Showing papers on "Four-force published in 1998"
TL;DR: In this paper, a test-theory for local Lorentz invariance for a noninertial observer in a space of arbitrary curvature using differential geometric techniques and the Frenet frame is derived.
136 citations
TL;DR: In this paper, the authors argue that Lorentzian relativity better describes nature than special relativity, and that the link between relativity and the causality principle involves issues of the meaning of gravitational waves and curved space-time analogies.
107 citations
01 Jan 1998
TL;DR: The emergence and early history of a rival mathematical formalism to the Sommerfeld-Laue spacetime calculus for use in relativity theory is described in this article, where the authors describe the early history and evolution of this formalism.
Abstract: The emergence and early history of a rival mathematical formalism to the Sommerfeld-Laue spacetime calculus for use in relativity theory is described.
68 citations
62 citations
TL;DR: In this paper, the authors apply relativistic electrodynamics to a rotating linear medium and derive general field equations in a rotating coordinate system, which are then derived in the rotating and laboratory reference frames.
Abstract: We apply relativistic electrodynamics to a rotating linear medium. Covariant field equations are used to derive general field equations in a rotating coordinate system. We argue that the relation between fields in the presence of matter and those in a vacuum is necessarily dependent upon the coordinate system used. Constitutive equations are then derived in the rotating and laboratory reference frames. We find that our constitutive equations in the laboratory frame agree with Minkowski’s constitutive equations, derived on the basis of special relativity in 1908. Thus we conclude that special relativity can be used in the analysis of experiments involving rotational motion. To exemplify the use of special relativity, we derive an experimentally observed result of a 1913 experiment performed by Wilson and Wilson in which a polarizable, permeable cylinder was rotated in a uniform, axially directed magnetic field.
37 citations
TL;DR: The recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study as mentioned in this paper, where general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail.
Abstract: The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted
28 citations
TL;DR: The theory of scale relativity as discussed by the authors generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions, which implies its fractal character, and the effects of non-differentiability (complex nature of wave function, new terms in differential equations of mean motion) are accounted for by a scale covariant derivative that transforms the equations of classical mechanics into the Schrodinger equation.
Abstract: The theory of scale relativity generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions. In this theory, we no longer assume that the space-time continuum is differentiable, this implying its fractal character. Both classical and quantum laws may emerge from a unique, more profound, scale law. The effects of nondifferentiability (complex nature of wave function, new terms in differential equations of mean motion) are accounted for by a scale- covariant derivative that transforms the equations of classical mechanics into the Schrodinger equation. Using an intermediate description in terms of a "fractal potential", we finally establish the m -1 dependence of the Compton- de Broglie wavelength. © Elsevier Science Ltd. All rights reserved
23 citations
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TL;DR: In this paper, a successful three-dimensional cartesian implementation of the Bona-Masso hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity is discussed.
Abstract: We discuss a successful three-dimensional cartesian implementation of the Bona-Masso hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity. The numerical code, which we call "Cactus," provides a general framework for 3D numerical relativity, and can in- clude various formulations of the evolution equations, initial data sets, and analysis modules. We show important code tests, including dynamically sliced flat space, wave spacetimes, and black hole spacetimes. We discuss the numerical convergence of each spacetime, and also compare results with previously tested codes based on other formalisms, including the traditional ADM formalism. This is the first time that a hyperbolic reformulation of Einstein's equations has been shown appropriate for three-dimensional numerical relativity in a wide variety of spacetimes.
22 citations
TL;DR: In this article, an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures is presented, where the structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory.
Abstract: We present an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.
17 citations
TL;DR: In this paper, the uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth for simultaneity in time-oriented spacetimes is discussed.
Abstract: In this note I briefly discuss some aspects of relative geometric-simultaneity in special relativity. After saying a. few words about the status and nature of Minkowski spacetime in special relativity I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.
17 citations
11 Nov 1998
TL;DR: The status of experimental tests of general relativity and of theoreti- cal frameworks for analysing them are reviewed in this article, where the equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special relativity, and the gravitational redshift experiment.
Abstract: The status of experimental tests of general relativity and of theoreti- cal frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP will search for new interactions aris- ing from unification or quantum gravity. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt ef- fect in lunar motion. Gravitational wave damping has been detected to half a percent using the binary pulsar, and new binary pulsar systems promise further improvements. When direct observation of gravita- tional radiation from astrophysical sources begins, new tests of general relativity will be possible.
TL;DR: In this article, the authors show that a CPT-conserved violation of local invariance can be demonstrated experimentally through the energy dependence of the K L − K S mass difference and discuss constraints imposed by present experiments.
TL;DR: In this paper, the authors consider the applicability of general relativity (GR) as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations.
Abstract: We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue that, as it stands, GR is deficient whether it is treated as a microscopic or a macroscopic theory of gravity. We briefly discuss some recent attempts at removing this shortcoming through the construction of a macroscopic theory of gravity. We point out that such macroscopic extensions of GR are likely to be nonunique and involve non-Riemannian geometrical frameworks.
TL;DR: In this paper, the authors integrate and consolidate foundational ideas of electrodynamics and special relativity theories into a consistent structure, from the point of view of the application-oriented applied scientist and engineer.
Abstract: An attempt is made here to integrate and consolidate foundational ideas of electrodynamics and special relativity theories into a consistent structure, from the point of view of the application-oriented applied scientist and engineer. A discussion of this kind is best served by minimizing the sophisticated mathematical tools to the bare minimum, and avoiding lengthy calculations. Some of the difficulties encountered in educating engineers and applied scientist are exactly of this kind, hence a topsy-turvy presentation of special relativity is used, in which fundamental postulates and conclusions exchange roles. With the recent interest in direct time-domain methods, the pre-sent discussion strives to elucidate the fundamental problems involved. Essentially it is argued that appending Maxwell's theory with constitutive relations is in general valid for systems homogeneous in time and space. Spatiotemporal constitutive relations are thus becoming differential operators. Strictly speaking, inhomogeneous systems in time and space are appropriate for non-dispersive systems, or as an approximation. Although Electrodynamics in moving media is often considered a purely academic subject, the understanding of its implementation as proposed by Minkwoski is a crucial cornerstone to our understanding of the physical models at hand. To that end, a generalized approach to the Minkowski method for electrodynamics in moving media is presented. This applies to linear as well as nonlinear media. Finally, a novel representation is proposed for nonlinear constitutive differential operators. This contributes to the spatiotemporal representation of Volterra type nonlinear constitutive parameters.
TL;DR: In this article, the Sum Over Paths quantum theory is used to command the electron to explore all paths, and students can model this command with the computer, pointing and clicking to tell the electron which paths to explore.
Abstract: Public hunger for relativity and quantum mechanics is insatiable, and we should use it selectively but shamelessly to attract students, most of whom will not become physics majors, but all of whom can experience “deep physics.” Science, engineering, and mathematics students, indeed anyone comfortable with calculus, can now delve deeply into special and general relativity and quantum mechanics. Big chunks of general relativity require only calculus if one starts with the metric describing spacetime around Earth or black hole. Expressions for energy and angular momentum follow, along with orbit predictions for particles and light. Feynman’s Sum Over Paths quantum theory simply commands the electron: Explore all paths. Students can model this command with the computer, pointing and clicking to tell the electron which paths to explore; wave functions and bound states arise naturally. A second full-year course in physics covering special relativity, general relativity, and quantum mechanics would have wide appeal—and might also lead to significant advancements in upper-level courses for the physics major.
10 Jan 1998
TL;DR: In this paper, the status of the canonical quantization of general relativity in terms of loops and spin networks is discussed and some solutions of the complete set of constraints related with knot and tangle invariants are described.
Abstract: The status of the canonical quantization of general relativity in terms of loops and spin networks is discussed. I describe some solutions of the complete set of constraints related with knot and tangle invariants.
TL;DR: In this paper, a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers was found, and it was shown that all measurements one can make in this theory are associated with cnumbers.
TL;DR: In this article, a parametrized general relativity (PGR) was proposed, where the Hamiltonian constraint is removed and some non-metricity in the connection is allowed, unlike in general relativity.
Abstract: A physical framework has been proposed which describes manifestly covariant relativistic evolution using a scalar time τ. Studies in electromagnetism, measurement, and the nature of time have demonstrated that in this framework, electromagnetism must be formulated in terms of τ-dependent fields. Such an electromagnetic theory has been developed. Gravitation must also use of τ-dependent fields, but many references do not take the metric's dependence on τ fully into account. Others differ markedly from general relativity in their formulation. In contrast, this paper outlines steps towards a τ-dependent classical intrinsic formulation of gravitation, patterned after general relativity, which we call parametrized general relativity (PGR). Given the existence of a preferred foliation, the Hamiltonian constraint is removed. We find that some nonmetricity in the connection is allowed, unlike in general relativity. Conditions on the allowable nonmetricity are found. Consideration of the initial value problem confirms that the metric signature should normally be O(3, 2) rather than O(4, 1). Following the lead of earlier works, we argue that concatenation (integration over τ) is unnecessary for relating parametrized physics to experience, and propose an alternative to it. Finally, we compare and contrast PGR with other relevant gravitational theories.
Book•
01 Jan 1998
TL;DR: In this paper, a pedagogical monograph describes some of the fundamental views of the laws of physics and derives the Lorentz transformations and the special theory of relativity without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism.
Abstract: This pedagogical monograph describes some of the fundamental views of the laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrodinger's idea of "quantization as an eigenvalue problem", the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, the Kepler problem in the special theory of relativity is studied starting from the energy law, and the applications to the Hulse-Taylor binary pulsar indicate that more data about the unseen companion are needed before the interpretation of the present data may be taken as the ultimate proof of the validity of the general theory of relativity.
TL;DR: In this article, the covariant canonical transformations of fields are defined as fundamentalsymmetry operations on fields, such that the physical outcomes of each field theory must be invariant under these transformations.
Abstract: The canonical formalism of fields consistentwith the covariance principle of special relativity isgiven here. The covariant canonical transformations offields are affected by 4-generating functions. All dynamical equations of fields, e.g., theHamilton, Euler–Lagrange, and other fieldequations, are preserved under the covariant canonicaltransformations. The dynamical observables are alsoinvariant under these transformations. The covariantcanonical transformations are therefore fundamentalsymmetry operations on fields, such that the physicaloutcomes of each field theory must be invariant under these transformations. We give here also thecovariant canonical equations of fields. These equationsare the covariant versions of the Hamilton equations.They are defined by a density functional that is scalar under both the Lorentz and thecovariant canonical transformations of fields.
TL;DR: In this paper, it is shown that the relation P = b/λ, where b is a constant, is valid and can be obtained from the application of classical nonquantumphysics.
Abstract: Beams of entities, such as electrons, mayproduce diffraction patterns. These patterns may beinterpreted in terms of particles and waves. One obviousquestion concerning these phenomena is, “What is the functional relation between the momentumof the entity and its wavelength?” While thisrelation is well known, it is of interest to look foranother way to arrive at this function using special relativity theory and the fundamentalobservation that the mathematical form of a law ofnature cannot contain any parameters relating to morethan one reference frame. It is shown, without makingany quantum assumptions, that the relation P = b/λ,where b is a constant, is valid. This result comesdirectly from the application of classical nonquantumphysics.
TL;DR: In this article, it was shown that the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving, provided that there is only a finite number of particles and that their speeds remain bounded.
Abstract: This paper and its predecessor ( Schmidt, 1997 ) are about the question: ‘Are the events in the entire universe encoded in and predictable from any of its parts?’ To approach a positive answer in classical physics, the following result is proved and commented on: in Newton’s theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving—provided that there is only a finite number of particles and that their speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed.
TL;DR: In this article, the REDUCE package Dimsym is used to find space-time symmetries in general relativity, in particular in the case of spacetime invariants.
TL;DR: In this paper, a simple model for the "corona" of a neutrino-radiating star showing critical behaviour is presented; for simplicity we assume spherical symmetry, and the physical properties of the model are analysed and the conditions for the existence or absence of a bounce (explosion) are discussed.
Abstract: A new simple model, in general relativity, for the `corona' of a neutrino-radiating star showing critical behaviour is presented; for simplicity we assume spherical symmetry. New solutions of the Einstein equations are exhibited. The physical properties of the model are analysed and the conditions for the existence or absence of a bounce (explosion) are discussed.
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TL;DR: In this paper, a brief but comprehensive introduction to certain mathematical techniques in General Relativity is presented, taking into account the complications of introducing a non-trivial space-time geometry.
Abstract: This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial space-time geometry. This transcript should be of use to the beginning student and assumes only very basic familiarity with tensor analysis and modern notation. This paper will also be of use to gravitational physicists as a quick reference.
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TL;DR: The relation between the special relativity and quantum mechanics is discussed in this paper based on the postulate that space-time inversion is equavalent to particle-antiparticle transformation, and the relativistic modification on Stationary Schr\"{o}dinger Equation is derived.
Abstract: The relation between the special relativity and quantum mechanics is discussed Based on the postulate that space-time inversion is equavalent to particle-antiparticle transformation, the essence of special relativity is explored and the relativistic modification on Stationary Schr\"{o}dinger Equation is derived