Showing papers on "Four-force published in 1997"
Book•
29 Nov 1997
TL;DR: The foundations of special relativity relativistic kinematics, electrodynamics in media, and the test theories of the special relativity this article have been discussed in detail in this article.
Abstract: The foundations of special relativity relativistic kinematics the test theories of special relativity relativistic mechanics electrodynamics in media the proca vector field test of constancy of velocity of light tests of time dilation electromagnetism tests tests of relativistic mechanics upper bounds on photon mass tests of Thomas precession appendix - Minkowvski space-time, four dimension formulation.
133 citations
TL;DR: In this article, an action for simplicial Euclidean general relativity involving only left-handed fields is presented, and the simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation.
Abstract: An action for simplicial Euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which Miller and Brewin have shown that the full field equations are much more restrictive than Einstein's in the continuum limit. The action and field equations of the proposed model are also significantly simpler than those of the Regge model when written directly in terms of their fundamental variables. An entirely analogous hypercubic lattice theory, which approximates Plebanski's form of general relativity, is also presented.
95 citations
TL;DR: In this paper, the well posedness of the evolution of the constraints in standard 3+1 general relativity is established by means of the Bianchi identities, which is relevant to the problem of unconstrained numerical evolution.
Abstract: The well posedness of the evolution of the constraints in standard 3+1 general relativity is established by means of the Bianchi identities. Other related nonstandard 3+1 cases which can be analyzed along similar lines are considered as well. The well posedness of the propagation of the constraints is relevant to the problem of unconstrained numerical evolution.
57 citations
Book•
01 Jan 1997TL;DR: In this paper, the authors presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant.
Abstract: Recently we presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of ordinary space and one dimension of the radial velocity.
49 citations
49 citations
TL;DR: In this paper, the authors present a method to find the apparent horizon (AH) on a special family of 3D spacelike hypersurfaces which has a symmetry around the $z$ axis as well as the reflection one with respect to the equatorial plane.
Abstract: We present a method to find the apparent horizon (AH) on a special family of three-dimensional (3D) spacelike hypersurfaces which has $\ensuremath{\pi}$-rotation symmetry around the $z$ axis as well as the reflection one with respect to the equatorial plane. In a nonaxisymmetric 3D hypersurface, the AH, if it exists, is determined by solving a 2D elliptic-type equation. In the present method, we solve the elliptic-type equation as a boundary value problem. To test this method, we apply it to a variety of nonaxisymmetric 3D hypersurfaces which can be obtained by solving the constraint equations in general relativity. We find that the present method works well in all cases.
33 citations
27 citations
01 Sep 1997
TL;DR: In this article, the line element of the Lorentz transformation has been extended to cosmology by the extension of the original line element to cosmological special relativity, and the Galilean transformation is considered as the most general transformation.
Abstract: Cosmological special relativity: fundamentals of special relativity present-day cosmology postulates cosmic frames space velocity in cosmology pre-special-relativty relative cosmic time inadequacy of classical transformation universe expansion versus light derivation of the transformation interpretation of the transformation another derivation consequencs of the transformation. Extension of the Lorentz Group to cosmology: the line element the transformations explicity the most general transformation. Fundamentals of special relativity: postulates of special relativity the Galilean transformation the Lorentz transformation consequences of the Lorentz transformation four-dimensional structure of spacetime the light cone mass, energy and momentum.
27 citations
TL;DR: The existence of a definite tangent space structure (metric with Lorentzian signature) in the general theory of relativity is the consequence of a fundamental assumption concerning the local validity of special relativity as mentioned in this paper.
Abstract: The existence of a definite tangent space structure (metric with Lorentzian signature) in the general theory of relativity is the consequence of a fundamental assumption concerning the local validity of special relativity. There is then at the heart of Einstein's theory of gravity an absolute element which depends essentially on a common feature of all the non‐gravitational interactions in the world, and which has nothing to do with space‐time curvature. Tentative implications of this point for the significance of the vacuum solutions in general relativity, and for the issue of quantising gravity, are briefly examined.
26 citations
TL;DR: In this article, the modified general relativity theory of Rastall, Al-Rawaf and Taha is discussed in both the radiation-and matter-dominated flat cosmological models.
Abstract: Aspects of the modified general relativity theory of Rastall, Al-Rawaf and Taha are discussed in both the radiation- and matter-dominated flat cosmological models. A nucleosynthesis constraint on the theory's free parameter is obtained and the implication for the age of the Universe is discussed. The consistency of the modified matter-dominated model with the neoclassical cosmological tests is demonstrated.
21 citations
TL;DR: In this paper, the authors reviewed old and recent ideas concerning the nature of time, starting from Mach's refusal of Newton's absolute time, and concluded that the slowing down of moving clocks is a real phenomenon.
Abstract: Old and recent ideas concerning the nature of time are reviewed, starting from Mach's refusal of Newton's absolute time. Many experiments show that the slowing down of moving clocks is a real phenomenon. Such must then also be the so-called “twin paradox,” which owes its name to its evident incompatibility with the philosophy of relativism (not to be confused with the theory of relativity). The Lorentz reformulation of special relativity started by postulating physical effects of the ether, but accepted Einstein's clock synchronization. Only because of this Lorentz could not understand the advantages of an easily deducible different theory. As stressed by Popper, one of the main problems of the usual approach is the introduction of a superdeterministic universe. Recent results obtained by the author show that a theory is possible, based on relative time but on absolute simultaneity, in which the conceptual difficulties of relativity are avoided.
TL;DR: The empirical content of the modern definition of relativity given in the Andersonian approach to spacetime theory has been overestimated and it does not imply the empirical relativity Galileo illustrated in his famous ship thought experiment as mentioned in this paper.
Abstract: The empirical content of the modern definition of relativity given in the Andersonian approach to spacetime theory has been overestimated. It does not imply the empirical relativity Galileo illustrated in his famous ship thought experiment. I offer a number of arguments-some of which are in essential agreement with a recent analysis of Brown and Sypel [1995]-which make this plausible. Then I go on to present example spacetime theories which are modern relativistic but violate Galileo's relativity. I end by briefly discussing the prospects for improving on modern relativity.
TL;DR: In this article, it is shown how to derive the three classic tests of general relativity from Newtonian gravity and special relativity in a form at least partly accessible to pre-university students.
Abstract: It is often assumed that the three classic tests of general relativity require the full mathematical apparatus of that theory for their derivation. In fact, it is possible to derive them from Newtonian gravity and special relativity in a form at least partly accessible to pre-university students.
TL;DR: In this article, the Kreuzer experiment was interpreted as providing an upper limit on the difference in the ratio of active to passive mass between fluorine and bromine, and an interesting interpretation was given by Thorne et al.
Abstract: In 1966, the Kreuzer experiment set an upper limit on the difference in the ratio of active to passive mass between fluorine and bromine, and an interesting interpretation was given by Thorne et al. However, in 1976 Will, with his new parameterized post-Newtonian (PPN) approach, interpreted this experiment as providing an upper limit on his parameter combination related to electromagnetism. We show that, from the viewpoint of general relativity, Will's approach remains to be justified. Moreover, his result originates from his unphysical nuclear model, which ignores the isospin-dependent nuclear forces and is actually inconsistent with general relativity. It seems that to determine the constraint on the gravitational coupling to electromagnetism is beyond the valid application of the PPN formalism. As a further step, experimental measurement for the coupling constant to electromagnetism is recommended.
TL;DR: A general coordinate-free method of integrating the functional Hamilton-Jacobi equation for gravity and matter is described in this article, which represents a large generalization of the spatial gradient expansion that had been employed earlier.
Abstract: Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is described. This series approximation method represents a large generalization of the spatial gradient expansion that had been employed earlier. Additional solutions may be constructed using a nonlinear superposition principle. This formalism may be applied to problems in cosmology.
TL;DR: In this paper, a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity is proposed, where matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations.
Abstract: We propose a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity. Matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A phase-space distribution function, constructed using covariant coherent states, obeys the relativistic Vlasov equation provided the de Broglie wavelength for the field is very much smaller than the scales of interest. We illustrate the method by solving for the evolution of a system of particles in a static, plane-symmetric, background spacetime.
TL;DR: In this article, the problem of what is observable in general relativity is investigated with the help of Landau's observable space interval, and the observational frames for individual observers are established.
Abstract: The problem of what is observable in general relativity is investigated. With the help of Landau's observable space interval, the observational frames for individual observers are established. Within the Ashtekar formulation of general relativity, we argue from the nonvanishing Poisson brackets of the Yang-Mills field and the constraints that Dirac observability does not apply to gravitational systems.
TL;DR: In this article, it has been shown that the very general symmetries of space-time do not necessarily lead to the special theory of relativity (STR), and that the experimental data gathered up to now are not able to definitely choose one of these versions.
Abstract: It has been shown that the very general symmetries of space-time do not necessarily lead to the special theory of relativity (STR). In this connection the general form of space-time kinematics has been developed. It includes three physical versions. One of them coincides with the STR, the second version comes to the Lorentz ether theory, the third version is not analysed in the present paper. It has been proved that the experimental data gathered up to now are not able to definitely choose one of these versions. Such a choice could be made in the modified Champeney experiment looking for the third order term in (1/c), where c stands for the speed of light.
TL;DR: In this paper, the rotating disk as an example of a non-Euclidean space is carefully examined; the basic arguments of Einstein are emphasized; a new approach is also presented which resolves the Ehrenfest paradox.
Abstract: In this paper, the rotating disk as an example of a non-Euclidean space is carefully examined; the basic arguments of Einstein are emphasized. A new approach is also presented which resolves the Ehrenfest paradox.
TL;DR: In this paper, it was shown via the principle of path independence that the (time gauge) constraint algebra derived by Charap et al. for vielbein general relativity is a generic feature of any covariant theory formulated in a viel-bein frame.
Abstract: It is shown via the principle of path independence that the (time gauge) constraint algebra derived by Charap et al for vielbein general relativity is a generic feature of any covariant theory formulated in a vielbein frame. In the process of doing so, the relationship between the coordinate and orthonormal frame algebera is made explicit.
TL;DR: In this article, the energy-momentum tensor for a dynamical string fluid in general relativity is presented using the Ray-Hilbert variational principle and the calculations are given for both the standard and the extended thermodynamics versions in which the latter includes the string as thermodynamic variables.
Abstract: The general, energy-momentum tensor for a dynamical, string fluid in general relativity is presented using the Ray-Hilbert variational principle The calculations are given for both the standard and the extended thermodynamics versions in which the latter includes the string as thermodynamic variables In general relativity, it is shown that the string does not Fermi-Walker transport Examples of solutions to the field equations are given and compared with solutions obtained from the postulated energy-momentum tensor of Letelier
TL;DR: In this article, the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds were investigated, which form the equivalent to the groups of large gauge transformations in Yang-Mills theories.
Abstract: We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
TL;DR: In this paper, the e-synchrony transformation is presented within this context in a sufficiently general manner that explores the connection of spatiotemporal measures to the choice of an e-simultaneity relation, and the feasibility of the latter is then investigated in terms of the two-component spinor formulation of special relativity.
Abstract: The assessment of the conventionality of simultaneity has commonly taken place so far within the traditional formulation of the special theory of relativity. The e-synchrony transformation is presented within this context in a sufficiently general manner that explores the connection of spatiotemporal measures to the choice of an e-simultaneity relation. Subsequently to the recent work of Zangari, the feasibility of the latter is then investigated in terms of the two-component spinor formulation of special relativity. This is motivated by the fact that the spinor formulation provides the most fundamental expression of a spacetime theory that is consistent with the principle of special relativity. It is shown within this context that the transformation elements of the spinor group (unlike its Lorentz counterparts) prevent the groups representations being extended to a representation of the e-class of non-standard synchrony transformations in four-dimensional space. The underlying reasons are traced down and discussed at length, whereas the compatibility of this finding with a general version of the principle of general relativity that is applicable to both tensor and spinor quantities is also demonstrated. It is finally established that the standard simultaneity relations far from constituting just a sensible choice in a range of conventional possibilities, is uniquely and objectively singled out by the properties of a spinor structure in Minkowski spacetime. The desirability of such a structure is anticipated by its fundamental status.
TL;DR: In this article, the authors used the periodicity in the redshift distribution of galaxies observed by Broadhurst et al. to determine the coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity.
Abstract: Recent theoretical work determines the correct coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity. The periodicity in the redshift distribution of galaxies observed by Broadhurst et al., if genuine, determines the coupling constant in the proposed scalar field models. As a result, these observations contain important information on the problem of whether general relativity is the correct theory of gravity in the region of the universe at redshifts z < 0.5.
TL;DR: In this article, an SU(2) covariant representation of the constraints of Euclidean general relativity in the Ashtekar variables is given, where the Gauss, diffeomorphism and Hamiltonian constraints become purely algebraic restrictions on the curvature and the torsion associated with this connection.
Abstract: We give an SU(2) covariant representation of the constraints of Euclidean general relativity in the Ashtekar variables. The guiding principle is the use of triads to transform all free spatial indices into SU(2) indices. A central role is played by a special covariant derivative. The Gauss, diffeomorphism and Hamiltonian constraints become purely algebraic restrictions on the curvature and the torsion associated with this connection. We introduce coordinates on the jet space of the dynamical fields, which cleanly separate the constraint and gauge directions from the true physical directions. This leads to a classification of all local diffeomorphism and Gauss invariant charges.
Book•
01 Jan 1997
TL;DR: In this article, a satellite gyroscope and a gravitational wave detector have been used to measure the strength of the Earth's magnetic field in the weak field approximation of general relativity.
Abstract: Preface Part I. Special Relativity: 1. Kinematics of a point mass 2. Changes of reference system 3. Experiments 4. Dynamics of a particle 5. Mathematical framework 6. The dynamics of continuous media 7. General coordinate systems Part II. Relativistic Gravitation: 1. Newtonian gravitation 2. Metric theories of gravity 3. Tests of metric theories in the Solar System 4. Newtonian cosmology 5. Relativistic cosmology 6. General relativity 7. Applications of Einstein's equations 8. General relativity in the weak field approximation 9. Two experimental projects: a satellite gyroscope and a gravitational wave detector Appendix A. Lagrange's equations Appendix B. Geometric framework of general relativity Useful numerical values Bibliography Index.
TL;DR: In this paper, it was shown that a violation of signal locality and unitarity occur in a particular merger of quantum mechanics and general relativity, where the signal locality is violated by a special case of the problem.
Abstract: It is shown that a violation of signal locality and unitarity occur in a particular merger of quantum mechanics and general relativity.
TL;DR: In this paper, a new formulation of classical relativistic Hamiltonian mechanics is proposed based on a proper-time implementation of special relativity using a transformation from observer proper time, which is not invariant, to system proper time which is a canonical contact transformation on extended phase space.
Abstract: We report on a new formulation of classical relativistic Hamiltonian mechanics which is based on a proper-time implementation of special relativity using a transformation from observer proper-time, which is not invariant, to system proper-time which is a canonical contact transformation on extended phase-space. This approach does not require the use of time as a fourth coordinate and so we prove that it satisfies the two postulates of special relativity. In the free particle case, our transformation theory generates a Poincare group which fixes time (system proper-time). We prove that the Fushchych-Shtelen transformation is an element of our group, which fixes time for Maxwell’s equations. In the interaction case, our transformation theory allows us to avoid the no-interaction theorem. We show that the Santilli Isotopes appear naturally when interaction is turned on.