Results for 'Bohr-Sommerfeld Quantization in General Relativity'

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  1. Bohr-Sommerfeld Quantization in General Relativity and Other Nonlinear Field and Particle Theories.Robert Hermann - 1980 - In A. R. Marlow (ed.), Quantum Theory and Gravitation. Academic Press. pp. 1--95.
     
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  2. Robert Hermann.Bohr-Sommerfeld Quantization in General Relativity - 1980 - In A. R. Marlow (ed.), Quantum Theory and Gravitation. Academic Press.
     
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  3.  98
    Deriving General Relativity From String Theory.Nick Huggett & Tiziana Vistarini - 2015 - Philosophy of Science 82 (5):1163-1174.
    Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain (...)
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  4.  41
    Area in Phase Space as Determiner of Transition Probability: Bohr-Sommerfeld Bands, Wigner Ripples, and Fresnel Zones. [REVIEW]W. Schleich, H. Walther & J. A. Wheeler - 1988 - Foundations of Physics 18 (10):953-968.
    We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both—to a “squeeze” in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner (...)
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  5.  67
    Energy and Angular Momentum of Systems in General Relativity.F. I. Cooperstock - 2001 - Foundations of Physics 31 (7):1067-1082.
    Stemming from our energy localization hypothesis that energy in general relativity is localized in the regions of the energy-momentum tensor, we had devised a test with the classic Eddington spinning rod. Consistent with the localization hypothesis, we found that the Tolman energy integral did not change in the course of the motion. This implied that gravitational waves do not carry energy in vacuum, bringing into question the demand for the quantization of gravity. Also if information is conveyed (...)
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  6.  22
    Elementary Particle Physics From General Relativity.Mendel Sachs - 1981 - Foundations of Physics 11 (3-4):329-354.
    This paper presents a qualitative comparison of opposing views of elementary matter—the Copenhagen approach in quantum mechanics and the theory of general relativity. It discusses in detail some of their main conceptual differences, when each theory is fully exploited as a theory of matter, and it indicates why each of these theories, at its presently accepted state, is incomplete without the other. But it is then argued on logical grounds that they cannot be fused, thus indicating the need (...)
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  7.  34
    Radial Quantization in Rotating Space–Times.Robert D. Bock - 2007 - Foundations of Physics 37 (6):977-988.
    We examine the time discontinuity in rotating space–times for which the topology of time is S1. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also (...)
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  8.  38
    Quantum Theory and Einstein's General Relativity.H. -H. V. Borzeszkowski & H. -J. Treder - 1982 - Foundations of Physics 12 (11):1113-1129.
    We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have (...)
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  9.  8
    A Fundamental Problem in Quantizing General Relativity.Lorenzo Maccone - 2019 - Foundations of Physics 49 (12):1394-1403.
    We point out a fundamental problem that hinders the quantization of general relativity: quantum mechanics is formulated in terms of systems, typically limited in space but infinitely extended in time, while general relativity is formulated in terms of events, limited both in space and in time. Many of the problems faced while connecting the two theories stem from the difficulty in shoe-horning one formulation into the other. A solution is not presented, but a list of (...)
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  10. Dependence relations in general relativity.Antonio Vassallo - 2020 - European Journal for Philosophy of Science 10 (1):1-28.
    The paper discusses from a metaphysical standpoint the nature of the dependence relation underpinning the talk of mutual action between material and spatiotemporal structures in general relativity. It is shown that the standard analyses of dependence in terms of causation or grounding are ill-suited for the general relativistic context. Instead, a non-standard analytical framework in terms of structural equation modeling is exploited, which leads to the conclusion that the kind of dependence encoded in the Einstein field equations (...)
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  11.  16
    Geometry and Motion in General Relativity.James Owen Weatherall - unknown
    A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent paper [Geroch & Weatherall, "The Motion of Small Bodies in Space-Time", Comm. Math. Phys. ], Bob Geroch and I have introduced a new approach to this problem, based on a notion we call "tracking". In the present paper, I situate the main (...)
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  12.  53
    Crafting the Quantum: Arnold Sommerfeld and the Older Quantum Theory.Suman Seth - 2008 - Studies in History and Philosophy of Science Part A 39 (3):335-348.
    Arnold Sommerfeld was among the most important students of the so-called ‘older’ quantum theory. His many contributions included papers in 1915 and 1916 extending Niels Bohr’s ‘planetary’ model of the atom beyond circular orbits and his incorporation of relativistic corrections in order to explain hydrogenic fine structure. Originally a realist in his use of Bohr’s model, Sommerfeld became increasingly disillusioned with model-building in general in the late nineteen-teens and early nineteen-twenties. This paper explores Sommerfeld’s (...)
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  13. Sommerfeld, the Quantum, and the Problem Approach to Physics: Suman Seth: Crafting the Quantum: Arnold Sommerfeld and the Practice of Theory, 1890–1926. Cambridge, MA: MIT Press, 2010, Viii+378 Pp, US $32.00 HB.Helge Kragh - 2011 - Metascience 20 (1):87-90.
    In the early phase of the new history of physics that emerged at about 1970 and was pioneered by John Heilbron, Thomas Kuhn, Paul Forman, and others, the quantum and atomic theories of the first three decades of the twentieth century played a central role. Since then, interest in the area has continued, but for the last few decades at a slower rate. While other areas of the new physics—such as the general theory of relativity—have attracted much attention, (...)
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  14.  93
    Is Prediction Possible in General Relativity?John Byron Manchak - 2008 - Foundations of Physics 38 (4):317-321.
    Here we briefly review the concept of "prediction" within the context of classical relativity theory. We prove a theorem asserting that one may predict one's own future only in a closed universe. We then question whether prediction is possible at all (even in closed universes). We note that interest in prediction has stemmed from considering the epistemological predicament of the observer. We argue that the definitions of prediction found thus far in the literature do not fully appreciate this predicament. (...)
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  15. Conceptual and Foundational Issues in the Quantization of Gravity.Steven Weinstein - 1998 - Dissertation, Northwestern University
    The quantization of gravity represents an important attempt at reconciling the two seemingly incompatible frameworks that lie at the base of modern physics, quantum theory and general relativity. The dissertation begins by looking at the incompatibilities between the two frameworks. The incompatibility with quantum theory, it is argued, is rooted in the profound differences between general relativity and ordinary field theories. The dissertation goes on to look at how, in practice, these incongruities are treated in (...)
     
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  16.  36
    Spinors and Torsion in General Relativity.Roger Penrose - 1983 - Foundations of Physics 13 (3):325-339.
    Conformal rescalings of spinors are considered, in which the factor Ω, inε AB ↦Ωε AB, is allowed to be complex. It is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative▽ a. It is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a (nonlocal) rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsion of the Einstein-Cartan-Sciama-Kibble theory. The results of these deliberations (...)
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  17. The Origins of the Spacetime Metric: Bell’s Lorentzian Pedagogy and its Significance in General Relativity.Harvey R. Brown & Oliver Pooley - 1999 - In Craig Callender & Nick Huggett (eds.), Physics Meets Philosophy at the Plank Scale. Cambridge University Press. pp. 256--72.
    The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general (...). (shrink)
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  18.  83
    A Remark About the "Geodesic Principle" in General Relativity.David Malament - unknown
    It is often claimed that the geodesic principle can be recovered as a theorem in general relativity. Indeed, it is claimed that it is a consequence of Einstein's equation (or of the conservation principle that is, itself, a consequence of that equation). These claims are certainly correct, but it may be worth drawing attention to one small qualification. Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein's (...)
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  19.  7
    Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity.J. Brian Pitts - unknown
    Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the (...)
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  20.  47
    Change in Hamiltonian General Relativity From the Lack of a Time-Like Killing Vector Field.J. Brian Pitts - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:68-89.
    In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially _tuned sum_ of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in (...)
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  21.  11
    Literal Versus Careful Interpretations of Scientific Theories: The Vacuum Approach to the Problem of Motion in General Relativity.Dennis Lehmkuhl - 2017 - Philosophy of Science 84 (5):1202-1214.
    The problem of motion in general relativity is about how exactly the gravitational field equations, the Einstein equations, are related to the equations of motion of material bodies subject to gravitational fields. This article compares two approaches to derive the geodesic motion of matter from the field equations: the ‘T approach’ and the ‘vacuum approach’. The latter approach has been dismissed by philosophers of physics because it apparently represents material bodies by singularities. I argue that a careful interpretation (...)
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  22. On the Role of Special Relativity in General Relativity.Harvey R. Brown - 1997 - International Studies in the Philosophy of Science 11 (1):67 – 81.
    The existence of a definite tangent space structure (metric with Lorentzian signature) in the general theory of relativity is the consequence of a fundamental assumption concerning the local validity of special relativity. There is then at the heart of Einstein's theory of gravity an absolute element which depends essentially on a common feature of all the non-gravitational interactions in the world, and which has nothing to do with space-time curvature. Tentative implications of this point for the significance (...)
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  23.  19
    Classical Elementary Particles in General Relativity.Mark Israelit & Nathan Rosen - 1991 - Foundations of Physics 21 (10):1237-1247.
    Elementary particles, regarded as the constituents of quarks and leptons, are described classically in the framework of the general relativity theory. There are neutral particles and particles having charges±1/3e. They are taken to be spherically symmetric and to have mass density, pressure, and (if charged) charge density. They are characterized by an equation of state P=−ρ suggested by earlier work on cosmology. The neutral particle has a very simple structure. In the case of the charged particle there is (...)
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  24.  76
    On the Possibility of Supertasks in General Relativity.John Byron Manchak - 2010 - Foundations of Physics 40 (3):276-288.
    Malament-Hogarth spacetimes are the sort of models within general relativity that seem to allow for the possibility of supertasks. There are various ways in which these spacetimes might be considered physically problematic. Here, we examine these criticisms and investigate the prospect of escaping them.
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  25.  43
    Fantastic Beasts and Where to Find Them: Local Gravitational Energy and Energy Conservation in General Relativity.Patrick M. Duerr - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 65:1-14.
  26.  8
    When Modern Physics Meets Nature of Science: The Representation of Nature of Science in General Relativity in New Korean Physics Textbooks.Wonyong Park, Seungran Yang & Jinwoong Song - 2019 - Science & Education 28 (9-10):1055-1083.
    The social reaction to the recent detection of the Higgs boson and gravitational waves provided evidence that public interest in modern physics has reached a high point. Although these modern physics topics are being introduced into the upper secondary physics curricula in a growing number of countries, their potential for teaching various aspects of scientific practice have yet to be explored. This article responds to this call by providing an analysis of new South Korean high school physics textbooks’ representations of (...)
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  27. Change Without Change, and How to Observe It in General Relativity.Richard Healey - 2004 - Synthese 141 (3):381 - 415.
    All change involves temporal variation of properties. There is change in the physical world only if genuine physical magnitudes take on different values at different times. I defend the possibility of change in a general relativistic world against two skeptical arguments recently presented by John Earman. Each argument imposes severe restrictions on what may count as a genuine physical magnitude in general relativity. These restrictions seem justified only as long as one ignores the fact that genuine change (...)
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  28.  8
    Equivalent Theories and Changing Hamiltonian Observables in General Relativity.J. Brian Pitts - 2018 - Foundations of Physics 48 (5):579-590.
    Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms (...)
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  29.  35
    If Metrical Structure Were Not Dynamical, Counterfactuals in General Relativity Would Be Easy.Erik Curiel - unknown
    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 (...)
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  30.  14
    General Relativity, Mental Causation, and Energy Conservation.J. Brian Pitts - forthcoming - Erkenntnis:1-43.
    The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, (...)
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  31. Prediction in General Relativity.C. McCoy - 2017 - Synthese 194 (2):491-509.
    Several authors have claimed that prediction is essentially impossible in the general theory of relativity, the case being particularly strong, it is said, when one fully considers the epistemic predicament of the observer. Each of these claims rests on the support of an underdetermination argument and a particular interpretation of the concept of prediction. I argue that these underdetermination arguments fail and depend on an implausible explication of prediction in the theory. The technical results adduced in these arguments (...)
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  32.  73
    The Role of Rods and Clocks in General Relativity and the Meaning of the Metric Field.Harvey Brown & D. E. Rowe - unknown
  33.  8
    Interpreting Non-Hausdorff (Generalized) Manifolds in General Relativity.Joanna Luc & Tomasz Placek - 2020 - Philosophy of Science 87 (1):21-42.
    The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.
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  34.  39
    Two Miracles of General Relativity.James Read, Harvey R. Brown & Dennis Lehmkuhl - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 64:14-25.
    We approach the physics of \emph{minimal coupling} in general relativity, demonstrating that in certain circumstances this leads to violations of the \emph{strong equivalence principle}, which states that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the \emph{dynamical perspective on relativity}, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we (...)
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  35. The Twins and the Bucket: How Einstein Made Gravity Rather Than Motion Relative in General Relativity.Michel Janssen - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (3):159-175.
    In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time (...)
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  36.  9
    General Relativity with a Background Metric.Nathan Rosen - 1980 - Foundations of Physics 10 (9-10):673-704.
    An attempt is made to remove singularities arising in general relativity by modifying it so as to take into account the existence of a fundamental rest frame in the universe. This is done by introducing a background metric γμν (in addition to gμν) describing a spacetime of constant curvature with positive spatial curvature. The additional terms in the field equations are negligible for the solar system but important for intense fields. Cosmological models are obtained without singular states but (...)
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  37. On the Existence of “Time Machines” in General Relativity.John Manchak - 2009 - Philosophy of Science 76 (5):1020-1026.
    Within the context of general relativity, we consider one definition of a “time machine” proposed by Earman, Smeenk, and Wüthrich. They conjecture that, under their definition, the class of time machine spacetimes is not empty. Here, we prove this conjecture. †To contact the author, please write to: Department of Philosophy, University of Washington, Box 353350, Seattle, WA 98195‐3350; e‐mail: manchak@uw.edu.
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  38. Does General Relativity Allow an Observer to View an Eternity in a Finite Time?Mark Hogarth - 1992 - Foundations Of Physics Letters 5:173--181.
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  39.  53
    On the Ontological Status of the Metric in General Relativity.Robert Weingard - 1975 - Journal of Philosophy 72 (14):426-431.
  40.  94
    Why General Relativity Does Need an Interpretation.Gordon Belot - 1996 - Philosophy of Science 63 (3):88.
    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 (...)
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  41. General Relativity Needs No Interpretation.Erik Curiel - 2009 - 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 (...)
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  42.  11
    The Twins and the Bucket: How Einstein Made Gravity Rather Than Motion Relative in General Relativity.Michel Janssen - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (3):159-175.
    In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time coordinate system (...)
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  43. Is There Incompatibility Between the Ways Time is Treated in General Relativity and in Standard Quantum Mechanics.Carlo Rovelli - 1991 - In A. Ashtekar & J. Stachel (eds.), Conceptual Problems of Quantum Gravity. Birkhauser. pp. 126--140.
     
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  44.  66
    On the Status of the "Geodesic Law" in General Relativity.David Malament - unknown
    Harvey Brown believes it is crucially important that the "geodesic principle" in general relativity is an immediate consequence of Einstein's equation and, for this reason, has a different status within the theory than other basic principles regarding, for example, the behavior of light rays and clocks, and the speed with which energy can propagate. He takes the geodesic principle to be an essential element of general relativity itself, while the latter are better seen as contingent facts (...)
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  45.  21
    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.
  46.  26
    On the Reduction of General Relativity to Newtonian Gravitation.Samuel C. Fletcher - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 68:1-15.
    Intertheoretic reduction in physics aspires to be both to be explanatory and perfectly general: it endeavors to explain why an older, simpler theory continues to be as successful as it is in terms of a newer, more sophisticated theory, and it aims to relate or otherwise account for as many features of the two theories as possible. Despite often being introduced as straightforward cases of intertheoretic reduction, candidate accounts of the reduction of general relativity to Newtonian gravitation (...)
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  47. The Ontology of General Relativity.Gustavo E. Romero - forthcoming - In M. Novello & S. E. Perez Bergliaffa (eds.), General Relativity and Gravitation. Cambridge University Press.
    I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges from physical relations among all existents. I also argue that there are no physical singularities in space-time. Singular space-time models do not belong to the ontology of the world: they are not things but concepts, i.e. defective solutions of Einstein’s field equations. I (...)
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  48.  48
    The Energy of a Dynamical Wave-Emitting System in General Relativity.F. I. Cooperstock & S. Tieu - 2003 - Foundations of Physics 33 (7):1033-1059.
    The problem of energy and its localization in general relativity is critically re-examined. The Tolman energy integral for the Eddington spinning rod is analyzed in detail and evaluated apart from a single term. It is shown that a higher order iteration is required to find its value. Details of techniques to solve mathematically challenging problems of motion with powerful computing resources are provided. The next phase of following a system from static to dynamic to final quasi-static state is (...)
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  49.  38
    On the Elementarity of Measurement in General Relativity: Toward a General Theory.Mendel Sachs - 1967 - Synthese 17 (1):29 - 53.
  50.  95
    On the Logical Status of Equivalence Principles in General Relativity Theory.Mendel Sachs - 1976 - British Journal for the Philosophy of Science 27 (3):225-229.
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