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I argue that the hole argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the hole argument is blocked. _1._ Introduction _2._ A Warmup Exercise _3._ The Hole Argument _4._ An Argument from Classical Spacetime Theory _5._ The Hole Argument Revisited. |
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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 (...) |
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Here, we briefly review the notion of observational indistinguishability within the context of classical general relativity. We settle a conjecture given by Malament (1977) concerning the subject and then strengthen the result considerably. The upshot is this: There seems to be a robust sense in which the global structure of every cosmological model is underdetermined. |
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Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of (...) |
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I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked. |
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An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) |
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Debates about the ontological implications of the general theory of relativity have long oscillated between spacetime substantivalism and relationism. I evaluate such debates by claiming that we need a third option, which I refer to as “structural spacetime realism.” Such a tertium quid sides with the relationists in defending the relational nature of the spacetime structure, but joins the substantivalists in arguing that spacetime exists, at least in part, independently of particular physical objects and events, the degree of “independence” being (...) |
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Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) |
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1.1 Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tangent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (...) |
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I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor T µ associated with them. I argue that T µ does not represent an intrinsic property of matter. For it will become evident that the definition of T µ depends on the metric field g µ in a variety of ways. Accordingly, since g µ represents the geometry of spacetime itself, the properties of (...) |
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Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe? |
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This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) |
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Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions. |
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I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) |
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The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the (...) |
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One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: (...) |
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iinstein oered the priniple of generl ovrine s the fundmentl physil priniple of his generl theory of reltivityD nd s responsile for extending the priniple of reltivity to elerted motionF his view ws disputed lmost immeditely with the ounterElim tht the priniple ws no reltivity priniple nd ws physilly vuousF he disgreeE ment persists todyF his rtile reviews the development of iinstein9s thought on generl ovrineD its reltion to the foundtions of generl reltivity nd the evolution of the ontinuing dete (...) |
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The paper defends two claims; Viewed from the perspective of the substantivalism/relationism debate, structural spacetime realism is a form of relationism; However, if we managed to reinforce Rynasiewicz’s point that the general theory of relativity makes the substantivalism/relationism dispute “outdated”, the re-elaboration of Stein ’s 1967 version of structural spacetime realism to be proposed here proves to be a good, antimetaphysical solution to the problem of the ontological status of spacetime. |
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There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...) |
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I argue that all current research programs in quantum gravity conform to the 17th century hypothetico-deductive model of scientific inquiry, perhaps of necessity given the current state of technology. In so far as they do not recognize and advertise the shortcomings of the research method they use, they do a disservice to the integrity of science, for the method admits of far less certainty accruing to its products than one would be led to believe by the pronouncements of researchers in (...) |
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Relationism claims that our physical theory does not commit us to spacetime points. I consider how a relationist might rewrite physical theories without referring to spacetime points, by appealing to possible objects and possible configurations of objects. I argue that a number of difficulties confront this project. I also argue that a relationist need not be Machian in the sense of claiming that objects' spatiotemporal relations determine whether any object is accelerating. |
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This paper argues that the much discussed issue between "scientific realism" and "instrumentalism" has not been clearly drawn. Particular attention is paid to the claim that only realism can "explain" the success of scientific theories and---more especially---the progressively increasing success of such theories in a coherent line of inquiry. This claim is used to attempt to reach a clearer conception of the content of the realist thesis that underlies it; but, it is here contended, that attempt fails, and the claim (...) |
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In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...) |
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I argue that the conviction, widespread among philosophers, that substantivalism enjoys a clear superiority over relationalism in both Newtonian and relativistic physics is ill-founded. There are viable relationalist approaches to understanding these theories, and the substantival-relational debate should be of interest to philosophers and physicists alike, because of its connection with questions about the correct space of states for various physical theories. |
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This paper examines Newton's argument from the phenomena to the law of universal gravitation-especially the question how such a result could have been obtained from the evidential base on which that argument rests. Its thesis is that the crucial step was a certain application of the third law of motion-one that could only be justified by appeal to the consequences of the resulting theory; and that the general concept of interaction embodied in Newton's use of the third law most probably (...) |
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The traditional absolutist-relationist debate is still clearly formulable in the context of General Relativity Theory (GTR), despite the important differences between Einstein's theory and the earlier context of Newtonian physics. This paper answers recent arguments by Robert Rynasiewicz against the significance of the debate in the GTR context. In his (1996) (‘Absolute vs. Relational Spacetime: An Outmoded Debate?’), Rynasiewicz argues that already in the late nineteenth century, and even more so in the context of General Relativity theory, the terms of (...) |
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A version of relationism that takes spatiotemporal structures—spatial geometry and a standard of inertia—to supervene on the history of relations between bodies is described and defended. The account is used to explain how the relationist should construe models of Newtonian mechanics in which absolute acceleration manifestly does not supervene on the relations; Ptolemaic and Copernican models for example. The account introduces a new way in which a Lewis-style ‘best system’ might capture regularities in a broadly Humean world; a defence is (...) |
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A criterion is proposed to ensure that classical relativistic fields do not propagate superluminally. If this criterion does indeed serve as a sufficient condition for no superluminal propagation it follows that various other criteria found in the physics literature cannot serve as necessary conditions since they can fail although the proffered condition holds. The rejected criteria rely on energy conditions that are believed to hold for most classical fields used in actual applications. But these energy conditions are known to fail (...) |
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Much controversy surrounds the question of what ought to be the proper definition of 'singularity' in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to 'missing points' has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into (...) |
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I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows any defect (...) |
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