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Profile: Erik Curiel (University of Western Ontario)
  1. Erik Curiel (2014). Classical Mechanics Is Lagrangian; It Is Not Hamiltonian. British Journal for the Philosophy of Science 65 (2):269-321.
    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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  2.  35
    Erik Curiel, A Primer on Energy Conditions.
    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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  3.  58
    Erik Curiel, On the Existence of Spacetime Structure.
    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 so-called 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 (...)
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  4.  33
    Erik Curiel, Measure, Topology and Probabilistic Reasoning in Cosmology.
    I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes (...)
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  5.  15
    Erik Curiel, Kinematics, Dynamics, and the Structure of Physical Theory.
    Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...)
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  6.  35
    Erik Curiel, Classical Black Holes Are Hot.
    In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area (...)
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  7.  30
    Erik Curiel, If Metrical Structure Were Not Dynamical, Counterfactuals in General Relativity Would Be Easy.
    General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on how counterfactuals should be interpreted and understood. Given the role of counterfactuals in the characterization of, inter alia, many accounts of scientific laws, theory confirmation and causation, general relativity once again presents us with idiosyncratic puzzles any attempt to analyze and understand the nature of (...)
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  8.  31
    Erik Curiel, On Geometric Objects, the Non-Existence of a Gravitational Stress-Energy Tensor, and the Uniqueness of the Einstein Field Equation.
    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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  9.  24
    Erik Curiel, A Weyl-Type Theorem for Geometrized Newtonian Gravity.
    I state and prove, in the context of a space having only the metrical structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's in a Lorentzian space. The theorem, loosely speaking, says that a projective structure and a suitably defined compatible conformal structure on such a space jointly suffice for fixing the metrical structure of a Newtonian spacetime model up to constant factors. It allows one to give a natural, physically compelling interpretation (...)
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  10.  14
    Erik Curiel, A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions.
    The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does (...)
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  11.  3
    Erik Curiel (forthcoming). On the Existence of Spacetime Structure. British Journal for the Philosophy of Science:axw014.
    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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  12. Erik Curiel (2000). The Constraints General Relativity Places on Physicalist Accounts of Causality. Theoria 15 (1):33-58.
    All accounts of causality that presuppose the propagation or transfer or some physical stuff to be an essential part of the causal relation rely for the force of their causal claims on a principle of conservation for that stuff. General Relativity does not permit the rigorous formulation of appropriate conservation principles. Consequently, in so far as General Relativity is considered and fundamental physical theory, such accounts of causality cannot be considered fundamental. The continued use of such accounts of causality ought (...)
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  13. Erik Curiel (2009). General Relativity Needs No Interpretation. Philosophy of Science 76 (1):44-72.
    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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  14. Erik Curiel, Classical Mechanics is Lagrangian; It is Not Hamiltonian; the Semantics of Physical Theory is Not Semantical.
    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 whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I (...)
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  15.  45
    Erik Curiel (1999). The Analysis of Singular Spacetimes. Philosophy of Science 66 (3):145.
    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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  16.  11
    Erik Curiel, Why Rigid Designation Cannot Stand on Scientific Ground.
    I do not think the notion of rigidity in designation can be correct, at least not in any way that can serve to ground a semantics purports both to be fundamental in a semiotical sense and to the best science of the day. A careful examination of both content and the character of our best scientific knowledge not cannot support anything like what the notion of rigidity requires, but actually shows the notion to be, at bottom, incoherent. In particular, the (...)
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  17.  66
    Erik Curiel (2001). Against the Excesses of Quantum Gravity: A Plea for Modesty. Proceedings of the Philosophy of Science Association 2001 (3):S424-.
    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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  18. David Atkinson, Jeanne Peijnenburg, Theo Kuipers, William T. Wojtach, Erik Curiel & Ronald Pisaturo (2009). 1. How to Confirm the Conjunction of Disconfirmed Hypotheses How to Confirm the Conjunction of Disconfirmed Hypotheses (Pp. 1-21). [REVIEW] Philosophy of Science 76 (1).
     
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  19.  8
    Erik Curiel, The Delicacy of Counterfactuals in General Relativity.
    General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory, problems that have gone unremarked on in the physics and in the philosophy literature. Because these problems arise from the dynamical nature of spacetime geometry, they are shared by all schools of thought on how counterfactuals should be interpreted and understood. Given the role of counterfactuals in the characterization of, inter alia, many accounts of scientific laws, theory-confirmation and causation, general relativity once again presents us (...)
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  20.  87
    Erik Curiel, On Tensorial Concomitants and the Non-Existence of a Gravitational Stress-Energy Tensor.
    Based on an analysis of what it may mean for one tensor to depend in the proper way on another, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of (...)
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  21.  10
    Erik Curiel, On the Formal Consistency of Theory and Experiment, with Applications to Problems in the Initial-Value Formulation of the Partial-Differential Equations of Mathematical Physics.
    The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...)
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  22.  6
    Erik Curiel, On the Propriety of Physical Theories as a Basis for Their Semantics.
    I argue that an adequate semantics for physical theories must be grounded on an account of the way that a theory provides formal and conceptual resources appropriate for---that have propriety in---the construction of representations of the physical systems the theory purports to treat. I sketch a precise, rigorous definition of the required forms of propriety, and argue that semantic content accrues to scientific representations of physical systems primarily in virtue of the propriety of its resources. In particular, neither the adequacy (...)
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  23.  38
    Erik Curiel, Singularities and Black Holes. Stanford Encyclopedia of Philosophy.
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  24.  1
    Erik Curiel (2001). Against the Excesses of Quantum Gravity: A Plea for Modesty. Philosophy of Science 68 (S3):S424-S441.
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