Showing papers on "Four-force published in 2001"

The Confrontation Between General Relativity and Experiment

Abstract: The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Relativity: Special, General, and Cosmological

Abstract: INTRODUCTION 1. From absolute space and time to influenceable spacetime: an overview PART I: SPECIAL RELATIVITY 2. Foundations of special relativity the Lorentz transformation 3. Relativistic kinematics 4. Relativistic optics 5. Spacetime and four-vectors 6. Relativistic particle mechanics 7. Four-tensors electromagnetism in vacuum PART II: GENERAL RELATIVITY 8. Curved spaces and the basic ideas of general relativity 9. Static and stationary spacetimes 10. Geodesics, curvature tensor, and vacuum field equations 11. The Schwarzschild metric 12. Black holes and Kruskal space 13. An exact plane gravitational wave 14. The full field equations de Sitter space 15. Linearized general relativity PART III: COSMOLOGY 16. Cosmological spacetimes 17. Light propagation in FRW universes 18. Dynamics of FRW universes

Spin foam model for Lorentzian general relativity

Abstract: We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a Euclidean model defined in terms of a field theory over a group. Its vertex amplitude turns out to be the one recently introduced by Barrett and Crane. As in the case of its Euclidean relatives, the model fully implements the desired sum over 2-complexes which encodes the local degrees of freedom of the theory.

Pre-socratic quantum gravity

Abstract: Physicists who work on canonical quantum gravity will sometimes remark that the general covariance of general relativity is responsible for many of the thorniest technical and conceptual problems in their field In particular, it is sometimes alleged that one can trace to this single source a variety of deep puzzles about the nature of time in quantum gravity, deep disagreements surrounding the notion of ‘observable’ in classical and quantum gravity, and deep questions about the nature of the existence of spacetime in general relativity Philosophers who think about these things are sometimes skeptical about such claims We have all learned that Kretschmann was quite correct to urge against Einstein that the “General Theory of Relativity” was no such thing, since any theory could be cast in a generally covariant form, and hence the general covariance of general relativity could not have any physical content, let alone bear the kind of weight that Einstein expected it to Friedman’s assessment is widely accepted: “As Kretschmann first pointed out in 1917, the principle of general covariance has no physical content whatever: it specifies no particular physical theory; rather, it merely expresses our commitment to a certain style of formulating physical theories” (1984, p 44) Such considerations suggest that general covariance, as a technically crucial but physically contentless feature of general relativity, simply cannot be the source of any significant conceptual or physical problems Physicists are, of course, conscious of the weight of Kretschmann’s points against Einstein Yet they are considerably more ambivalent than their philosophical colleagues Consider Kuchař’s conclusion at the end of a discussion of this topic:

Unimodular relativity and cosmological constant

Abstract: Unimodular relativity is a theory of gravity and space–time with a fixed absolute space–time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems to break general covariance, some have suggested that it permits a nonzero covariant divergence of the material stress-energy tensor and a variable cosmological “constant.” In Lagrangian unimodular relativity, however, even with higher derivatives of the gravitational field in the dynamics, the usual covariant continuity holds and the cosmological constant is still a constant of integration of the gravitational field equations.

Teleparallel spin connection

Abstract: A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.

A Finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity

Abstract: We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.

Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers

Abstract: In the recent monograph [8], G.L. Naber provides an interesting introduction to the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.

No time machines in classical general relativity

Abstract: Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).

Newton to Einstein: The Trail of Light: An Excursion to the Wave-Particle Duality and the Special Theory of Relativity

Abstract: Preface 1. How light behaves 2. Newton's particle theory 3. A wave theory of light 4. Interference 5. Electromagnetic waves 6. The photon 7. The wave-particle duality 8. Does the speed of light depend on the motion of the source of light? 9. The principles of the Special Theory of Relativity 10. Time dilation and length contraction 11. E=mc2 12. The twins 13. The Lorentz transformations 14. Space and time Glossary Appendices Index.

The relativistic particle as a mechanical system with non-holonomic constraints

Abstract: The geometric theory of non-holonomic systems on fibred manifolds is applied to describe the motion of a particle within the theory of special relativity General motion equations for material particles subjected to potential forces are found They cover, as particular cases, standard motion equations as well as a generalization of the special relativity theory proposed by Dicke Moreover, they offer new possibilities for studying the dynamics of relativistic particles interacting with an electromagnetic and/or a scalar field

Affine generalization of the Komar complex of general relativity

Abstract: On the basis of the ``on shell'' Noether identities of the metric-affine gauge approach of gravity, an affine superpotential is derived which comprises the energy- and angular-momentum content of exact solutions. In the special case of general relativity (GR) or its teleparallel equivalent, the Komar or Freud complex, respectively, are recovered. Applying this to the spontaneously broken anti--de Sitter gauge model of McDowell and Mansouri with an induced Euler term automatically yields the correct mass and spin of the Kerr-AdS solution of GR with a (induced) cosmological constant without the factor two discrepancy of the Komar formula.

Scale relativity and gauge invariance

Abstract: The theory of scale relativity extends Einstein’s principle of relativity to scale transformations of resolutions. It is based on the giving up of the axiom of dieren tiability of the space-time continuum. As a consequence, spacetime becomes fractal, i.e., explicitly resolution-dependent. The requirement that this geometry satises the principle of scale relativity leads to introduce scale laws having a Galilean form (constant fractal dimension), then a logLorentzian form. In this framework, the Planck length-time scale becomes a minimal impassable scale, invariant under dilations. Then we attempt to construct a generalized scale relativity which includes scale-motion coupling. In this last framework, one can reinterpret gauge invariance as scale invariance on the internal resolutions. This approach allows one to set new constraints in the standard model, concerning in particular the Higgs boson mass, which we nd to be p 2mW = 113:73 0:06 GeV in a large class of models.

Space-time exchange invariance: Special relativity as a symmetry principle

Abstract: Special relativity is reformulated as a symmetry property of space-time: space-time exchange invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dynamical application, the laws of electrodynamics and magnetodynamics are derived from those of electrostatics and magnetostatics respectively. The four-vector nature of the electromagnetic potential plays a crucial role in the last two derivations.

Relationism Rehabilitated? II: Relativity

Abstract: In a companion paper (Pooley & Brown 2001) it is argued that Julian Barbour's Machian approach to dynamics provides a genuinely relational interpretation of Newtonian dynamics and that it is more explanatory than the conventional, substantival interpretation. In this paper the extension of the approach to relativistic physics is considered. General relativity, it turns out, can be reinterpreted as a perfectly Machian theory. However, there are difficulties with viewing the Machian interpretation as more fundamental than the conventional, spacetime interpretation. Moreover, this state of affairs provides little solace for the relationist for, even when interpreted along Machian lines, general relativity is a substantival theory although the basic entity is space, not spacetime.

Scale relativity in Cantorian space and average dimensions of our world

Abstract: A Cantorian–fractal space-time, a family member of von Neumann's noncommutative geometry, is introduced as a geometry underlying a new relativity theory which is similar to the relation between general relativity and Riemannian geometry. Based on this model and the new relativity theory, an ensemble distribution of all the dimensions of quantum space-time is derived with the help of Fermat's last theorem. The calculated average dimension is very close to the value of 4+ φ 3 (where φ is the golden mean) obtained by El Naschie on the basis of a different approach. It is shown that within the framework of the new relativity, the cosmological constant problem is nonexistent, since the universe self-organizes and self-tunes according to the renormalization group (RG) flow with respect to a local scaling microscopic arrow of time. This implies that the world emerged as a result of a nonequilibrium process of self-organized critical phenomena launched by vacuum fluctuations in Cantorian–fractal space-time E ∞ . It is shown that we are living in a metastable vacuum and are moving towards a fixed point ( D av =4+ φ 3 ) of the RG. After reaching this point, a new phase transition will drive the universe to a quasi-crystal phase of the lower average dimension of φ 3 .

Elements for a Theory of Relativistic Coordinate Systems:. Formal and Physical Aspects

Abstract: Basic elements for a relativistic theory of coordinate systems are introduced. The main purposes of such a theory are to precise the physical and geometrical status of coordinate systems in general relativity, to structure those presently known, to offer a convenient scheme to incorporate new ones, to reveal voids in our knowledge of their mutual relations, and to incitate their study. Relativistic operational criteria to construct coordinate systems are given, with particular attention to satellite positioning systems, to which the current GPS could be related.

Equivalence Principle and the Principle of Local Lorentz Invariance

Abstract: In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory We show that it is the class of the LLRFγs that is associated with the PLLI Next we give a definition of physically equivalent reference frames Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found We prove moreover that PIRFs are not physically equivalent

General relativity histories theory: spacetime diffeomorphisms and the Dirac algebra of constraints

Abstract: We show that representations of the group of spacetime diffeomorphisms and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure introduced previously in history theory: namely, the existence in non-relativistic physics of two types of time translation; and the existence in relativistic field theory of two distinct Poincar? groups.

The Principle of Equivalence

Abstract: start from John Norton's analysis (1985) of the reach of Einstein's version of the principle of equivalence which is not a local principle but an extension of the relativity principle to reference frames in constant acceleration on the background of Minkowski spacetime. We examine how such a point of view implies a profound, and not generally recognised, reconsideration of the concepts of inertial system and field in physics. We then reevaluate the role that the infinitesimal principle, if adequately formulated, can legitimately be claimed to play in general relativity. We show that what we call the 'punctual equivalence principle' has significant physical content and that it permits the derivation of the geodesic law. (C) 2001 Elsevier Science Ltd. All rights reserved.

Signature change, mixed problems and numerical relativity

Abstract: Classical general relativity takes place on a manifold with a metric of fixed, Lorentzian, signature However, attempts to amalgamate general relativity with quantum theory frequently involve manifolds with metrics whose signatures are Lorentzian in some regions and Euclidean in others (Indeed even more exotic possibilities are discussed frequently) Most theoretical calculations rely on analyticity arguments to continue variables from the Euclidean to the Lorentzian regime and vice versa This paper examines models of signature change It looks at a single second-order quasi-linear partial differential equation on a fixed background, whose principal part is elliptic in one regime and hyperbolic in another, ie a mixed problem It introduces some examples, explains heuristically the concept of a well-posed problem and then discusses the issues involved in constructing a robust numerical algorithm to solve well-posed problems The paper includes a worked example illustrating the proposed techniques, and a discussion of the role of the potential curvature singularity on the transition hypersurface

Singularities and Scalar Fields: Matter Theory and General Relativity

Abstract: Philosophers of physics should be more attentive to the role energy conditions play in General Relativity. I review the changing status of energy conditions for quantum fields-presently there are no singularity theorems for semiclassical General Relativity. So we must reevaluate how we understand the relationship between General Relativity, Quantum Field Theory, and singularities. Moreover, on our present understanding of what it is to be a physically reasonable field, the standard energy conditions are violated classically. Thus the singularity theorems are unavailable for classical General Relativity. Our understanding of singularities in General Relativity turns on delicate issues of what it is to be a matter field-issues distinct from the content of the theory.

Review of “Kinematic Relativity: A Sequel to Relativity, Gravitation, and World Structure”

Abstract: This book is a presentation of the author ’s theory of cosmology and physics. It is a sequel to his study Relativity, gravitation and world structure (1935), but can well be read independently from the earlier volume. It is a fascinating treatise, centered around a brilliant idea, excellently presented and showing unusual skill in the elaboration of some of the details. Even though the reviewer could not agree with all parts of the book, his admiration never slackened for the scope of the work and the wealth of results obtained by the author with the help of only a handful of collaborators.

General Relativity as a Symmetry of a Unified Space-Time-Action Geometrical Space

Abstract: We derive the basic principles of Electromagnetism and general relativity from a common (geometrical) starting formulation we call START, from its geometrical structure as a Space– Time–Action Relativity Theory. Gravitation results from the epistemological approach of defining a test particle which explores the physical world in such a form that its trajectory indicates the influence of the rest of the system. Electromagnetism defines a collection of test particles, we call carriers, in interaction among themselves and with the rest of the system. General Relativity is then derived from a symmetry transformation of the quadratic space geometry corresponding to space–time and action and the philosophical principles of Einstein’s general relativity theory.

Why the principles of inertia and of equivalence hold despite self-interaction

Abstract: When self-interaction is included, the equation of motion without an external force yields solutions that violate the principle of inertia. This problem is a century old. Recently, it has been shown that there could also be solutions that violate the principle of equivalence. The present paper solves these problems by the observation that the dynamic part of the self-interaction is induced by the external force: there is no such interaction without an external force.

Anisotropic fluids in the case of stationary and axisymmetric spaces of General Relativity

Abstract: We present a stationary axisymmetric solution belonging to Carter's family [A] of spaces and representing an anisotropic fluid configuration.

Optical multilayers as a tool for visualizing special relativity

Abstract: We re-elaborate on the recent basic result that the action of any multilayer is equivalent to a proper Lorentz transformation. As a consequence, we propose simple optical measurements that can serve as an analogue computer for simulating special relativity. Special attention is paid to the question of the Wigner rotation, showing that it can be easily observed in multilayers.