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Space, Time, and Ontology in Classical and Quantum Gravity

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Space, Time, and Ontology in Classical and Quantum Gravity WHATEVER IS NEVER AND NOWHERE IS NOT: SPACE, TIME, AND ONTOLOGY IN CLASSICAL AND QUANTUM GRAVITY by Gordon Belot B.Sc., University of Toronto, 1991 M.Sc., University of Toronto, 1993 Submitted to the Graduate Faculty of University of Pittsburgh in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 1996 John Earman Joseph Camp Adolf Grünbaum John Norton Carlo Rovelli ii WHATEVER IS NEVER AND NOWHERE IS NOT: SPACE, TIME, AND ONTOLOGY IN CLASSICAL AND QUANTUM GRAVITY Gordon Belot, Ph.D. University of Pittsburgh, 1996 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 (GR). 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 iii 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. iv PREFACE I suppose that the preface of a dissertation is the appropriate place to discuss the context of discovery and to acknowledge debts acquired along the way. So let me begin by saying that my project had its genesis in a talk which Chris Isham delivered to the Sigma Club in Cambridge during the winter of 1994. At that time, I had been working for several months on the hole argument. This argument, due to John Earman and John Norton, is supposed to show that if one believes that the points of spacetime are real existents, then one is committed to believing that general relativity is an indeterministic theory. It is an ingenious synthesis of Einstein’s original hole argument with some themes that have been at the center of philosophy of space and time since the Leibniz-Clarke correspondence. My attitude towards the hole argument had gone through a number stages—which would be, I suspect, quite familiar to anyone who has worked in this area for any length of time. When I was first exposed to it in John Earman’s seminar on the philosophy of space and time in the fall of 1991, I had been impressed by its ingenuity—but had been quite sure that it was based on a simple mistake. When I returned to it in the fall of 1993, and began to work through the details of the burgeoning literature of critiques and commentaries focused on the hole argument, I came to appreciate that the situation was considerably more subtle than I had at first thought. This literature contains some very engaging ideas, and I found it quite exciting to pick my way through them in my attempt to reach a stable position, and to understand how the various sorts of response to the hole argument were related to one another and to larger issues within philosophy. Ultimately, however, I was somewhat dissatisfied with this work. In the introduction to his canonical World Enough and Spacetime, Earman had promised that the hole argument would usher in an era of renewed scientific relevance for the philosophy of space and time: v In recent decades the absolute-relational controversy has largely become a captive of academic philosophers. That the controversy is interminably debated in philosophical journals and Ph.D. dissertations is a warning sign that it has lost the relevance to contemporary science that the great natural philosophers of the seventeenth through nineteenth centuries thought it so obviously had for the science of their day. I will attempt to correct this impression by showing, for example, how some of the very concerns raised by Leibniz and Clarke form the core of ongoing foundation problems in the general theory of relativity and how these problems in turn can be used to revitalize what has become an insular and bloodless philosophical discussion. (Earman 1989, p. 3) Having spent the autumn of 1993 surveying the philosophical literature on the hole argument, I was convinced that Earman’s promise was bound to go unfulfilled—this literature consisted of a sizable number of journal articles and a handful of doctoral dissertations, but nowhere was there to be found any substantive connection with ongoing research in physics. Rather, there was a mixture of metaphysical and technical discussion, which, while often ingenious, was just as insular as ever. It was at this point that I attended Isham’s talk “Prima Facie Questions in Quantum Gravity” (Isham 1994 is a more technically demanding version of this talk). Isham spoke about the central conceptual difficulty facing attempts to quantize gravity—the fact that time seems to play no role in the quantum theory—and about how this “problem of time” arises in the various approaches to quantum gravity. Along the way he took time to emphasize that he—and many of his colleagues as well—believed that the problem of time was closely related to the hole argument (both following directly from the general covariance of general relativity), and that interpretative questions concerning the ontological status of the spacetime of general relativity had a role to play in determining the best way forward in the face of the formidable technical and conceptual difficulties facing those who were attempting to quantize gravity. I was very surprised and excited to hear that there were people who thought that the hole argument was relevant to physics after all. I was fortunate to be in the right place at the right time—over the next several months I was able to attend a large number of talks on quantum gravity, at Cambridge and in Durham. I seldom understood very much of what was said. But more than once I was treated to the sight of one or another distinguished physicist leaping up in the middle of a talk in order to denounce the speaker on the grounds that his vi approach was founded upon the outrageous belief that spacetime points did, or did not, exist. I decided that I wanted to know how this worked. This dissertation is the result. In t h e f i n a l C h a p t e r I a r g u e t h a t I s h am et al are correct—what one believes about the existence of the spacetime points of general relativity influences and is influenced by what one believes about quantum gravity. It takes me a rather long time to reach this conclusion. This is because the way that philosophers think about these issues really has lost touch with the way that physicists think about them. Almost all philosophers of physics seem to believe that it is mandatory to believe that the spacetime points of general relativity enjoy a robust variety of existence. Few physicists would agree. On the other hand, although physicists think of the general covariance of general relativity as being a gauge freedom—and this influences much of what they say about the relation between the interpretative problems of classical and quantum gravity—few philosophers of physics are conversant with this way of talking about things. In order understand the role of interpretative positions in quantum gravity, I had learn to think about general relativity in a new way, and to unlearn some old prejudices. I also, of course, had to learn the rudiments of quantum gravity. This dissertation is a recapitulation of this process—a rather long preamble about the substantival-relational debate and general relativity as a gauge theory, followed by a (relatively) brief discussion of the interplay between interpretative positions in classical and quantum gravity. This dissertation is not easy to read. The reader is required to change gears a number of times—from a relatively freewheeling survey of the substantival-relational debate to a tightly focused technical discussion; from the technical and conceptual apparatus of general relativity to those of quantum theory, and back again. In particular, the reader is required to bring some knowledge of both the philosophy of quantum mechanics and the philosophy of space and time.
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