Showing papers on "Four-force published in 1994"
Book•
01 Jan 1994
TL;DR: Maudlin's Quantum Non-Locality and Relativity is a beautifully crafted book that attempts to answer this question by evaluating four purported restrictions imposed by Relativity and concludes that such accounts exact a high philosophical price.
Abstract: It is sometimes stated that composite quantum systems in entangled states are fundamentally ‘non-local’(i.e. a measurement on one component system can affect a spacelike separated system ‘instantaneously’) and therefore, non-relativistic quantum mechanics violates Relativity theory. This conclusion is usually thought to follow directly from Bell's Theorem in quantum mechanics and the upper limit on velocities provided by the speed of light in Relativity. But exactly what if the conflict between the kind of non-locality exhibited by entangled quantum systems and either the Special or General Theory of Relativity? Maudlin's Quantum Non-Locality and Relativity is a beautifully crafted book that attempts to answer this question by evaluating four purported restrictions imposed by Relativity. He also considers four attempts to formulate Lorentz invariant quantum theories and concludes that such accounts exact a high philosophical price. Maudlin has achieved his first goal: he gives a lucid exposition of the tension between quantum non-locality and Relativity theory which is accessible to the non-specialist. But is there a high philosophical price to be paid for Lorentz invariant quantum theories and can we afford it?
455 citations
TL;DR: In this paper, it is argued that time as such does not exist but that instants, defined as complete relative configurations of the universe, do, and that the classical mechanics of a complete universe can be expressed solely in terms of such relative configurations.
Abstract: The issue of time is addressed. It is argued that time as such does not exist but that instants, defined as complete relative configurations of the universe, do. It is shown how the classical mechanics (both non-relativistic and generally relativistic) of a complete universe can be expressed solely in terms of such relative configurations. Time is therefore a redundant concept, as are external inertial frames of reference (so that Machian ideas about the relativity of motion are fully implemented). Although time plays no role in kinematics, it can be recovered as an effective concept associated with any classical history of the universe. In the case of classical mechanics, this operationally defined time is identical to the astronomers' ephemeris time. In the case of general relativity it is shown how local proper time is a kind of local ephemeris time. It is argued that because general relativity is timeless in a deep and precise sense, the standard representation of the theory as a theory of curved spacetime disguises important aspects of its structure and that just these aspects may be the most important for the quantum form of the theory. This issue and the effective recovery of time from a genuinely timeless quantum theory are addressed in a following companion paper.
211 citations
TL;DR: A relativistic generalization of the classical virial theorem is obtained for any stationary and asymptotically flat spacetime as mentioned in this paper, which may be useful as a consistency check of numerical solutions of the Einstein equations.
Abstract: A relativistic generalization of the classical virial theorem is obtained for any stationary and asymptotically flat spacetime. This formulation is derived within the 3+1 formalism of general relativity. It may be useful as a consistency check of numerical solutions of the Einstein equations.
82 citations
TL;DR: In this paper, the authors describe the present state of an attempt at understanding the quantum behaviour of microphysics in terms of a non-differentiable space-time continuum having fractal (i.e. scaledependent) properties.
Abstract: This paper describes the present state of an attempt at understanding the quantum behaviour of microphysics in terms of a nondifferentiable space-time continuum having fractal (i.e. scale-dependent) properties. The fundamental principle upon which we rely is that of scale relativity, which generalizes Einstein's principle of relativity to scale transformations. After having related the fractal and renormalization group approaches, we develop a new version of stochastic quantum mechanics, in which the correspondence principle and the Schrodinger equation are demonstrated by replacing the classical time derivative by a ‘quantum-covariant’ derivative. Then we recall that the principle of scale relativity leads one to generalize the standard ‘Galilean’ laws of scale transformation into a Lorentzian form, in which the Planck length-scale becomes invariant under dilations, and so plays for scale laws the same role as played by the velocity of light for motion laws. We conclude by an application of our new framework to the problem of the mass spectrum of elementary particles.
74 citations
TL;DR: A systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields, using a conformal transformation of the three-metric as well as a line integral in superspace to solve the Hamiltonian constraint.
Abstract: We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates ("gauge invariant"). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.
72 citations
TL;DR: In this paper, it was shown that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3) connections.
Abstract: I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of General Relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated with the complex character of the latter.
64 citations
TL;DR: A unified approach towards spectral shifts in general relativity brings the cosmological and gravitational redshifts within the same framework as the more familiar Doppler effect was first proposed by Synge [Relativity: The General Theory (North‐Holland, Amsterdam 1960)] and described here in a more simplified form as mentioned in this paper.
Abstract: A unified approach towards spectral shifts in general relativity brings the cosmological and gravitational redshifts within the same framework as the more familiar Doppler effect. This approach was first proposed by Synge [Relativity: The General Theory (North‐Holland, Amsterdam 1960)] and is described here in a more simplified form.
54 citations
TL;DR: In this article, the kinematic results of the special theory of relativity are derived using only the first (Galilean) postulate and the results of one simple thought experiment.
Abstract: The kinematic results of the special theory of relativity are derived using only the first (Galilean) postulate and the results of one simple thought experiment. Our method is mathematically simple and, therefore, can be used in an algebra based introductory physics course. It is also pedagogically attractive because the relativistic results follow as a natural extension of the familiar Newtonian ones.
44 citations
39 citations
TL;DR: In this article, the authors investigated the physical interpretation of the loop states of non-perturbative quantum general relativity in the regime of graviton physics, and they constructed the general form of loop state functionals invariant under the linearized constraints.
Abstract: We investigate the physical interpretation of the loop states of non-perturbative quantum general relativity in the regime of graviton physics, namely the regime of first order excitations around the Poincare-invariant vacuum. We construct the general form of the loop state functionals invariant under the linearized constraints. We present explicitly the loop state functionals that represent the Poincare-invariant vacuum and the graviton states. We find that physical information emerges entirely from intersections of loops. We obtain these results by utilizing the recently introduced `map ', which relates the loop-space states of non-perturbative quantum general relativity to the state space of the linearized theory. The general picture of the linearization of the loop-space quantum general relativity is discussed.
39 citations
TL;DR: In this paper, the first postulate of relativity was used to develop a general theory, termed taiji relativity, which has four-dimensional symmetry and is consistent with experiments.
Book•
01 Jan 1994
TL;DR: The recent developments in canonical transforms, matrix theory, block Kronecker multiplications, and other areas are applied to extend and simplify results in the theory of first order systems and special relativity as mentioned in this paper.
Abstract: The recent developments in canonical transforms, matrix theory, block Kronecker multiplications, and other areas are applied to extend and simplify results in the theory of first order systems and special relativity. Especially noteworthy are the author's results on Fourier transforms in dimensions lower than the surrounding space and his approach to the Doppler effect, which has never been published previously and supersedes previous works on this topic, which failed to solve the Doppler effect exactly. Some of the goals of this work are: to develop the theory of complex symmetric matrices as the rigorous foundations of first order systems, to exhibit in full generality the author's method of duality, and to discuss the neglected area of three dimensional effects in special relativity. The section on special relativity has been especially simplified so that it may be used as a beginning graduate text in this area. It includes the first full discussion of the Lorentz group in a book since Silberstein's pioneering 1913 treatment.
Book•
01 Jan 1994
TL;DR: The theory of Relativity is the Theory of Absoluteness as discussed by the authors, and Relativity at Work III: Quantum Mechanics 11 Relativity and Causality 12 Applied Relativity, Relativistic Engineering 14 A Bit of General Relativity Appendices
Abstract: 1 Introduction 2 Light and Relativity 3 The Velocities' Play 4 Space-Time 5 Relativity at Work I: Mechanics 6 Relativity at Work II: Electromagnetism and Optics 7 Relativistic Paradoxes 8 Miracles of a Spinning World 9 The Theory of Relativity is the Theory of Absoluteness 10 Relativity at Work III: Quantum Mechanics 11 Relativity and Causality 12 Applied Relativity and Relativistic Engineering 14 A Bit of General Relativity Appendices
TL;DR: A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced, which are globally regular, asymptotically flat and in general have no isometries, but a U( 1) × U(1) group of conformal isometry.
Abstract: A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a U(1) × U(1) group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.
TL;DR: In this article, the authors give a definition of rigid congruences in both General and Special Relativity, and try to make the definition plausible, and apply the definition to the Earth-Sun system in the post-Newtonian approximation.
Abstract: We give a definition of rigid congruences in both General and Special Relativity, and we try to make the definition plausible. To this end we recall Fermat's principle in General Relativity and we show that this principle allows us to reinterpret the “quotient metric” as the quadratic form which defines the optical length in a gravitational field. We apply the definition to the Earth-Sun system in the post-Newtonian approximation. Furthermore we compute the Fermat tensor and the corresponding relative variation of the speed of light in a Michelson-Morley like experiment performed on the Earth's surface. According to all measurements to date, this quantity is extremely small (10 -13 ).
TL;DR: In this article, it is suggested how Bernhard Riemann might have discovered General Relativity soon after 1854 and how today's undergraduate students can be given a glimpse of this before, or independently of, their study of Special Relativity.
Abstract: It is suggested how Bernhard Riemann might have discovered General Relativity soon after 1854 and how today’s undergraduate students can be given a glimpse of this before, or independently of, their study of Special Relativity At the same time, the whole field of relativity theory is briefly surveyed from the space–time point of view
01 Jan 1994
TL;DR: In this article, the authors discuss the basis of the Lorentz transformations and find the complete set of theories empirically equivalent to the special theory of relativity under the assumption that the one-way velocity of light is not measurable.
Abstract: The purpose of this paper is twofold: (1) to discuss the basis of the Lorentz transformations showing that the invariance of the velocity of light has in them a role even more important than usually believed, and (2) to find the complete set of theories empirically equivalent to the special theory of relativity (STR) under the assumption that the one-way velocity of light is not measurable.
TL;DR: In this paper, a class of spinor-curvature identities for Riemannian or Cartan geometries is described. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential.
Abstract: We describe a class of spinor-curvature identities which exist for Riemannian or Riemann--Cartan geometries Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential Certain special cases in three and four dimensions which have been or could be used in applications to general relativity are noted
TL;DR: In this paper, a complete picture of the relativity of wave fronts, heretofore lacking, is presented in the context of an expanding spherical light wave as recorded in two Lorentz frames in relative motion.
Abstract: A complete picture of the relativity of wave fronts, heretofore lacking, is presented in the context of an expanding spherical light wave as recorded in two Lorentz frames in relative motion.
TL;DR: In this paper, it was shown that it is possible to solve some of the constraints of the $SO(3)$-ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework.
Abstract: I show in this letter that it is possible to solve some of the constraints of the $SO(3)$-ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework. I discuss the advantages of using the ADM formalism and compare the result with similar proposals for different Hamiltonian formulations of general relativity.
TL;DR: For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of "asymptotic spinors" as discussed by the authors.
Abstract: For an asymptotically flat initial‐data set in general relativity, the total mass‐momentum may be interpreted as a Hermitian quadratic form on the complex, two‐dimensional vector space of ‘‘asymptotic spinors.’’ A generalization to an arbitrary initial‐data set is obtained. The mass‐momentum is retained as a Hermitian quadratic form, but the space of ‘‘asymptotic spinors’’ on which it is a function is modified. Indeed, the dimension of this space may range from zero to infinity, depending on the initial data. There is given a variety of examples and general properties of this generalized mass‐momentum.
Posted Content•
TL;DR: In this article, it was shown that general relativity is not a parametrized field theory and that there are essentially no local observables for vacuum spacetimes for canonical gravity.
Abstract: We present 2 recent results on the problems of time and observables in canonical gravity. (1) We cannot use parametrized field theory to solve the problem of time because, strictly speaking, general relativity is not a parametrized field theory. (2) We show that there are essentially no local observables for vacuum spacetimes.
TL;DR: In this article, the authors clarified the Reichenbach-Grunbaum thesis of the conventionality of distant simultaneity of special relativity by developing relativity within a medium, where instead of light, spatially distant clocks are imagined to have been synchronized by an acoustic signal.
Abstract: The Reichenbach-Grunbaum thesis of the conventionality of distant simultaneity of special relativity is clarified by developing relativity within a medium. Instead of light, spatially distant clocks are imagined to have been synchronized by 'acoustic signal'. Einstein's procedure for synchrony which assumes that the two-way speed of the synchronizing signal along a given line is the same as its one-way speed, has however been retained. It is shown that by deliberately opting for the non-luminal synchrony (but at the same time following Einstein's procedure for it) and hence by obtaining the transformation equations for the relativistic world one is able to visualize more clearly the conventionality ingredients in the standard formulation of special relativity. The Sjodin point of view of clock synchronization which requires the concept of a preferred inertial frame is seen to be more appropriate in the present context. First, the transformations have been obtained generally and later some special cases have been investigated. The common confusions concerning the 'real' and 'apparent' effects in special relativity have been made clear by studying the transformation equations for the relativistic world and that for the Galilean world under the non-luminal synchrony. It is shown that gamma-factors of special relativity partly originate from Einstein's procedure for clock synchrony.
TL;DR: Galilean relativity and absolute space basic postulates of special relativity and relativistic kinematics were derived by as mentioned in this paper for binary collisions tachyons in a vacuum environment, and they were used to define the relativistically kinematic model of binary collisions.
Abstract: Galilean relativity and absolute space basic postulates of special relativity and relativistic kinematics relativistic mechanics relativistic optics relativity and electromagnetism in vacuum relativistic kinematics of binary collisions tachyons.
Book•
01 Apr 1994
TL;DR: The Newtonian Universe Waves and their differences from Particles Fields: Space Is Not Empty Probability: What Does It Measure? Special Relativity: Only One Velocity Is Absolute Quantum Theory: New Phenomena, New Principles General Relativity as discussed by the authors.
Abstract: The Newtonian Universe Waves and Their Differences from Particles Fields: Space Is Not Empty Probability: What Does It Measure? Special Relativity: Only One Velocity Is Absolute Quantum Theory: New Phenomena, New Principles General Relativity: Gravity as Field Distortions A Look Down Further Roads Neither Determinism Nor Indeterminism Road to the Stars Appendices Index.
TL;DR: In this article, a general formalism for numerically evolving initial data in general relativity is discussed, in which the complex Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables.
Abstract: We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge constraints and twelve reality conditions must be solved. The analysis is applied to a Petrov type \{1111\} planar spacetime where we find a spatially constant volume element to be an appropriate coordinate gauge choice.
TL;DR: In this paper, it was shown that for time independent fields, the two seemingly different and unrelated Tolman and Moller mass-energy formulae in general relativity are, in fact, completely equivalent.
Abstract: It is shown that, for time independent fields, the two seemingly different and unrelated Tolman and Moller mass-energy formulae in general relativity are, in fact, completely equivalent.
01 Jan 1994
TL;DR: In this paper, an anholonomic formalism is developed for the intrinsic Cauchy problem in General Relativity (gravitational equations), in the case of non polar continua, with one scalar supplementary field (non-orthogonal 1 x 3 structure).
Abstract: Starting from an ordinary frame of reference in General Relativity, and its anholonomic structure, we consider a review of more general quasi-product structure, in a differentiable (or riemannian) manifold, that can be deal with the same anholonomic techniques. The general case contains, in particular, the generalization of ordinary frame of reference, in the sense of polar continua, with one scalar supplementary field (non-orthogonal 1 x 3 structure). Finally, the anholonomic formalism is developed for the intrinsic Cauchy problem in General Relativity (gravitational equations), in the case of non polar continua; properly spatial variables are the following: metric γik , vector potential γi, deformation rate \( {{\tilde{K}}_{{ik}}} \) pure mass density µ 0 , heat flux \( {{\tilde{Q}}_{i}} \) and temperature T.