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Inertial motion, explanation, and the foundations of classical spacetime theories

In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. Boston, USA: Birkhauser. pp. 13-42 (2017)

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  1. On Gravitational Energy in Newtonian Theories.Neil Dewar & James Owen Weatherall - 2018 - Foundations of Physics 48 (5):558-578.
    There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized theory without introducing further structure. We then address a potential response by showing that (...)
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  • A Primer on Energy Conditions.Erik Curiel - 2017 - In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. Birkhäuser. pp. 43-104.
    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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  • Would Two Dimensions Be World Enough for Spacetime?Samuel C. Fletcher, J. B. Manchak, Mike D. Schneider & James Owen Weatherall - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 63:100-113.
    We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.
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  • The Meaning of Relativity and the Liberation of the Relationalists.Patrick Dürr - unknown
    We analyse the various conceptual notions that go under the umbrella “relationalism/substantivalism”. Our focus will be on evaluating the ontological status of spacetime in General Relativity. To this end we systematically develop the ontological framework that implicitly underlies the traditional debate and common understanding of physics. We submit that spacetime with its chronogeometric and inertial structure, represented by the triple of the bare manifold, the metric and the affine structure, is best construed as the totality of possible and actual spatiotemporal (...)
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  • Explanation, Geometry, and Conspiracy in Relativity Theory.James Read - unknown
    I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that the debate takes a substantially different form in the two cases; different versions of the geometrical approach—only some of which are viable—should be distinguished; in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two ‘miracles’ of general (...)
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  • General Relativity as a Hybrid Theory: The Genesis of Einstein's Work on the Problem of Motion.Dennis Lehmkuhl - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 67:176-190.
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  • Conservation, Inertia, and Spacetime Geometry.James Owen Weatherall - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 67:144-159.
    As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude (...)
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  • Sophistication About Symmetries.Neil Dewar - 2019 - British Journal for the Philosophy of Science 70 (2):485-521.
    Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.
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  • Classical Spacetime Structure.James Owen Weatherall - unknown
    I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.
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