Showing papers on "Four-force published in 1970"
223 citations
TL;DR: In this article, it was shown that if space-time is nonempty at one time, it will be non-empty at all times provided that the energy momentum tensor of the matter satisfies a physically reasonable condition.
Abstract: It is shown that in classical general relativity, if space-time is nonempty at one time, it will be nonempty at all times provided that the energy momentum tensor of the matter satisfies a physically reasonable condition. The apparent contradiction with the quantum predictions for the creation and annihilation of matter particles by gravitons is discussed and is shown to arise from the lack of a good energy momentum operator for the matter in an unquantised curved space-time metric.
56 citations
TL;DR: Several theories of quantum general relativity have been formulated as discussed by the authors, including Canonical, sum-over-histories and source theory approaches to the quantization of the gravitational field in the absence of matter.
Abstract: Several theories of quantum general relativity have been formulated. Each of these theories has elements of arbitrariness and ambiguity as well as technical difficulty which make it less than satisfactory. However, the construction of these theories has revealed much about the structure of general relativity as a dynamical system and has spurred the development of new approaches to quantum theory. Canonical, sum-over-histories and source theory approaches to the quantization of the gravitational field in the absence of matter are reviewed in terms of a unified notation. Discussions of quantum theory and general relativity are provided to make the review self-contained for readers with a general physics background. The quantization of open space-time geometries (graviton scattering) is treated in sufficient detail to reveal the basic mathematical structure of the formalism. The quantization of closed universes (quantum cosmology) is discussed with particular attention to the superspace concept and the construction of finite-dimensional model quantum theories. Superspace, the domain manifold of the quantum state functional in general relativity, is also discussed separately.
43 citations
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TL;DR: In this article, a rigorous and simple formulation of the isotropy principle is presented, which appears to be more general than those usually presented and which, together with the results of a preceding paper, allows us to carry out such a deduction in the physical case of a 4-dimensional space-time in a straightforward and considerably simplified way.
Abstract: It is well known that it is possible to deduce the Lorentz transformations solely on the basis of the principles of relativity, space‐time homogeneity, and isotropy of space, without making any use of the principles of reciprocity and of the invariance of the velocity of light. Here we put forward a rigorous and simple formulation of the isotropy principle, which appears to be more general than those usually presented and which, together with the results of a preceding paper, allows us to carry out such a deduction in the physical case of a 4‐dimensional space‐time in a straightforward and considerably simplified way.
30 citations
TL;DR: In this paper, the conservation laws based upon the existence of curvature and Ricci collineations are investigated and the results given recently by Katzin, Levine and Davis are reinterpreted and generalized.
Abstract: The conservation laws based upon the existence of curvature and Ricci collineations are investigated and the results given recently by Katzin, Levine and Davis are reinterpreted and generalized. The concept of a ‘Maxwell collineation’ is introduced and corresponding conservation laws are found.
29 citations
TL;DR: Elasticity theory in general relativity formulated from classical nonlinear three dimensional theory, discussing thermodynamics and weak field limit was discussed in this paper, where the authors discussed thermodynamics, weak fields, and weak fields.
Abstract: Elasticity theory in general relativity formulated from classical nonlinear three dimensional theory, discussing thermodynamics and weak field limit
24 citations
Book•
01 Jan 1970
TL;DR: In this article, the authors present a history of the history of Einstein's geometry as a branch of physics, including the development of the theory of Superspace and its application in general physics.
Abstract: Soluble Models of Quantum Gravitation.- The Quantization Program for General Relativity.- Particles and Geometry.- The Sandwich Conjecture.- Classical and Quantum Dynamics of a Closed Universe.- Post-Newtonian Methods and Conservation Laws.- Relativistic Boltzmann Theory and the Grad Method of Moments.- A Lemma on the Einstein-Liouville Equations.- Gravitational Radiation Experiments.- General Relativity Experiments Using Low Temperature Techniques.- Contribution to the History of Einstein's Geometry as a Branch of Physics.- Gravitational Radiation Damping.- The Nature of the Schwarzschild Singularity.- Singularities.- Energy-Momentum of Radiating Systems.- The Theory of Superspace.- Spacetime as a Sheaf of Geodesics in Superspace.- Author Index.
21 citations
TL;DR: In this paper, a generalLorentz-Covariant calculus for the Ricci calculus and of the spinor calculus is presented, which implies the equivalence principle of space-time covariance and allows the geometrisation of gravitational fields according toEinstein's principle of equivalence.
Abstract: The principle of general relativity means the principle of generalLorentz-covariance of the physical equations in the language of tetrads and metrical spinors. A generalLorentz-Covariant calculus and the generalLorentz-covariant generalisations of the Ricci calculus and of the spinor calculus are given. The generalLorentz-covariant representation implies theEinstein principle of space-time covariance and allows the geometrisation of gravitational fields according toEinstein's principle of equivalence.
01 Jan 1970
TL;DR: In this article, the problem of the construction of a quantum theory of gravitation is attacked by a variety of methods, and the fundamental epistemological difficulties are ellucidated and certain novel qualitative features of the sought-for quantum theory are described.
Abstract: The problem of the construction of a quantum theory of gravitation is attacked by a variety of methods. The fundamental epistemological difficulties are ellucidated and certain novel qualitative features of the sought-for quantum theory are described.
TL;DR: To answer the question, the most successful theory of symmetry that has emerged in twentieth century physics—the theory of relativity is referred to.
Abstract: THE question I wish to discuss is: what is the most general mathematical representation of a given theory that is based on a symmetry principle ? To answer the question, I refer to the most successful theory of symmetry that has emerged in twentieth century physics—the theory of relativity.
TL;DR: In this paper, simple theorems and relations for charged- dust distributions in general relativity were presented, and some simple relations for the distribution of charged-dust distributions were established.
Abstract: The paper presents some simple theorems and relations for charged- dust distributions in general relativity.
TL;DR: In the treatment of problems involving rotating coordinate frames one of two types of viewpoint is conventionally adopted, with use of an explicit coordinate transformation for uniform rotation in going from the inertial frame to the rotating frame.
Abstract: IN the treatment of problems involving rotating coordinate frames one of two types of viewpoint is conventionally adopted. The assumption may either be made that the use of principles familiar in special relativity can be extended to the rotating coordinate case, or a general-relativistic treatment may be used, with use of an explicit coordinate transformation for uniform rotation in going from the inertial frame to the rotating frame.
TL;DR: In this article, a detailed analysis is given as to the actual physical methods involved when introducing three or four-dimensional reference systems and the orthogonal transformations and also the Lorentz transformations are introduced not so much as coordinate transformations but as operators reflecting physical properties of material systems.
Abstract: The facts that led to establishment of the special theory of relativity are reanalyzed. The analysis leads to the well-known formalism, involving, however, somewhat unusual notations. The object of the analysis is to start more closely from the directly observed experimental facts than is usually done; at the same time, great stress is laid on giving formulations independent of the representation in particular reference systems. A detailed analysis is given as to the actual physical methods involved when introducing three- or four-dimensional reference systems. The orthogonal transformations and also the Lorentz transformations are introduced not so much as coordinate transformations but as operators reflecting physical properties of material systems. The principle of relativity is replaced by a mathematically equivalent principle denoted as theLorentz principle which reflects certain symmetries of the known physical laws.
TL;DR: The principles of relativity are assertions about the structure of physical laws, whose validity or nonvalidity can only be empirically confirmed or falsified as mentioned in this paper, and the weakest forms of those principles are the so-called global propositions, which furnish statements as to which operations, assumed to be performed simultaneously throughout the whole universe, have no influence upon the physical events.
Abstract: The principles of relativity are assertions about the structure of physical laws, whose validity or nonvalidity can only be empirically confirmed or falsified. The weakest forms of those principles are the so-calledglobal propositions. They furnish statements as to which operations—assumed to be performed simultaneously throughout the whole universe—have no influence upon the physical events. Much stronger principles are those of alocal nature. These assert that the physical properties of a system do not change, when the relation of the system is altered vis-a-vis the universe at large. On formulating these local principles, we presuppose either that it is possible to eliminate any influence of the environment or that the influence can be compensated as in the case of universal forces (e.g., gravitational) which can principally not be removed. Still weaker, however, are those formulations of the relativity principles which postulate relativity only for infinitesimally small space-time domains or regions. This distinction yields clarification of all discussions about existence and meaning of a general relativity principle. Such an analysis was already performed by Einstein and Abraham in 1912.
TL;DR: In this paper, the motion of incoherent matter and hence of test particles in the presence of fields with an arbitrary energy-momentum tensor is studied. But the equations of motion are obtained from Einstein's field equations and are written in the form of geodesic equations of an affine connection.
Abstract: This paper deals with the motion of incoherent matter, and hence of test particles, in the presence of fields with an arbitrary energy-momentum tensor. The equations of motion are obtained from Einstein's field equations and are written in the form of geodesic equations of an affine connection. The special cases of the electromagnetic field, the Proca field and a scalar field are discussed.
TL;DR: In this paper, it was shown that the Lagrangian of general relativity can be chosen so thatS = ∫pmngmnd3x without the requirement of special boundary conditions.
Abstract: In follow-up of an earlier paper by Komar it is shown that the Lagrangian of general relativity can be chosen so thatS=∫pmngmnd3x. This result holds without the requirement of special boundary conditions.
TL;DR: In this article, it was shown that the reinterpretation principle is incompatible with the causality principle and paradoxial situations arise when both principles are used, and the final conclusion is that particles cannot travel on a macroscopic scale faster than light if space and time are homogeneous.
Abstract: Arguments are added to the growing number of arguments against the possibility of faster-than-light particles. Causal loops with faster-than-light particles are discussed in the framework of non-quantum special relativity. Thought experiments with steady currents of faster-than-light particles show that the reinterpretation principle is incompatible with the causality principle. If both principles are used consequently paradoxial situations arise. These are visualized utilizing Brehme diagrams. The final conclusion is that particles cannot travel on a macroscopic scale faster than light if space and time are homogeneous and if the relativity and causality principles are valid.
TL;DR: The resolution of this paradox has an important bearing on the foundations of general relativity because, to resolve it, some authors have taken the extreme position that either general relativity or Mach's principle must be abandoned.
Abstract: THIRRING'S solution for a rotating mass shell is frequently used to illustrate the appearance of centrifugal and Coriolis force in general relativity In the equations of motion of test particles within the shell, terms appear which are of second order in the shell angular velocity, ω These terms are conventionally identified with “centrifugal force”, yet they do bear the relationship to “Coriolis force” that one would expect from Mach's principle The resolution of this paradox has an important bearing on the foundations of general relativity because, to resolve it, some authors have taken the extreme position that either general relativity or Mach's principle must be abandoned In this communication we resolve the paradox without abandoning either
TL;DR: In this paper, the problem of singularity is examined from the perspective of a local observer, and it is proved that any inhomogeneity in the singularity can be obtained from any proper rest mass density.
Abstract: The problem of singularities is examined from the standpoint of a local observer. A singularity is defined as a state with an infinite proper rest mass density. It is proved that any inhomogeneity ...
01 Jan 1970
TL;DR: In this paper, the authors describe an experiment to test Einstein's theory of general relativity in a satellite in space by means of a nearly perfect gyroscope, which is uniquely made possible by complete use of a low temperature environment and the properties of superconductors including the use of zero magnetic fields and ultra-sensitive magnetometry.
Abstract: In this paper we will describe an experiment to test Einstein’s theory of general relativity in a satellite in space by means of a nearly perfect gyroscope.1 This experiment is uniquely made possible by complete use of a low temperature environment and the properties of superconductors including the use of zero magnetic fields and ultrasensitive magnetometry. In the last part of the talk we will mention other relativity experiments which make use of low temperature physics and ultra-sensitive magnetometers.
TL;DR: In this article, it was shown that the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter.
Abstract: It is shown that — in contrast to the classical physics and special relativity — the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle.