This chapter contains sections titled: Relationism, Substantivalism and Space‐time Conventionalism about Space‐time Black Holes and Singularities Horizons and Uniformity Conclusion.

Some Philosophical Prehistory of General Relativity As history, my remarks will form rather a medley. If they can claim any sort of unity (apart from a ...

This book, explores the conceptual foundations of Einstein's theory of relativity: the fascinating, yet tangled, web of philosophical, mathematical, and physical ideas that is the source of the theory's enduring philosophical interest. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of (...) the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

In Philosophies of Space and Time, Howard Congdon presents a collection of readings from antiquity to the present, showing how philosophers have thought about and understood the concepts of space and time. This examination shows how human thinking has evolved in attempting to answer the questions embedded in the concepts of space and time.

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

This volume is a comprehensive collection of critical essays on The Taming of the Shrew, and includes extensive discussions of the play's various printed versions and its theatrical productions. Aspinall has included only those essays that offer the most influential and controversial arguments surrounding the play. The issues discussed include gender, authority, female autonomy and unruliness, courtship and marriage, language and speech, and performance and theatricality.

Foundations of Space-Time Theories, by Michael Friedman, falls naturally into two parts. In the first, he presents the general framework within which he will characterize and discuss space-time theories, and then he devotes a chapter each to Newtonian physics, special relativity, and general relativity. Although there is some rich philosophical discussion along the way, these chapters are, of necessity, somewhat technical expositions of the general framework in action. It is in the second part, consisting of two (...) substantial chapters, one on relationalism, the other on conventionalism, that more general philosophical issues are addressed. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a (...) geometrical approach, emphasizing intrinsic space-time structure rather than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

Prompted by the "Panel Discussion of Grünbaum's Philosophy of Science" (Philosophy of Science 36, December, 1969) and other recent literature, this essay ranges over major issues in the philosophy of space, time and space-time as well as over problems in the logic of ascertaining the falsity of a scientific hypothesis. The author's philosophy of geometry has recently been challenged along three main distinct lines as follows: (i) The Panel article by G. J. (...) Massey calls for a more precise and more coherent account of the Riemannian conception of an intrinsic as opposed to an extrinsic metric, which the author has invoked as his basis for the distinction between non-conventional and convention-laden ascriptions of metrical equality and inequality; (ii) the latter distinction has been claimed to suffer from the liabilities of the so-called "standard conception" of scientific theories [36]; and (iii) pursuant to H. Putnam's "An Examination of Grünbaum's Philosophy of Geometry" [56], J. Earman [16, 17] and R. Swinburne [65] have contended that the difference between intrinsic and extrinsic metrics is scientifically unilluminating, and that the associated distinction between non-conventional and convention-laden metrical comparisons does not have the kind of relevance to extant scientific theories that the author has claimed for it. The essay consists of two installments. The present installment, comprising the Introduction and Part A, is devoted to the clarification, correction and further development of the author's prior writings on the philosophy of geometry. Its main objective is constructive elaboration rather than offering polemics. But rebuttals to Earman, [16, 17], Swinburne [65] and Demopoulos [13] are included, because their inclusion conduced to clarity in giving the new exposition. Part B is to appear in a subsequent issue and will be devoted to replies to critiques contained in the Panel Discussion and in other recent literature. It will range over issues in the philosophy of geometry and in the logic of ascertaining the falsity of a scientific hypothesis. By way of merely elliptical anticipation of much more precise statements given in Part A, section 3(ii), the Introduction dissociates the notion of convention-ladenness developed in Part A from the quite different notion integral to the so-called "standard conception" of scientific theories. Thereby, the Introduction prepares the ground for seeing, as a corollary to Part A, section 3(ii), that the notion advocated in the present essay has nothing to fear from the following fact, noted by C. G. Hempel ([36]; cf. also his 1970 Carus Lectures): "even though a sentence may originally be introduced as true by stipulation, it soon joins the club of all other member-statements of the theory and becomes subject to revision in response to further empirical findings and theoretical developments." Part A, which begins with a fairly detailed table of contents, endeavors to meet the aforementioned three-fold challenge to the author's philosophy of geometry. Massey's call for the provision of clear and detailed characterizations of intrinsic and extrinsic metrics is answered with the invaluable aid rendered personally by Massey himself. These characterizations are shown to permit a precise explication of the portions of Riemann's Inaugural Dissertation relevant to (1) Riemann's brilliant anticipation of Einstein's dynamical conception of physical geometry, and (2) the author's philosophical characterization of the metrics and geometries of space, time, and space-time {section 2(c)}. A byproduct of the analysis is to raise two major philosophical doubts concerning Clifford's sketch of a so-called "space-theory of matter" as elaborated in J. A. Wheeler's relativistic geometrodynamics. That theory's vision of understanding matter as a manifestation of empty curved space is questioned in regard to (1) the existence of an intra-geometrodynamic basis for individuating the metrically homogeneous world points of its space-time manifold {section 1(a)}, and (2) the compatibility of the theory with the Riemannian metrical philosophy apparently espoused by its proponents {section 2(c)(i)}. (shrink)

This article documents the general tendency of seventeenth-century natural philosophers, irrespective of whether they were atomists or anti-atomists, to regard space, time and matter as magnitudes having the same internal composition. It examines the way in which authors such as Fromondus, Basson, Sennert, Arriaga, Galileo, Magnen, Descartes, Gassendi, Charleton as well as the young Newton motivated their belief in the isomorphism of space, time and matter, and how this belief reflected on their views concerning the relation (...) between geometry and physics. Special attention is paid to the fact that most of the authors mentioned above regarded rarefaction and condensation, on the one hand, and acceleration and deceleration, on the other hand, as analogous phenomena, which consequently had to be explained in similar terms. (shrink)

In this paper we study the emergence of Minkowski space–time from a discrete causal network representing a classical information flow. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity—including space–time—be defined through precise measurement procedures. Topological homogeneity is a requirement for having space–time metric emergent from the pure topology of (...) causal connections, whereas physically homogeneity corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock. The illustrated simple classical construction can be extended to space dimension greater than one, with the price of anisotropy of the maximal speed, due to the Weyl-tiling problem. This issue is cured if the causal network is quantum, as e.g. in a quantum cellular automaton, and isotropy is recovered by quantum coherence via superposition of causal paths. We thus argue that in a causal network description of space–time, the quantum nature of the network is crucial. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the inconsistency (...) mentioned above is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and (...) physical measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

In this paper I attempt to trace certain aspects of the evolution of theories of space-time and mechanics as revealed by a brief comparative study of Newtonian theory, Robb's theory, general relativity, and Milne's kinematical relativity. The first object is to emphasise how each theory leaves us in a position in which the succeeding one appears as a perfectly natural next step in the development of ideas. The second object is to show how, in spite of superficial differences (...) in character, the theories all necessarily possess the same general structure constituted by the presence of hypotheses, from which certain general mathematical relations are deduced, which in their turn are used to predict relations between observable quantities. (shrink)

Ordinarily, what we experience does not jump from one place or time to another—we have to pass through all the intermediate times and places. But in films, what we experience can jump in both dimensions, both separately and together. This phenomenon has been memorably described in film criticism by Rudolph Arnheim and it has been deployed philosophically by Suzanne Langer and Colin McGinn. But discussion of space-time discontinuity remains hampered by the lack of attunement between film critical (...) and philosophical investigations. Without philosophy, the valuable insights of film criticism lack rigour and have been blunted by conceptual imprecision and confusion; without film criticism, the provocative claims of philosophy lack support, floating free of the evidence that a suitably sharp awareness of the details of particular films alone provides. This paper brings philosophy and film criticism to bear on each other so that we stand to make headway on the issue of film and space-time discontinuity. (shrink)

I present a discussion of some open issues in the philosophy of space-time theories. Emphasis is put on the ontological nature of space and time, the relation between determinism and predictability, the origin of irreversible processes in an expanding Universe, and the compatibility of relativity and quantum mechanics. In particular, I argue for a Parmenidean view of time and change, I make clear the difference between ontological determinism and predictability, propose that the origin of (...) the asymmetry observed in physical processes is related to the existence of cosmological horizons, and present a non-local concept of causality that can accommodate both special relativity and quantum entanglement. (shrink)

An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein’s 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein’s operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate (...) a particular philosophical position --- in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity. The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein’s approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional ‘absolute world’. As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski’s general position was not very unlike the one in the back of Einstein’s mind. However, in Minkowski’s formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity. (shrink)

This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of (...) class='Hi'>space, that of giving operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics. (shrink)

Hegel’s Philosophy of Nature begins with the concepts of space and time, and all of the concepts and phenomena that follow in the text are spatio-temporal. But the actual content of Hegel’s theory of space and time has remained obscure despite two centuries of interpretation, and obscure for at least two reasons. First, it is unclear how Hegel’s theory relates to those of his immediate predecessors (Newton, Leibniz, Kant) as well as other theories in the (...) history of philosophy. Second, the theoretical function to be played by this theory of space and time has remained unclear. In this paper, we clarify the first issue by interpreting Hegel’s theory as a theory of space-time, and we clarify the second issue by interpreting that theory as securing the theoretical possibility of motion. Of course, it will not be the same theory of space-time as the one that proceeds from modern relativistic physics; but designating Hegel’s theory as a theory of space-time helps to mark it out from its most prominent predecessors and helps to make sense of some of its most distinctive features—particularly Hegel’s insistence that time has three dimensions just as space does. This latter feature—the three-dimensionality of time—serves to distinguish Hegel’s view both from the classical mechanics of Newton and Kant (in which time does not interact with the spatial directions) and from contemporary relativistic physics (in which there is such interaction but time is only a single dimension added to the spatial dimensions). In Hegelian space-time, three-dimensional time is the flip side of three-dimensional space—it is this conception that makes Hegel’s view so distinctive. (shrink)

A journey surveying the land of space, time and motion Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9575-8 Authors Christian Wüthrich, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0119, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

THE VOLUME CONTAINS PAPERS BY J L MACKIE, JON DORLING, ELIE ZAHAR, LAWRENCE SKLAR, RICHARD Swinburne, Richard A HEALEY, W H NEWTON-SMITH, NANCY CARTWRIGHT, JEREMY BUTTERFIELD, MICHAEL REDHEAD AND PETER GIBBONS. THEY CONCERN THE IMPLICATIONS FOR OUR UNDERSTANDING OF SPACE, TIME AND CAUSATION OF THE DEVELOPMENTS OF MODERN PHYSICS AND ESPECIALLY OF RELATIVITY THEORY AND QUANTUM THEORY.