The Hole Argument for Covariant Theories
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General Relativity and Cosmology: Unsolved Questions and Future Directions
Article General Relativity and Cosmology: Unsolved Questions and Future Directions Ivan Debono 1,∗,† and George F. Smoot 1,2,3,† 1 Paris Centre for Cosmological Physics, APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France; [email protected] 2 Physics Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, 94720 CA, USA 3 Helmut and Anna Pao Sohmen Professor-at-Large, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China * Correspondence: [email protected]; Tel.: +33-1-57276991 † These authors contributed equally to this work. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 August 2016; Accepted: 14 September 2016; Published: 28 September 2016 Abstract: For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR. -
Conceptual Barriers to a Unified Theory of Physics 1 Introduction
Conceptual barriers to a unified theory of physics Dennis Crossley∗ Dept. of Physics, University of Wisconsin-Sheboygan, Sheboygan, WI 53081 August 31, 2012 Abstract The twin pillars of twentieth-century physics, quantum theory and general relativity, have conceptual errors in their foundations, which are at the heart of the repeated failures to combine these into a single unified theory of physics. The problem with quantum theory is related to the use of the point-particle model, and the problem with general relativity follows from a misinterpretation of the significance of the equivalence principle. Correcting these conceptual errors leads to a new model of matter called the space wave model which is outlined here. The new perspective gained by space wave theory also makes it clear that there are conceptual errors in the two main thrusts of twenty-first- century theoretical physics, string theory and loop quantum gravity. The string model is no more satisfactory than the point-particle model and the notion that space must be quantized is, frankly, nonsensical. In this paper I examine all of these conceptual errors and suggest how to correct them so that we can once again make progress toward a unified theory of physics. 1 Introduction { the challenge of the unification program The goal of theoretical physics is to construct a single unified description of fundamental particles and their interactions, but flaws in the foundations of physics have prevented physi- cists from achieving this goal. In this essay I examine conceptual errors that have led to this impasse and propose alternatives which break this impasse and let us once again move forward toward the goal of a unified theory of physics. -
(TEGR) As a Gauge Theory: Translation Or Cartan Connection? M Fontanini, E
Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection? M Fontanini, E. Huguet, M. Le Delliou To cite this version: M Fontanini, E. Huguet, M. Le Delliou. Teleparallel gravity (TEGR) as a gauge theory: Transla- tion or Cartan connection?. Physical Review D, American Physical Society, 2019, 99, pp.064006. 10.1103/PhysRevD.99.064006. hal-01915045 HAL Id: hal-01915045 https://hal.archives-ouvertes.fr/hal-01915045 Submitted on 7 Nov 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection? M. Fontanini1, E. Huguet1, and M. Le Delliou2 1 - Universit´eParis Diderot-Paris 7, APC-Astroparticule et Cosmologie (UMR-CNRS 7164), Batiment Condorcet, 10 rue Alice Domon et L´eonieDuquet, F-75205 Paris Cedex 13, France.∗ and 2 - Institute of Theoretical Physics, Physics Department, Lanzhou University, No.222, South Tianshui Road, Lanzhou, Gansu 730000, P R China y (Dated: November 7, 2018) In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). -
The Hole Argument for Covariant Theories 6 2.1 Theory, Models, Covariance and General Covariance
The Hole Argument for Covariant Theories Iftime, M.∗, Stachel, J. † Abstract The hole argument was developed by Einstein in 1913 while he was searching for a relativistic theory of gravitation. Einstein used the lan- guage of coordinate systems and coordinate invariance, rather than the language of manifolds and diffeomorphism invariance. He formulated the hole argument against covariant field equations and later found a way to avoid it using coordinate language. In this paper we shall use the invariant language of categories, mani- folds and natural objects to give a coordinate-free description of the hole argument and a way of avoiding it. Finally we shall point out some im- portant implications of further extensions of the hole argument to sets and relations for the problem of quantum gravity. Keywords: General Relativity, Differential Geometry ∗School of Arts and Sciences, MCPHS, Boston, MA, USA †Department of Physics and Center for Philosophy and History of Science, Boston, MA, USA arXiv:gr-qc/0512021v2 8 Apr 2006 1 Contents 1 The Hole Argument in General Relativity 3 1.1 TheOriginalHoleArgument . 3 1.2 The Hole Argument for Inhomogeneous Einstein’s Field Equations 5 2 The Hole Argument for Covariant Theories 6 2.1 Theory, Models, Covariance and General Covariance . ... 6 2.2 Background Independent vs Background Dependent Theories.. 7 2.3 TheHoleArgumentforGeometricObjects . 8 2.4 Blocking the Formulation of the Hole Argument . 11 3 Conclusion 11 4 Acknowledgements 12 2 1 The Hole Argument in General Relativity 1.1 The Original Hole Argument In Einstein’s most detailed account of the hole argument [3], G(x) represents a metric tensor field that satisfies the field equations in the x-coordinate system and G′(x′) represents the same gravitational field in the x′-coordinate system. -
Quantum Gravity: a Primer for Philosophers∗
Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts. -
Einstein's Hole Argument
Einstein's Hole Argument Alan Macdonald Luther College Decorah, Iowa 52101 [email protected] February 17, 2020 Much improved version of Am. J. Phys. 69, 223-225 (2001) Abstract In general relativity, a spacetime and a gravitational field form an indi- visible unit: no field, no spacetime. This is a lesson of Einstein's hole argument. We use a simple transformation in a Schwartzschild spacetime to illustrate this. On the basis of the general theory of relativity . space as opposed to \what fills space" . has no separate existence. There is no such thing as an empty space, i.e., a space without [a gravitational] field. Space-time does not claim existence on its own, but only as a structural quality of the field. Albert Einstein, 1952. Introduction. What justification can be given for Einstein's words,1 writ- ten late in his life? The answer to this question has its origin in 1913, when Einstein was searching for a field equation for gravity. Einstein was aware of the possibility of generally covariant field equations, but he believed { wrongly, it turned out { that they could not possess the correct Newtonian limit. He then proposed a field equation covariant only under linear coordinate transforma- tions. To buttress his case against generally covariant field equations, Einstein devised his hole argument, which purported to show that no generally covariant field equation can be satisfactory. When Einstein discovered his fully satisfac- tory generally covariant field equation for general relativity in 1915, it became apparent that there is a hole in the argument.2 The twin and pole-in-the-barn \paradoxes" of special relativity3 are invalid arguments whose elucidation helps us better understand the theory. -
On the Goldstonic Gravitation Theory
Pramina-J. Phys., Voi. 29, No. 1, July 1987, pp. 21-37. © Printed in India. On the Goldstonic gravitation theory D IVANENKO and G SARDANASHVILY Physics Faculty, Moscow University, 117234, Moscow, USSR Abstract. The physical specificity of gravity as a Goldstone-typ¢ field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supcrgrav- ity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular"dislocation" structure of a space-time due to Poincar6 translation gauge fields and the corresponding modification of Newton's gravitational potential are predicted. Keywords. Gauge theory; gravity; supergravity; Goldstone field. PACS Nos 04.50; 11.15 1. Introduction The geometric nature of gravity as a metric field was established by Einstein's general relativity which we take as the base of gravitation theory. The physical specificity of gravity as the Goldstone-type field is now clarified by means of gauge approach to gravitation theory (Sardanashvily 1980; Ivanenko and Sardanashvily 1983; Ivanenko et al 1985). At present, gauge theory is well known to provide the theoretical base of most part of current unification attempts in particle physics. Apparently, a necessary step for including gravity in the unified gauge picture of, fundamental interactions consists in constructing a comprehensive gauge gravitation theory itself. We share the opinion of many authors that a gauge gravitation theory must contain Einstein's general relativity as the particular case. However, the main dilemma that one faces is that Einstein's gravitational field is a metric (or tetrad) field, whereas gauge potentials are connections on fibre bundles. -
Regarding the 'Hole Argument' and the 'Problem of Time'
Regarding the ‘Hole Argument’ and the ‘Problem of Time’ Sean Gryb∗1 and Karim P. Y. Th´ebault†2 1Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands 2Department of Philosophy, University of Bristol, United Kingdom December 5, 2015 Abstract The canonical formalism of general relativity affords a particu- larly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argu- ment to the problem of time in classical and quantum gravity. In this paper we examine the connection between these two much dis- cussed problems in the foundations of spacetime theory along two interrelated lines. First, from a formal perspective, we consider the extent to which the two problems can and cannot be precisely and distinctly characterised. Second, from a philosophical perspective, we consider the implications of various responses to the problems, with a particular focus upon the viability of a ‘deflationary’ attitude to the relationalist/substantivalist debate regarding the ontology of space- time. Conceptual and formal inadequacies within the representative language of canonical gravity will be shown to be at the heart of both the canonical hole argument and the problem of time. Interesting and fruitful work at the interface of physics and philosophy relates to the challenge of resolving such inadequacies. ∗email: [email protected] †email: [email protected] 1 Contents 1 Introduction 2 2 The Hole Argument 3 2.1 A Covariant Deflation . .3 2.2 A Canonical Reinflation . .6 3 The Problem of Time 13 3.1 The Problem of Refoliation . -
The Hole Argument and Some Physical and Philosophical Implications
Living Rev. Relativity, 17,(2014),1 ,)6).' 2%6)%73 http://www.livingreviews.org/lrr-2014-1 doi:10.12942/lrr-2014-1 INRELATIVITY The Hole Argument and Some Physical and Philosophical Implications John Stachel Center for Einstein Studies, Boston University 745 Commonwealth Avenue Boston, MA 02215 U.S.A. email: [email protected] Accepted: 17 November 2013 Published: 6 February 2014 Abstract This is a historical-critical study of the hole argument, concentrating on the interface between historical, philosophical and physical issues. Although it includes a review of its history, its primary aim is a discussion of the contemporary implications of the hole argument for physical theories based on dynamical, background-independent space-time structures. The historical review includes Einstein’s formulations of the hole argument, Kretschmann’s critique, as well as Hilbert’s reformulation and Darmois’ formulation of the general-relativistic Cauchy problem. The 1970s saw a revival of interest in the hole argument, growing out of attempts to answer the question: Why did three years elapse between Einstein’s adoption of the metric tensor to represent the gravitational field and his adoption of the Einstein field equations? The main part presents some modern mathematical versions of the hole argument, including both coordinate-dependent and coordinate-independent definitions of covariance and general covariance; and the fiber bundle formulation of both natural and gauge natural theories. By abstraction from continuity and di↵erentiability, these formulations can be extended from di↵erentiable manifolds to any set; and the concepts of permutability and general permutability applied to theories based on relations between the elements of a set, such as elementary particle theories. -
New Perspectives on the Hole Argument
Editorial: New Perspectives on the Hole Argument Bryan W. Roberts and James Owen Weatherall April 29, 2020 Abstract This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives. 1 Introduction Few topics in the philosophy of physics have received more attention in the past forty years than Einstein's hole argument. The history of the subject is perhaps well-known, but worth repeating. In 1913, Einstein presented the hole argument in an effort to show that there could be no adequate \generally covariant" or diffeomorphism-invariant theory of gravity, instead advocating his erroneous Entwurf field equations1. But by the end of 1915, he had rejected the hole argument and the Entwurf theory, in part because he had found general relativity. Over the subse- quent decades, the hole argument would reappear in the work of various groups on quantum gravity, usually together with a standard story: Ein- stein's 1913 blunder was a failure to realise that he had chosen a preferred coordinate system, and so prematurely rejected general covariance. In the Entwurf theory the preferred coordinate system arose in the description of a Newtonian limit, and in the hole argument it arose in the explicit choice of a metric.2 This simple perspective on the hole argument changed following a re- markable event in the history of science: the discovery of Einstein's note- book of scratchpad calculations during those crucial years. They were discovered by John D. -
Reading List in Philosophy of Spacetime and Symmetry David Wallace, June 2018
Reading list in Philosophy of Spacetime and Symmetry David Wallace, June 2018 1. Introduction .............................................................................................................................................. 2 2. Math and Physics resources ...................................................................................................................... 4 3. The substantivalist/relationist debate ...................................................................................................... 6 4. The Hole Argument ................................................................................................................................. 10 5. General Covariance, Background Independence, and the Meaning of Coordinates.............................. 13 6. Dynamical vs geometrical approaches to spacetime theories ............................................................... 15 7. Spacetime structure in pre-relativistic physics ....................................................................................... 17 8. Spacetime topics in quantum gravity ..................................................................................................... 18 9. Philosophy of Symmetry ......................................................................................................................... 19 10. Other topics in special and general relativity ....................................................................................... 22 A note on electronic resources When I include a book -
Spacetime Geometric Structures and the Search for a Quantum Theory of Gravity
Spacetime geometric structures and the search for a Quantum Theory of Gravity Mihaela Iftime Abstract. One of the biggest challenges to theoretical physics of our time is to ¯nd a background-independent quantum theory of gravity. Today one encounters a profusion of di®erent attempts at quantization, but no fully accepted - or acceptable, theory of quantum gravity. Any such approach requires a response to a question that lies at the heart of this problem. \How shall we resolve the tension between the background de- pendence of all hitherto-successful quantum theories, both non-relativistic quantum mechanics and special-relativistic quantum ¯eld theory, and the background independence of classical general relativity?" (see [28]) The need for a background-independent quantization procedure forms the starting point of my approach. In this paper I shall present a gauge-natural formulation of general relativity, and provide some insights into the struc- ture of the space of geometries, which plays an important role in the construction of a non-perturbative quantum gravity using a path integral approach, as well as in string theory (see e.g., [2, 18, 31]) M.S.C. 2000: 53-XX, 83-XX. Key words: Di®erential geometry, Relativity and gravitational theory. 1 Historical-Physical Motivation The most succesful among all gravitational theories is Einstein's theory of general relativity. In general relativity the ¯eld equations 1 are described in purely geometric terms: the space-time is a fairly smooth manifold M of dim n = 4 with a normal hyperbolic Riemannian structure { Lorentzian metric tensor g transforms at each point to the flat Minkowski metric ´ = diag(1; 1; 1; ¡1), and its timelike and null geodesics represent the paths of freely falling particles and light rays.