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Showing papers on "Four-force published in 2007"


Book
01 Sep 2007
TL;DR: The field of Canonical Quantum General Relation (CQGR) as mentioned in this paper is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum.
Abstract: This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory providing a first substantial evidence for a theory in which the gravitational field acts as a natural UV cut-off. An effort has been made to provide a self-contained exposition of a restricted amount of material at the appropriate level of rigour which at the same time is accessible to graduate students with only basic knowledge of general relativity and quantum field theory on Minkowski space.

1,686 citations


Posted Content
TL;DR: The 3+1 formalism of general relativity as mentioned in this paper is the foundation of most modern numerical relativity, and it can be found in the lecture notes of the present paper, with detailed calculations and numerous examples.
Abstract: These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.

326 citations


Book
01 Jan 2007
TL;DR: In this paper, Newtonian physics and special Relativity are discussed, including the special theory of Relativity, and the theory of the Schwarzschild solution and Black Holes, as well as the metric junction method and the Kaluza-Klein theory.
Abstract: I. Introduction: Newtonian Physics and Special Relativity- 1. Relativity Principals and Gravitation 2. The Special Theory of Relativity II. The Mathematics of the General Theory of Relativity- 3. Vectors, Tensors, and Forms 4. Basis Vector Fields and Metric Tensor 5. Non-inertial Reference Frames 6. Differentiation, Connections and Integration 7. Curvature II. Einstein's Field Equations- 8. Einstein's Field Equations 9. The Linear Field Approximation 10. The Schwarzschild Solution and Black Holes IV. Cosmology- 11. Homogeneous and Isotropic Universe Models 12. Universe Models with Vacuum Energy 13. An Anisotropic Universe V. Advanced Topics- 14. Covariant decomposition, Singularities, and Canonical Cosmology 15. Homogeneous Spaces 16. Israel's Formalism: The metric junction method 17. Brane-worlds 18. Kaluza-Klein Theory VI. Appendices- A. Constrants of Nature B. Penrose diagrams C. Anti-de Sitter spacetime D. Suggested further reading

288 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the symmetry group ISIM(2) admits a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincar\'e group: space-time remains flat.
Abstract: We ask whether Cohen and Glashow's very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincar\'e group: space-time remains flat. Only a 1-parameter family ${\mathrm{DISIM}}_{b}(2)$ of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point-particle action invariant under ${\mathrm{DISIM}}_{b}(2)$ is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive ${\mathrm{DISIM}}_{b}(2)$-invariant wave equations for particles of spins 0, $\frac{1}{2}$, and 1. The experimental bound, $|b|l{10}^{\ensuremath{-}26}$, raises the question ``Why is the dimensionless constant $b$ so small in very special relativity?''

281 citations



Journal ArticleDOI
TL;DR: In this paper, a special relativity based on the de Sitter group is introduced, which is a theory that might hold up in the presence of a non-vanishing cosmological constant.
Abstract: A special relativity based on the de Sitter group is introduced, which is a theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincare group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime—modified by the presence of the de Sitter horizon—are briefly discussed.

95 citations


Book
17 Oct 2007

86 citations


Book ChapterDOI
01 Jan 2007
TL;DR: This chapter discusses the development of models of Specrel in first-order logic, and describes the motivation for special relativistic kinematics in place of Newtonian kinematic.
Abstract: 2 Special relativity 4 2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Axiomatization Specrel of special relativity in first-order logic 15 2.4 Characteristic differences between Newtonian and special relativistic kinematics . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Explicit description of all models of Specrel, basic logical investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Observer-independent geometries in relativity theory; duality and definability theory of logic . . . . . . . . . . . . . . . . . 47 2.7 Conceptual analysis and “reverse relativity” . . . . . . . . . . 59

64 citations


Journal ArticleDOI
TL;DR: In this article, the relative velocity of one observer with respect to the other in four different ways is defined independently of any coordinate system, i.e., independently of spacelike simultaneity.
Abstract: Given two observers, we define the “relative velocity” of one observer with respect to the other in four different ways All four definitions are given intrinsically, ie independently of any coordinate system Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given in the framework of observed (lightlike) simultaneity Properties and physical interpretations are discussed Finally, we study relations between them in special relativity, and we give some examples in Schwarzschild and Robertson-Walker spacetimes

54 citations


Journal ArticleDOI
TL;DR: Hilbert as discussed by the authors was the first to discover the correct form of the law of warpage (i.e., the form that obeys his relativity principle) in space-time.
Abstract: Remarkably, Einstein was not the first to discover the correct form of the law of warpage [of space-time, i.e. the gravitational field equations], the form that obeys his relativity principle. Recognition for the first discovery must go to Hilbert. In autumn 1915, even as Einstein was struggling toward the right law, making mathematical mistake after mistake, Hilbert was mulling over the things he had learned from Einstein’s summer visit to Göttingen. While he was on an autumn vacation on the island of Rugen in the Baltic the key idea came to him, and within a few weeks he had the right law–derived not by the arduous trial-and-error path of Einstein, but by an elegant, succinct mathematical route. Hilbert presented his derivation and the resulting law at a meeting of the Royal Academy of Sciences in Göttingen on 20 November 1915, just five days before Einstein’s presentation of the same law at the Prussian Academy meeting in Berlin. 2

48 citations


Journal ArticleDOI
01 Nov 2007
TL;DR: In this article, the problem of computing initial data for the Cauchy problem of 3+1 general relativity is addressed, where the main task is to solve the constraint equations.
Abstract: This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York, is presented. Two standard methods, the conformal transverse-traceless one and the conformal thin sandwich, are discussed and illustrated by some simple examples. Finally a short review regarding initial data for binary systems (black holes and neutron stars) is given.

Posted Content
TL;DR: In this article, the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories, including the universal light cone principle of special relativity and the equivalence principle.
Abstract: This paper concerns relational first principles from which the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories. This was accompanied by a number of results and conjectures about matter theories and general features of physics -- such as gauge theory, the universal light cone principle of special relativity and the equivalence principle -- being likewise picked out. I have previously shown that many of these matter results and conjectures are contingent on further unrelational simplicity assumptions. In this paper, I point out 1) that the exhaustive procedure in these cases with matter fields is slower than it was previously held to be. 2) While the example of equivalence principle violating matter theory that I previously showed how to accommodate on relational premises has a number of pathological features, in this paper I point out that there is another closely related equivalence principle violating theory that also follows from those premises and is less pathological. This example being known as an `Einstein--aether theory', it also serves for 3) illustrating limitations on the conjectured emergence of the universal light cone special relativity principle.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation and show that since the redefinition of the scalar field is not differentiable at the limit of general relativity, correspondence between two frames is lost at this limit.
Abstract: We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence between the two frames is lost at this limit. To clarify the situation we analyze the dynamics of the scalar field in different frames for two distinct scalar-tensor cosmologies with specific coupling functions and demonstrate that the corresponding scalar field phase portraits are not equivalent for regions containing the general relativity limit. Therefore the answer to the question of whether general relativity is an attractor for the theory depends on the choice of the frame.

Journal ArticleDOI
TL;DR: In this article, the Finsler line element is not invariant under the deformed Lorentz transformations of doubly special relativity, and it is shown in detail some simple applications of the formalism.
Abstract: We discuss the recent proposal of implementing doubly special relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. In particular, the Finsler line element is not invariant under the deformed Lorentz transformations of doubly special relativity. We study in detail some simple applications of the formalism.

Journal ArticleDOI
TL;DR: There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation.
Abstract: There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length l P and the scale R = (3/Λ)1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = l P /R ∼ 10−61.

Journal ArticleDOI
TL;DR: The Lagrangian of RcR is invariant under Poincare transformation, which preserves Beltrami metric Bμν and the Lagrangians Hamiltonian formulism is formulated in this article.
Abstract: The Lagrangian of Einstein's special relativity with universal parameter c (Rc) is invariant under Poincare transformation, which preserves Lorentz metric ημν The Rc has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric Bμν There are two universal parameters, c and R, in this Special Relativity (denoted as RcR) The Lagrangian-Hamiltonian formulism of RcR is formulated in this paper The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived The canonical quantization of the mechanics for RcR-free particle is performed The physics related to it is discussed



Journal ArticleDOI
TL;DR: In this paper, it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients.
Abstract: In this paper two things are done. First it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited.

Journal ArticleDOI
TL;DR: In this paper, the authors propose a canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables.
Abstract: A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3 + 1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deparametrization to special relativity and the subsequent possibility to take the non-relativistic limit.

Book
01 Jan 2007
TL;DR: In this paper, the geometrical structure of space-time and the transformation of the Electromagnetic Field were discussed. And the results of General Relativity were discussed as well.
Abstract: Space and Time Before Einstein.- In Search of the Ether.- Space and Time in Special Relativity.- Geometric Structure of Space-Time.- Transformation of the Electromagnetic Field.- Energy and Momentum.- Covariant Formulation.- Inertia and Gravity.- Results of General Relativity.

Book
26 Nov 2007
TL;DR: In this article, Westwell-Roper discusses the ontology and methodology in Relativity, and how Euclidean geometry has misled metaphysics and how to make things have happened.
Abstract: Preface Introduction Part I. Ontology and Methodology in Relativity: 1. On learning from the mistakes of Positivists 2. What ontology can be about with Andrew Westwell-Roper 3. Special relativity is not based on causality 3. Simultaneity and convention in special relativity 5. Motion and change of distance Part II. Variable Curvature and General Relativity: 6. How Euclidean geometry has misled metaphysics 7. What can geometry explain? 8. Is curvature intrinsic to physical space? 9. Holes in the hole argument Part III. Time and Causation: 10. Can time be finite? 11. How to make things have happened Bibliography Index.

Proceedings ArticleDOI
TL;DR: A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given in this paper, with a brief overview of the current theoretical understandings and constraints.
Abstract: Einstein-aether theory is general relativity coupled to a dynamical unit timelike vector field. A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given.

Book
16 Apr 2007
TL;DR: Particle on a Two-dimensional Surface Curvilinear coordinate systems Particle on two-dimensional surface - Revisited Some Tensor Analysis Special Relativity General Relativity Precession of Perihelion Gravitational Redshift Neutron Stars Cosmology Gravitational Radiation Special Topics Problems Problems.
Abstract: Particle on a Two-Dimensional Surface Curvilinear Coordinate Systems Particle on a Two-Dimensional Surface -- Revisited Some Tensor Analysis Special Relativity General Relativity Precession of Perihelion Gravitational Redshift Neutron Stars Cosmology Gravitational Radiation Special Topics Problems.

Journal ArticleDOI
TL;DR: In this article, it was shown that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of 5D Ricci-flat equations with an effective 4D Cosmological "constant" Λ that is a specific function of the extra coordinate.
Abstract: We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological “constant” Λ that is a specific function of the extra coordinate. For unified theories of the forces in higher dimensions, this has major physical implications.



Posted Content
TL;DR: In this paper, a review of the nature of time in physics is presented, both qualitatively and quantitatively, and it is interesting to note that general relativity is contaminated with non-trivial geometries that generate closed timelike curves, and thus violates causality.
Abstract: The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical systems seem to evolve in paths of increasing entropy and of complexity, and thus, the arrow of time shall be explored in the context of thermodynamic irreversibility and quantum physics. In Newtonian physics, time flows at a constant rate, the same for all observers; however, it necessarily flows at different rates for different observers in special and general relativity. Special relativity provides important quantitative elucidations of the fundamental processes related to time dilation effects, and general relativity provides a deep analysis to effects of time flow, such as in the presence of gravitational fields. Through the special theory of relativity, time became intimately related with space, giving rise to the notion of spacetime, in which both parameters cannot be considered as separate entities. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note that general relativity is contaminated with non-trivial geometries that generate closed timelike curves, and thus apparently violates causality. The notion of causality is fundamental in the construction of physical theories; therefore time travel and its associated paradoxes have to be treated with great caution. These issues are briefly analyzed in this review paper.

Journal ArticleDOI
TL;DR: The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored in this paper, where it is shown that if the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened in order to accommodate this form of discrete conformal invariance and a further generalization of relativity theory is required.
Abstract: The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened in order to accommodate this form of discrete conformal invariance, and a further generalization of relativity theory is required.

Journal ArticleDOI
TL;DR: Using only ideas from Galilean relativity, the covariance of the relationship between work and kinetic energy as we move from one inertial reference frame to another is considered in this paper.
Abstract: As the topic of relativity is developed in a first-year physics class, there seems to be a tendency to move as quickly as possible to the fascinating ideas set forth in Einstein's special theory of relativity1 In this paper we linger a little with the Galilean side of relativity and discuss an intriguing problem and its solution to illustrate a sometimes omitted issue in relativity Using only ideas from Galilean relativity, we will consider the covariance of the relationship between work and kinetic energy as we move from one inertial reference frame to another