Showing papers on "Four-force published in 1973"
01 Jan 1973
TL;DR: The purpose of these lectures was to give a survey of Einstein’s theory of gravitation and the connection between physical and mathematical concepts and ideas.
Abstract: The purpose of these lectures was to give a survey of Einstein’s theory of gravitation. Since special astrophysical topics have been covered by other lecturers and the principal mathematical tools of general relativity were also considered separately, I tried to concentrate on the general structure of the theory and the connection between physical and mathematical concepts and ideas; examples and applications have been mentioned briefly only.
212 citations
TL;DR: In this article, strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed are presented, which limit perturbations of non-flat closed initial solutions.
Abstract: There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.
101 citations
TL;DR: In this article, the authors suggest that the singularity is avoided only because of the high symmetry of the model used, which is not the case in the case of intrinsic spin effects.
Abstract: TRAUTMAN has suggested1 that the introduction of intrinsic spin effects into general relativity through the Einstein-Cartan torsion theory may avert a gravitational singularity. In this note we suggest that the singularity is avoided only because of the high symmetry of the model used.
57 citations
43 citations
TL;DR: In this paper, it was shown that changes of topology in the spacetime of classical general relativity are consistent with stable causality, future causal geodesic completeness, and finite, positive energy density.
Abstract: It is shown that ‘changes of topology’ (of spacelike sections) in the spacetime of classical general relativity are consistent with the following requirements: (i) stable causality, (ii) future causal geodesic completeness, and (iii) finite, positive energy density This amounts to showing that the framework of classical general relativity encompasses ‘changes of topology’
37 citations
Book•
01 Jan 1973
TL;DR: In this article, the theory of parallels has been used for Minkowski space-time axioms for collinearity in 3D kinematics, including the notion of parallel particles.
Abstract: Kinematic axioms for Minkowski space-time.- Conditionally complete particles.- Implications of collinearity.- Collinear sub-SPRAYS after coincidence.- Collinear particles.- Theory of parallels.- One-dimensional kinematics.- Three-dimensional kinematics.- Concluding remarks.
31 citations
01 Jan 1973
TL;DR: The nature and role of the various relativity principles has been correspondingly unclear as discussed by the authors, and exactly how they are associated with given physical theories, has been far from clear, as well as the nature of the role of these principles.
Abstract: Traditionally, certain physical theories have been thought to have relativity principles associated with them. Associated with Newtonian mechanics is the principle of Galilean relativity, associated with special relativity is the special or restricted principle of relativity, associated with general relativity is the general principle of relativity, etc. Such relativity principles are often expressed in terms of groups of transformations. The principle of Galilean relativity is expressed by the ‘invariance’ of Newtonian mechanics under the Galilean group, that of special relativity by the ‘invariance’ of special relativity under the Lorentz group, and that of general relativity by the ‘invariance’ (or ‘covariance’) of general relativity under the group of all 1–1 transformations with non-vanishing Jacobian. Unfortunately, just what these various groups are groups of, and exactly how they are associated with given physical theories, has been far from clear. Similarly, the nature and role of the various relativity principles has been correspondingly unclear.
25 citations
TL;DR: In this article, it was pointed out that if one did not know the Einstein-HamiltonJacobi equation one might hope to derive it straight off from plausible first principles, without ever going through the formulation of the Einstein field equations themselves.
Abstract: It is pointed out that if one did not know the Einstein--HamiltonJacobi equation one might hope to derive it straight off from plausible first principles, without ever going through the formulation of the Einstein field equations themselves. (auth)
25 citations
TL;DR: Two generalisations of Birkhoff's theorem for the cases where the three-parameter group of motions acts on two-dimensional time-like and null orbits are proved in this article.
Abstract: Two generalisations of Birkhoff's theorem are proved for the cases where the three-parameter group of motions acts on two-dimensional time-like and null orbits. A complete list of possible extensions of the three-parameter group to one of four parameters and of the resulting metrics is given.
21 citations
18 citations
TL;DR: In this paper, a theory of gravitation, where the stress energy tensor of the gravitational field is part of the source term of the geometric curvatures, is presented, which predicts correctly all the Newtonian and post-Newtonian effects of gravity currently considered as crucial.
TL;DR: In this paper, the transformation equations of kinematic, thermodynamic and electromagnetic quantities as well as their spatial and temporal derivatives are derived and their objectivity examined and the restrictions on the form of constitutive equations of continuum physics imposed by the principle of objectivity are studied.
Abstract: In this study we propose a principle of objectivity which is appropriate to the theory of relativity. The transformation equations of kinematic, thermodynamic and electromagnetic quantities as well as their spatial and temporal derivatives are derived and their objectivity examined. Finally the restrictions on the form of constitutive equations of continuum physics imposed by the principle of objectivity are studied.
TL;DR: In this paper, the authors investigate the possibility of describing particles that travel faster than light within the special theory of relativity, introducing faster-than-light inertial frames and extending the principle of relativity to all inertial frame, slow and fast.
Abstract: We investigate the possibility of describing particles that travel faster than light within the special theory of relativity, introducing faster-than-light inertial frames and extending the principle of relativity to all inertial frames, slow and fast. The direct consequence of this hypothesis, which imposes a complete symmetry between slow and fast worlds, is that tachyons and bradyons can exchange only internal quantum numbers. Furthermore this symmetry allows us to develop a kinematics of faster-than-light particles in which the proper mass of a tachyon is interpreted by a real number, even if not corresponding to any possible direct observation.
TL;DR: In this article, Clausius processes are defined as noninteracting physical processes for which there is interaction and associated Lorentz transformation, and the relativistic changes occur only in association with physical interactions and are direct alterations in the variables of the observed system.
Abstract: In the established space-time coordinate-transformation (STCT) interpretation of special relativity theory, relativistic changes are consequent upon the Lorentz transformation of coordinate clocks and rods between relatively moving systems. In the proposed alternative interpretation, relativistic changes occur only in association with physical interactions, and are direct alterations in the variables of the observed system. Since space-time and momentum-energy are conjugate four-vectors, transformation of a space or time variable of a system is to be expected only if there is a concomitant transformation of the corresponding momentum or energy variable. The Lorentz invariance of the scalar entropy functionS supports the interaction interpretation; timet=f(S) of a macroscopic, entropy clock should give a Lorentz-invariant time measure, and an illustrative entropy clock is discussed. Noninteracting physical processes may be called Clausius processes, in contrast to Lorentz processes for which there is interaction and associated Lorentz transformation. Changes of energy and frequency, withE=hv, are instances of the parallel relativistic transformations. Likewise, the variation with velocity in decay time of mesons follows directly from the relativistic energy transformation of decay products; this relationship is shown for muons by a simple calculation with β-decay theory.
TL;DR: In this article, the Lorentz-covariant two-body problem was shown to be solvable for straight-line motiom and admits solutions in which the charges move in circles about a commom center.
Abstract: S>We treat a Lorentz-covariant two-body problem due to Fokker: One electric charge experiences the retarded field of a second, while the he first; this is pure action at a distance, with no self-action; conservation principles exist. We show that this (apparently generally soluble) time-asymmetric problem is exactly soluble for straight-line motiom and admits solutions in which the charges move in circles about a commom center. We briefly consider nonelectrodynamic time-asymmetric interactions and aspects of quantizing thc motions. (auth)
TL;DR: In this article, a covariant decomposition of the general relativistic inertial acceleration into its impressed, D'Alembert, Coriolis, centrifugal, Euler, and tidal gravitational components is presented.
TL;DR: In this paper, an argument is presented that negative energy tachyons do not exist, based on an apparent inconsistency with special relativity, and a misunderstanding of the Dirac-Stueckelburg-Feynman-Sudarshan reinterpretation principle.
Abstract: An argument is presented that negative-energy tachyons do not exist. The argument is based on an apparent inconsistency with special relativity, and a misunderstanding of the Dirac-Stueckelburg- Feynman-Sudarshan reinterpretation principle''. (LBS)
TL;DR: In this article, an initial value problem for an axisymmetric perfect fluid in general relativity is considered by specifying data on an initial null hypersurface, and a solution to the problem is shown to exist provided that the metric and physical variables are expanded in positive powers of a radial parameter and certain restrictive conditions at the origin are satisfied.
Abstract: An initial value problem for an axisymmetric perfect fluid in general relativity is considered by specifying data on an initial null hypersurface. The approach is an adaptation of the techniques introduced by Bondi, van der Burg & Metzner (1962) for dealing with asymptotically flat, empty space-time. A solution to the problem is shown to exist provided that the metric and physical variables are expanded in positive powers of a radial parameter and certain restrictive conditions at the origin are satisfied.
TL;DR: In this article, the properties of the most general (infinitesimal) mapping in phase space which preserves a congruence of classical trajectories have been determined, and the application of these results to the problem of determining the observables of the general theory of relativity is indicated.
Abstract: We determine the properties of the most general (infinitesimal) mapping in phase space which preserves a congruence of classical trajectories. Although such mappings need not be canonical, we find that they can nevertheless be associated in a unique fashion with constants of the motion. The application of these results to the problem of determining the observables of the general theory of relativity is indicated.
TL;DR: In this article, the authors consider models of the universe containing linear and nonlinear spinor matter, and assume that the linear spinors are described by the generally covariant Dirac equation, and the nonlinear ones by the general covariant Ivanenko-Heisenberg equation.
Abstract: We consider models of the universe containing linear and nonlinear spinor matter. It is assumed that the linear spinor matter is described by the generally covariant Dirac equation, and the nonlinear by the generally covariant Ivanenko-Heisenberg equation.
TL;DR: In this paper, a global formulation of projective theories of relativity in the framework of projectively projective manifolds is presented, that is, manifolds based on the pseudogroup of homogeneous transformations in R5.
Abstract: We present a global formulation of projective theories of relativity in the framework of projective manifolds, that is, manifolds based on the pseudogroup of homogeneous transformations in R5 Apart from formulating every previously considered geometric object and physical relation in an invariant manner, some new results, such as the theorem on the semidirect product structure of the invariance group of Einstein‐Maxwell equations, and theorems on topological restrictions on the underlying five‐dimensional projective manifold, etc have been obtained The relationship between space‐time and the auxiliary 5‐manifold is clarified and investigated in detail A more general geometric definition of the electromagnetic field tensor and a geometric interpretation of the charge/mass ratio is given
TL;DR: In this paper, the relationship between the Petrov classification of Riemannian space times and the Debever-Penrose principal null directions is developed in explicit algebraic terms, and the relation between Petrov's classification and the principal null direction is analyzed in terms of algebraic relations.
Abstract: The relationship between the Petrov classification of Riemannian space‐times and the Debever‐Penrose principal null directions is developed in explicit algebraic terms.
TL;DR: In this paper, conservation laws for dynamical systems in Riemannian space-time in the Vierbein formalism are deduced from the existence of motions in the space time.
Abstract: Conservation laws for dynamical systems in Riemannian space-time in the Vierbein formalism are deduced from the existence of motions in the space-time. The result is applied to Dirac's equation in General Relativity.
TL;DR: In this article, the authors extend the usual treatment of constraints in the canonical formalism to cases where the restrictions on the canonical variables take the form of inequalities, and apply this prescription to eliminate the positivity conditions in a model theory and in general relativity.
Abstract: We extend the usual treatment of constraints in the canonical formalism to cases where the restrictions on the canonical variables take the form of inequalities. The result is a general prescription for eliminating such restrictions from the canonical formalism. We apply this prescription to eliminate the positivity conditions in a model theory and in general relativity. In the case of the model we find that elimination of the positivity conditions makes the construction of observables much simpler; in the full theory, however, the spatial constraints introduce complications, and we have not been able to carry out all the calculations explicitly.
TL;DR: For a class of pivot events, it is possible to define a skew symmetric torque tensor so as to warrant relativistically invariant equilibrium conditions for extended bodies.