quantum gravity, this means that substantivalism and relationalism suggest, and are suggested by, distinct approaches to quantizing GR.
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Some Philosophical Prehistory of the (Earman-Norton) Hole Argument.James Owen Weatherall - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 70:79-87.
Time and Structure in Canonical Gravity.Dean Rickles - 2004 - In Dean Rickles, Steven French & Juha T. Saatsi (eds.), The Structural Foundations of Quantum Gravity. Clarendon Press.
Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics.Karim P. Y. Thébault - 2012 - British Journal for the Philosophy of Science 63 (4):789-824.
Sklar's Maneuver.Bradford Skow - 2007 - British Journal for the Philosophy of Science 58 (4):777-786.
Structural Realism and Quantum Gravity.Tian Yu Cao - 2006 - In Dean Rickles, Steven French & Juha Saatsi (eds.), The Structural Foundations of Quantum Gravity. Oxford University Press.

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