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Exactly soluble sector of quantum gravity
 Phy. Rev. D
, 1997
"... Cartan’s spacetime reformulation of the Newtonian theory of gravity is a generallycovariant Galileanrelativistic limitform of Einstein’s theory of gravity known as the NewtonCartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the dege ..."
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Cited by 11 (1 self)
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Cartan’s spacetime reformulation of the Newtonian theory of gravity is a generallycovariant Galileanrelativistic limitform of Einstein’s theory of gravity known as the NewtonCartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate ‘metric ’ structure of spacetime remains fixed with two mutually orthogonal nondynamical metrics, one spatial and the other temporal. The spacetime according to this theory is, nevertheless, curved, duly respecting the principle of equivalence, and the nonmetric gravitational connectionfield is dynamical in the sense that it is determined by matter distributions. Here, this generallycovariant but Galileanrelativistic theory of gravity with a nonzero cosmological constant, viewed as a parameterized gauge theory of a gravitational vectorpotential minimally coupled to a complex Schrödingerfield (bosonic or fermionic), is successfully cast — for the first time — into a manifestly covariant Lagrangian form. Then, exploiting the fact that NewtonCartan spacetime is intrinsically globallyhyperbolic with a fixed causal structure, the theory is recast both into a constraintfree Hamiltonian form in 3+1dimensions and into
Fibered Manifolds, Natural Bundles, Structured Sets, GSets and all that: The Hole Story from Space Time to Elementary Particles, grqc/0505138 12
 Isenberg, J., Marsden
, 2005
"... [M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol ..."
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Cited by 8 (3 self)
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[M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol 1. No. 3, pp 235245) In this paper we review the hole argument for the spacetime points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract from differentiability and even continuity, the hole argument is applied to a much wider class of mathematical objects. We discuss the problem concerning the individuation of the objects in more general settings such that fibered manifolds, fibered
Theories of Newtonian Gravity and Empirical Indistinguishability’, Studies in History and Philosophy of Modern
 Physics
, 2004
"... In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’ ’ version and a ‘‘strong’ ’ version. The strong v ..."
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Cited by 5 (3 self)
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In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’ ’ version and a ‘‘strong’ ’ version. The strong version has a constrained Hamiltonian formulation and consequently a welldefined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’ ’ version in NeoNewtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism.
Events, Topology, and Temporal Relations
, 1996
"... this paper we present an alternative account, based primarily on the basic network of formal ontological relationsspecifically, mereological and topological relationsthat a domain of events must arguably satisfy. The motivations for this approach are quite general and lie beyond the specific i ..."
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Cited by 3 (0 self)
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this paper we present an alternative account, based primarily on the basic network of formal ontological relationsspecifically, mereological and topological relationsthat a domain of events must arguably satisfy. The motivations for this approach are quite general and lie beyond the specific issue of temporal constructions. Among other things, we also believe it may shed light on the first question above. In the following, however, we shall not go much beyond the main issue that we just outlined; our only concern will be to show how mereological and topological reasoningwhich we take to be among the basic tools for ontological analysisprovides adequate grounds for the construction of temporal relations.
Towards a geometrical understanding of the CPT theorem
, 2007
"... The CPT theorem of quantum field theory states that any relativistic (Lorentzinvariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of th ..."
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The CPT theorem of quantum field theory states that any relativistic (Lorentzinvariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence of a CPT theorem seems to show that it is not possible for a wellformulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable — capable of admitting a temporal orientation — this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a littleknown classical analog of the CPT theorem. 1
Geometry and Motion
, 2005
"... I will discuss only one of the several entwined strands of the philosophy of ..."
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I will discuss only one of the several entwined strands of the philosophy of
The Quantization of Gravity — an introduction
, 2000
"... This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically been the two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The quantization of gravity is discussed by analogy with th ..."
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This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically been the two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The quantization of gravity is discussed by analogy with the quantization of the electromagnetic field. The conceptual and technical problems of both approaches are discussed, and the paper concludes with a discussion of evidence for quantum gravity from the rest of physics. The paper assumes some familiarity with nonrelativistic quantum mechanics, special relativity, and the Lagrangian and Hamiltonian formulations of classical mechanics; some experience with classical field theory, quantum electrodynamics and the gauge principle in electromagnetism might be helpful but is not required. No knowledge of general relativity or of quantum field theory in general is assumed. 1
On the calculating power of Laplace’s demon (Part I)
, 2006
"... We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a s ..."
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We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a start on our programme by proposing a general logical framework for describing physical theories, and analysing several possible formulations of a simple Newtonian theory from the point of view of determinism. Our emphasis throughout is on clarifying the precise physical and metaphysical assumptions that typically underlie a claim that some physical theory is ‘deterministic’. A sequel paper is planned, in which we shall apply similar methods to the analysis of other physical theories. Along the way, we discuss some possible repercussions of this kind of investigation for both physics and logic. 1
Holism and Structuralism in Classical and Quantum GR
 FORTHCOMING IN STRUCTURALISM AND QUANTUM GRAVITY, S.FRENCH (ED.), OUP
, 2004
"... The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from ongoing attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus ..."
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The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from ongoing attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the related question of the identity of points, by basing our investigation on the Hamiltonian formulation of GR. In particular, we argue that the adoption of a peculiar gaugefixing within the canonical reduction of ADM metric gravity may yield a new solution to the debate between substantivalists and relationists, by suggesting a tertium quid between these two ageold positions. Such a third position enables us to evaluate the controversial relationship between entity realism and structural realism in a welldefined case study. After having indicated the possible developments of this approach in Quantum