General relativity once seemed to be philosophically clear. Physics, according to the logical positivists, had come together with the leading ideas of epistemology, metaphysics, and the foundations of geometry into a single coherent picture – something that had not happened since the philosophy of Kant. In Kant's case, however, what united Newtonian physics, Euclidean geometry, and the critical philosophy was a naive conception of mathematics as a creature of sensible intuition. That conception was, as we saw, overthrown by nineteenth-century ideas: the emergence of non-Euclidean geometry, the rise of conventionalism, and, in general, the separation of formal mathematics from intuition. To the positivists, general relativity was no more or less than the synthesis of these post-Kantian ideas with an empiricist view of science.

The positivists' notion now seems to be as naive as Kant's. But this is not because they were utterly misguided about the philosophical significance of relativity. Rather, it was because they misunderstood the philosophical relations between relativity and what came before it. They could not fully understand the nature of the radical change that Einstein effected, as long as they failed to appreciate the essential philosophical continuities between his theories and those of Newton. They could not see a satisfactory alternative to Kant's theory of the synthetic a priori, as long as they were fixed on the idea of arbitrary convention.

This book concerns the philosophy of space and time, and its connection with the evolution of modern physics. As these are already the subjects of many excellent books and papers – the literature of the “absolute versus relational” debate – the production of yet another book may seem to require some excuse. I don't claim to defend a novel position in that controversy, or to defend one of the standard positions in a novel way. Still less do I pretend to offer a comprehensive survey of such positions and how they stand up in light of the latest developments in physics. My excuse is, rather, that I hope to address an entirely different set of philosophical problems. The problems I have in mind certainly have deep connections with the problems of absolute and relative space, time, and motion, and the roles that they play, or might play, in the history and future of physics. But they can't be glossed by the standard questions on space-time metaphysics: is motion absolute or relative? Are space and time substantival or relational? Rather, they are problems concerning how any knowledge of space, time, and motion – or spatio-temporal relations – is possible in the first place. How do we come to identify aspects of our physical knowledge as knowledge of space and time? How do we come to understand features of our experience as indicating spatio-temporal relations? How do the laws of physics reveal something to us about the nature of space and time?

Newton presented not only a theory of absolute space and time, but a philosophical approach to the analysis of space and time quite unlike anything contemplated by his contemporaries. It cannot be viewed as a complete philosophical account of space and time, however, because it treats space and time solely from the perspective of classical mechanics – that is, as concepts implicitly presupposed by the classical mechanical understanding of causality and force. A philosophically thorough treatment of the problem would embrace, not only the implicit metaphysics of physics, but the general epistemological problem of space and time and the ways in which physics, and human knowledge generally, have some access to them. In other words, the step beyond what Newton accomplished required an attack on what later became known as “the problem of physical geometry.” The revolutionary development of space-time geometry in the twentieth century, in both special and general relativity, is only the most spectacular of the many far-reaching consequences of this philosophical effort.

As we saw, Newton's theory was forced into confrontation with the most prominent general philosophical accounts of space and time, namely those of Descartes and Leibniz. But its rejoinder to them was only that those philosophical views could not be reconciled with their own views of physics. Undoubtedly this was a compelling argument as far as it goes, one which neither Descartes nor Leibniz was in a position to answer on its own terms.

SPACE AND TIME IN THE HISTORY OF PHYSICS

In the history of modern physics, space and time have after all played something like the role attributed to them by Kant. Not as forms of intuition: this was only incidentally the case, in a context where the geometry of space and the intuitive means of knowing about space seemed inseparable from one another. In that context, the processes of “representing to ourselves” in the productive imagination and of conceptualizing the relative situations of physical things appeared to be seamlessly connected. That is, the infinite Euclidean space in which physics treated the positions and motions of bodies was the most straightforward extension of the space in which we move, grasp our relation to our immediate surroundings, and situate our spatial point of view. But they have played the quasi-Kantian role of a framework that enables physics to constructively define its fundamental concepts of force and causality, by giving physics the means to construct such concepts as measurable theoretical quantities. The familiar and vague notion of force, through the work of Galileo, Huygens, Newton, and others, became a physical concept with a constructive spatio-temporal definition, one that did not really violate the common notion – even if it seemed to at first – but that rendered it a powerful tool of physical investigation, and thereby made the discovery of physical forces a clear and attainable goal.

Why is there a “philosophy of space and time”? It seems obvious that any serious study of the nature of space and time, and of our knowledge of them, must raise questions of metaphysics and epistemology. It also seems obvious that we should expect to gain some insight into those questions from physics, which does take the structure of space and time, both on small and on cosmic scales, as an essential part of its domain. But this has not always seemed so obvious. That physics has an illuminating, even authoritative, perspective on these matters was not automatically conceded by philosophy, as if in recognition of some inherent right. No more did physics simply acquire that authority as a result of its undoubted empirical success. Rather, the authority came to physics because physicists – over several centuries, in concert with mathematicians and philosophers – engaged in a profound philosophical project: to understand how concepts of space and time function in physics, and how these concepts are connected with ordinary spatial and temporal measurement. Indeed, the empirical success of physics was itself made possible, in some part, by the achievements of that philosophical effort, in defining spatio-temporal concepts in empirically meaningful ways, often in defiance of the prevailing philosophical understanding of those concepts. In other words, the physics of space and time has not earned its place in philosophy by suggesting empirical answers to standing philosophical questions about space and time.

At a time when the relativity of motion was just beginning to be understood, Newton introduced a theory of absolute motion in absolute space and time. The controversy that then began has never ceased. What right did Newton have to explain the observable relative motions by an appeal to these unobservable entities? What role can such metaphysical hypotheses play in empirical science? By re-examining Newton's arguments for his theory, and understanding its role in the science that he helped to develop, we can see that these questions are misdirected. Newton's theory of space and time was never a mere metaphysical hypothesis. Instead, it was his attempt to define the concepts presupposed by the new mechanical science – the conceptual framework that made relative motion physically intelligible within a conception of causal interaction. Rather than an empirically questionable addition to his scientific work, it was an essential part of his work to construct an empirical science of motion. Rather than mere metaphysical baggage carried by an otherwise empirically successful theory, it was inseparable from Newton's effort to define the empirically measurable quantities of classical mechanics.

NEWTON AND THE HISTORY OF THE PHILOSOPHY OF SCIENCE

The history of Newton's ideas of space and time was once part of a philosophical justification for general relativity. For much of the twentieth century, the standard view of that history was something like this. When Newton introduced the theory, it was immediately obvious to his wisest philosophical contemporaries that this was a backward step.

INTRODUCTION: PHILOSOPHICAL CONTROVERSY OVER NEWTON’S IDEAS OF SPACE, TIME, AND MOTION

Newton's concepts of “absolute space,” “absolute time,” and “absolute motion” met with serious objections from such philosophical contemporaries as Huygens, Leibniz, and Berkeley. Among philosophers of the early twentieth century, after the advent of Special and General Relativity, the objections bordered on scorn: Newton's concepts were not only lately outmoded, but they were also epistemologically inherently defective, empirically unfounded - concepts not scientific at all, but “metaphysical,” in so far as science is concerned precisely with “sensible measures” rather than obscure notions of what is “absolute.” The prevailing idea was that Einstein had established not only a new theory of space and time, but a deeper philosophical viewpoint on space and time in general. From this viewpoint, space, time, and motion are essentially relative, and to call them absolute was an elementary philosophical error. As Einstein put it, General Relativity had taken from space and time “the last remnant of physical objectivity.”

The philosophical motivation for this viewpoint seems obvious. Space cannot be observed; all that we can observe is the relative displacement of observable things. Therefore, if we observe two bodies in relative motion, to say that one of them is “really” moving, or that it is moving “relative to absolute space,” is to pass beyond the bounds of empirical science. If we wish to decide which bodies are moving, we have to construct a frame of reference – that is, we must designate some reference-points to be fixed, and compare the motions of other bodies to these.