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  1. How to Teach General Relativity.Guy Hetzroni & James Read - forthcoming - British Journal for the Philosophy of Science.
    Supposing that one is already familiar with special relativistic physics, what constitutes the best route via which to arrive at the architecture of the general theory of relativity? Although the later Einstein would stress the significance of mathematical and theoretical principles in answering this question, in this article we follow the lead of the earlier Einstein (circa 1916) and stress instead how one can go a long way to arriving at the general theory via inductive and empirical principles, without invoking (...)
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  • Watching the Clocks: Interpreting the Page–Wootters Formalism and the Internal Quantum Reference Frame Programme.Emily Adlam - 2022 - Foundations of Physics 52 (5):1-49.
    We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an (...)
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  • Four Attitudes Towards Singularities in the Search for a Theory of Quantum Gravity.Karen Crowther & Sebastian De Haro - 2022 - In Antonio Vassallo (ed.), The Foundations of Spacetime Physics: Philosophical Perspectives. New York, NY: Routledge. pp. 223-250.
    Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is to achieve. Here, we first evaluate how particular types of singularities may suggest an incompleteness of current theories. We then classify four different 'attitudes' towards singularities in the search for QG, and show, through examples in the physics literature, that these lead to (...)
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  • Does General Relativity Highlight Necessary Connections in Nature?Antonio Vassallo - 2021 - Synthese 199 (1-2):1-23.
    The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...)
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  • The Equivalence Principle(s).Dennis Lehmkuhl - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    I discuss the relationship between different versions of the equivalence principle in general relativity, among them Einstein's equivalence principle, the weak equivalence principle, and the strong equivalence principle. I show that Einstein's version of the equivalence principle is intimately linked to his idea that in GR gravity and inertia are unified to a single field, quite like the electric and magnetic field had been unified in special relativistic electrodynamics. At the same time, what is now often called the strong equivalence (...)
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  • The Hole Argument in Homotopy Type Theory.James Ladyman & Stuart Presnell - 2020 - Foundations of Physics 50 (4):319-329.
    The Hole Argument is primarily about the meaning of general covariance in general relativity. As such it raises many deep issues about identity in mathematics and physics, the ontology of space–time, and how scientific representation works. This paper is about the application of a new foundational programme in mathematics, namely homotopy type theory, to the Hole Argument. It is argued that the framework of HoTT provides a natural resolution of the Hole Argument. The role of the Univalence Axiom in the (...)
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  • Franco Selleri and the rotating disk.Alexander Afriat - unknown
    I concentrate on the \emph{pars destruens}, rather than the \emph{pars construens}, of Selleri's work on the Sagnac effect. He speaks of the ``impossibilità di spiegare la fisica sulla piattaforma ruotante con la TRS,'' and may have a point. By confining our attention to the world-cylinder above a circle on the disk we avoid broader integrability issues that just cause confusion. A rate of rotation foliates the cylinder into timelike spirals, and also into the simultaneity spirals hyperbolically orthogonal to them; together (...)
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  • Erich Kretschmann as a proto-logical-empiricist: Adventures and misadventures of the point-coincidence argument.Marco Giovanelli - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (2):115-134.
    The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (...)
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  • False Vacuum: Early Universe Cosmology and the Development of Inflation.Chris Smeenk - 2005 - In Eisenstaedt Jean & Knox A. J. (eds.), The Universe of General Relativity. Birkhauser. pp. 223-257.
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  • (1 other version)Reviews. [REVIEW]Michael Redhead - 1985 - British Journal for the Philosophy of Science 36 (1):100-104.
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  • (1 other version)‘But one must not legalize the mentioned sin’: Phenomenological vs. dynamical treatments of rods and clocks in Einstein׳s thought.Marco Giovanelli - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (1):20-44.
    The paper offers a historical overview of Einstein's oscillating attitude towards a "phenomenological" and "dynamical" treatment of rods and clocks in relativity theory. Contrary to what it has been usually claimed in recent literature, it is argued that this distinction should not be understood in the framework of opposition between principle and constructive theories. In particular Einstein does not seem to have plead for a "dynamical" explanation for the phenomenon rods contraction and clock dilation which was initially described only "kinematically". (...)
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  • General Covariance, Diffeomorphism Invariance, and Background Independence in 5 Dimensions.Antonio Vassallo - 2015 - In Tomasz Bigaj & Christian Wüthrich (eds.), Metaphysics in Contemporary Physics. Boston: Brill | Rodopi.
    The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum non-locality (...)
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  • Einstein and Relativity: What Price Fame?David E. Rowe - 2012 - Science in Context 25 (2):197-246.
    ArgumentEinstein's initial fame came in late 1919 with a dramatic breakthrough in his general theory of relativity. Through a remarkable confluence of events and circumstances, the mass media soon projected an image of the photogenic physicist as a bold new revolutionary thinker. With his theory of relativity Einstein had overthrown outworn ideas about space and time dating back to Newton's day, no small feat. While downplaying his reputation as a revolutionary, Einstein proved he was well cast for the role of (...)
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  • A Case for Lorentzian Relativity.Daniel Shanahan - 2014 - Foundations of Physics 44 (4):349-367.
    The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One (...)
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  • The Definition of Mach’s Principle.Julian Barbour - 2010 - Foundations of Physics 40 (9-10):1263-1284.
    Two definitions of Mach’s principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity.
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  • (1 other version)Talking at cross-purposes: how Einstein and the logical empiricists never agreed on what they were disagreeing about.Marco Giovanelli - 2013 - Synthese 190 (17):3819-3863.
    By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod objection” against (...)
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  • Substantivalist and Relationalist Approaches to Spacetime.Oliver Pooley - 2013 - In Robert Batterman (ed.), The Oxford Handbook of Philosophy of Physics. Oxford University Press USA.
    Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...)
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  • Substantive General Covariance: Another Decade of Dispute.Oliver Pooley - 2009 - In Mauricio Suárez, Mauro Dorato & Miklós Rédei (eds.), EPSA Philosophical Issues in the Sciences: Launch of the European Philosophy of Science Association. Dordrecht, Netherland: Springer. pp. 197--209.
    John Earman's recent proposal that a substantive version of general covariance consists in the requirement that diffeomorphism invariance be a gauge symmetry is critically assessed. I argue that such a principle does not serve to differentiate general relativity from pre-relativistic theories. A model-theoretic characterization of two formulations of specially-relativistic theories is suggested. Diffeomorphisms are symmetries of only one such style of formulation and, I argue, Earman's proposal does not provide a reason to deny diffeomorphisms the status of gauge transformations relative (...)
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  • Did Einstein stumble? The debate over general covariance.John D. Norton - 1995 - Erkenntnis 42 (2):223 - 245.
    The objection that Einstein's principle of general covariance is not a relativity principle and has no physical content is reviewed. The principal escapes offered for Einstein's viewpoint are evaluated.
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  • Why did Einstein's programme supersede lorentz's? (II).Elie Zahar - 1973 - British Journal for the Philosophy of Science 24 (3):223-262.
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  • Nothing but coincidences: the point-coincidence and Einstein’s struggle with the meaning of coordinates in physics.Marco Giovanelli - 2021 - European Journal for Philosophy of Science 11 (2):1-64.
    In his 1916 review paper on general relativity, Einstein made the often-quoted oracular remark that all physical measurements amount to a determination of coincidences, like the coincidence of a pointer with a mark on a scale. This argument, which was meant to express the requirement of general covariance, immediately gained great resonance. Philosophers such as Schlick found that it expressed the novelty of general relativity, but the mathematician Kretschmann deemed it as trivial and valid in all spacetime theories. With the (...)
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  • The relativity of inertia and reality of nothing.Alexander Afriat & Ermenegildo Caccese - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):9-26.
    The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaning---which is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energy-momentum---is considered, along with the dependence of reality on invariance and of causal explanation (...)
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  • Background Independence, Diffeomorphism Invariance, and the Meaning of Coordinates.Oliver Pooley - 2016 - In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. New York, NY: Birkhauser.
    Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the ``observables'') of background-independent theories and those of background-dependent (non-diffeomorphism-invariant) theories are essentially different in nature. I argue against both claims. Background-dependent theories can be formulated in a diffeomorphism-invariant manner. This suggests that the nature of the physical magnitudes of relevantly analogous theories (one background free, the other background dependent) is essentially the same. The temptation (...)
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  • Effective spacetime geometry.Eleanor Knox - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):346-356.
    I argue that the need to understand spacetime structure as emergent in quantum gravity is less radical and surprising it might appear. A clear understanding of the link between general relativity's geometrical structures and empirical geometry reveals that this empirical geometry is exactly the kind of thing that could be an effective and emergent matter. Furthermore, any theory with torsion will involve an effective geometry, even though these theories look, at first glance, like theories with straightforward spacetime geometry. As it's (...)
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  • Interpreting Heisenberg interpreting quantum states.Simon Friederich - 2012 - Philosophia Naturalis 50 (1):85-114.
    The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...)
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  • Events and Observables in Generally Invariant Spacetime Theories.Hans Westman & Sebastiano Sonego - 2008 - Foundations of Physics 38 (10):908-915.
    We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.
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  • On the ontology of spacetime in a frame of reference.Alexander Poltorak - unknown
    The spacetime ontology is considered in General Relativity (GR) in view of the choice of a frame of reference (FR). Various approaches to a description of the FR, such as coordinate systems, monads and tetrads are reviewed. It is shown that any of the existing FR definitions require a preexisting background spacetime, which, if defined independently of the FR, renders the spacetime absolute in violation of the principle of relativity, or, if defined within an inertial FR (IFR), as it is (...)
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  • Einstein’s Principle of Equivalence and the Heuristic Significance of General Covariance.Joseph K. Cosgrove - 2021 - Foundations of Physics 51 (1):1-23.
    The philosophy of physics literature contains conflicting claims on the heuristic significance of general covariance. Some authors maintain that Einstein's general relativity distinguishes itself from other theories in that it must be generally covariant, for example, while others argue that general covariance is a physically vacuous and trivial requirement applicable to virtually any theory. Moreover, when general covariance is invested with heuristic significance, that significance as a rule is assigned to so-called “active” general covariance, underwritten by the principle of background (...)
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  • General-Relativistic Covariance.Neil Dewar - 2020 - Foundations of Physics 50 (4):294-318.
    This is an essay about general covariance, and what it says about spacetime structure. After outlining a version of the dynamical approach to spacetime theories, and how it struggles to deal with generally covariant theories, I argue that we should think about the symmetry structure of spacetime rather differently in generally-covariant theories compared to non-generally-covariant theories: namely, as a form of internal rather than external symmetry structure.
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  • The Dynamical Approach to Spacetime Theories.Harvey R. Brown & James Read - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    We review the dynamical approach to spacetime theories---in particular, its origins in the development of special relativity, its opposition to the contemporary `geometrical' approach, and the manner in which it plays out in general relativity. In addition, we demonstrate that the approach is compatible with the `angle bracket school'.
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  • Artificial versus Substantial Gauge Symmetries: A Criterion and an Application to the Electroweak Model.Jordan François - 2019 - Philosophy of Science 86 (3):472-496.
    To systematically answer the generalized Kretschmann objection, I propose a mean to make operational a criterion widely recognized as allowing one to decide whether the gauge symmetry of a theory is artificial or substantial. My proposition is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. This general scheme allows one in particular to straightforwardly argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak theory. (...)
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  • Einstein, the reality of space, and the action-reaction principle.Dennis Lehmkuhl, P. Ghose & Harvey Brown - unknown
    Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both (...)
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  • Logic of Gauge.Alexander Afriat - 2019 - In Carlos Lobo & Julien Bernard (eds.), Weyl and the Problem of Space: From Science to Philosophy. Springer Verlag.
    The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements---which for want of better terms can be called \emph{geometrical justice}, \emph{matter wave}, \emph{second clock effect}, \emph{twice too many energy levels}---are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a \emph{non-Abelian structure group} (say $\mathbb{SU}\textrm{(}N\textrm{)}$).
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  • Schlick, Conventionalism, and Scientific Revolutions.Steven Bland - 2012 - Acta Analytica 27 (3):307-323.
    Abstract Schlick quite clearly maintains that the shift from classical physics to the theories of relativity is not necessitated by experience, but motivated by the pragmatic payoff of simplifying space-time ontology. However, there is in his work another, heretofore unrecognized argument for the revolutionary shift from classical to relativistic physics. According to this conceptual line of argument, the principles that define simultaneity and motion in classical physics fail to establish a univocal correspondence to physical quantities, and therefore must be revised, (...)
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  • Einstein's theories and the critics of Newton.M. Strauss - 1968 - Synthese 18 (2-3):251 - 284.
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  • Geometrical Constructivism and Modal Relationalism: Further Aspects of the Dynamical/Geometrical Debate.James Read - 2020 - International Studies in the Philosophy of Science 33 (1):23-41.
    I draw together some recent literature on the debate between dynamical versus geometrical approaches to spacetime theories, in order to argue that there exist defensible versions of the geometr...
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  • Conventionalism in Early Analytic Philosophy and the Principle of Relativity.Ori Belkind - 2020 - Erkenntnis 87 (2):827-852.
    In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms, the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities, and conventions that are made possible by (...)
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  • Lost in the tensors: Einstein's struggles with covariance principles 1912–1916.John Earman & Clark Glymour - 1978 - Studies in History and Philosophy of Science Part A 9 (4):251-278.
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  • Mesh and measure in early general relativity.Olivier Darrigol - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):163-187.
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  • Leibniz Equivalence. On Leibniz's Influence on the Logical Empiricist Interpretation of General Relativity.Marco Giovanelli - unknown
    Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...)
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  • Einstein, Cassirer, and General Covariance — Then and Now.T. A. Ryckman - 1999 - Science in Context 12 (4):585-619.
    The ArgumentRecent archival research has brought about a new understanding of the import of Einstein's puzzling remarks (1916) attributing a physical meaning to general covariance. Debates over the scope and meaning of general covariance still persist, even within physics. But already in 1921 Cassirer identified the significance of general covariance as a novel stage in the development of the criterion of objectivity within physics; an account of this development, and its implications, is the primary task undertaken in his monograph of (...)
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  • Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity.Karen Crowther - 2014 - Dissertation, University of Sydney
    Quantum gravity is understood as a theory that, in some sense, unifies general relativity (GR) and quantum theory, and is supposed to replace GR at extremely small distances (high-energies). It may be that quantum gravity represents the breakdown of spacetime geometry described by GR. The relationship between quantum gravity and spacetime has been deemed ``emergence'', and the aim of this thesis is to investigate and explicate this relation. After finding traditional philosophical accounts of emergence to be inappropriate, I develop a (...)
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  • A Metaphysical Reflection on the Notion of Background in Modern Spacetime Physics.Antonio Vassallo - 2016 - In Laura Felline (ed.), New Developments in Logic and Philosophy of Science. pp. 349-365.
    The paper presents a metaphysical characterization of spatiotemporal backgrounds from a realist perspective. The conceptual analysis is based on a heuristic sketch that encompasses the common formal traits of the major spacetime theories, such as Newtonian mechanics and general relativity. It is shown how this framework can be interpreted in a fully realist fashion, and what is the role of background structures in such a picture. In the end it is argued that, although backgrounds are a source of metaphysical discomfort, (...)
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  • Einstein and the Representation of Reality.Friedel Weinert - 2006 - Facta Philosophica 8 (1-2):229-252.
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  • Coordinates, observables and symmetry in relativity.Hans Westman & Sebastiano Sonego - unknown
    We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a "point-coincidence" between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a (...)
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  • 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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  • (1 other version)Another look at general covariance and the equivalence of reference frames.Dennis Dieks - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (1):174-191.
    In his general theory of relativity Einstein sought to generalize the special-relativistic equivalence of inertial frames to a principle according to which all frames of reference are equivalent. He claimed to have achieved this aim through the general covariance of the equations of GR. There is broad consensus among philosophers of relativity that Einstein was mistaken in this. That equations can be made to look the same in different frames certainly does not imply in general that such frames are physically (...)
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  • 'No success like failure ...': Einstein's Quest for general relativity, 1907-1920.Michel Janssen - unknown
    This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.
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  • Who's afraid of background independence?Dean Rickles - 2008 - In Dennis Geert Bernardus Johan Dieks (ed.), The Ontology of Spacetime II. Elsevier. pp. 133--52.
    Background independence is generally considered to be ‘the mark of distinction’ of general relativity. However, there is still confusion over exactly what background independence is and how, if at all, it serves to distinguish general relativity from other theories. There is also some confusion over the philosophical implications of background independence, stemming in part from the definitional problems. In this paper I attempt to make some headway on both issues. In each case I argue that a proper account of the (...)
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  • (1 other version)Einstein’s First Systematic Exposition of General Relativity.Michel Janssen - unknown
    This paper will serve as the editorial note on Einstein's 1916 review article on general relativity in a planned volume with all of Einstein's papers in Annalen der Physik. It summarizes much of my other work on history of general relativity and draws heavily on the annotation of Einstein's writings and correspondence on general relativity for Vols. 4, 7, and 8 of the Einstein edition.
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