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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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  • 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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  • Conservation, Inertia, and Spacetime Geometry.James Owen Weatherall - forthcoming - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.
    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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