Showing papers on "Four-force published in 1996"
TL;DR: The scale covariant theory as mentioned in this paper is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, that consists of generalizing Einstein's principle of relativity (up to now applied to motion laws) to scale transformations.
Abstract: The theory of scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, that consists of generalizing Einstein's principle of relativity (up to now applied to motion laws) to scale transformations. Namely, we redefine space-time resolutions as characterizing the state of scale of the reference system and require that the equations of physics keep their form under resolution transformations (i.e. be scale covariant). We recall in the present review paper how the development of the theory is intrinsically linked to the concept of fractal space-time, and how it allows one to recover quantum mechanics as mechanics on such a non-differentiable space-time, in which the Schrodinger equation is demonstrated as a geodesies equation. We recall that the standard quantum behavior is obtained, however, as a manifestation of a “Galilean” version of the theory, while the application of the principle of relativity to linear scale laws leads to the construction of a theory of special scale relativity, in which there appears impassable, minimal and maximal scales, invariant under dilations. The theory is then applied to its preferential domains of applications, namely very small and very large length- and time-scales, i.e. high energy physics, cosmology and chaotic systems.
174 citations
TL;DR: A modified version of the field equations of general relativity is obtained on relaxing the covariant energy-momentum conservation condition as discussed by the authors, which introduces a single arbitrary constant and does not appear to upset the successes of the general relativity in or outside cosmology.
Abstract: A modified version of the field equations of general relativity is obtained on relaxing the covariant energy-momentum conservation condition. This introduces a single arbitrary constant and does not appear to upset the successes of general relativity in or outside cosmology. The matter-dominated cosmological model, based on the generalized field equations, is discussed. It is shown to provide more room for consistency with the observational data.
145 citations
TL;DR: In this paper, a quaternionic algebra on reals was proposed to reformulate Special Relativity by real linear quaternions and showed that the appropriate transformations on the 3+1 space-time may be overcome.
Abstract: We reformulate Special Relativity by a quaternionic algebra on reals. Using real linear quaternions, we show that previous difficulties, concerning the appropriate transformations on the 3+1 space–time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.
76 citations
TL;DR: It is shown through the study of specific diagrams that cancellations occur which restore the expected behaviour of the energy expansion and by considering the power counting in a physical gauge it is shown that the apparent bad behavior is a gauge artifact, and that the quantum loops enter with a well behaved energy expansion.
Abstract: A class of loop diagrams in general relativity appears to have a behavior which would upset the utility of the energy expansion for quantum effects We show through the study of specific diagrams that cancellations occur which restore the expected behaviour of the energy expansion By considering the power counting in a physical gauge we show that the apparent bad behavior is a gauge artifact, and that the quantum loops enter with a well behaved energy expansion
70 citations
TL;DR: A simpler but approximate scheme for systems near equilibrium, such as binary neutron stars, is proposed and tested on isolated, rapidly rotating, relativistic stars.
Abstract: Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, such as binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation works well if we are to believe its predictions for more complicated systems such as binaries. Our results are very encouraging.
67 citations
TL;DR: The parametrized post-Newtonian parameter (which identically vanishes in general relativity) plays a dual role in that it is associated both with a violation of the momentum conservation law and with the existence of a preferred frame as mentioned in this paper.
Abstract: General relativity predicts that energy and momentum conservation laws hold and that preferred frames do not exist. The parametrized post-Newtonian formalism phenomenologically quantifies possible deviations from general relativity. The parametrized post-Newtonian parameter (which identically vanishes in general relativity) plays a dual role in that it is associated both with a violation of the momentum conservation law and with the existence of a preferred frame. By considering the effects of in certain binary pulsar systems, it is shown that (90% CL). This limit improves on previous results by several orders of magnitude, and shows that pulsar tests of rank (together with Hughes - Drever-type tests) among the most precise null experiments of physics.
65 citations
TL;DR: A modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations with Riemannian and Lorentzian signatures is given.
Abstract: We study in this paper a new approach to the problem of relating solutions to the Einstein field equations with Riemannian and Lorentzian signatures. The procedure can be thought of as a “real Wick rotation”. We give a modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations. We show how this procedure works for the Schwarzschild metric and discuss some possible applications of the formalism in the context of signature change, the problem of time, black hole thermodynamics... PACS 04.20Cv, 04.20Fy. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by CERN Document Server
65 citations
TL;DR: In this article, an especially simple version of the optical-mechanical analogy is extended to general relativity and a variational principle for the trajectories of photons and particles is obtained which is applicable to a broad class of metrics.
Abstract: The optical–mechanical analogy involves the expression of geometrical optics and particle mechanics in the same mathematical language. In this paper, an especially simple version of the optical–mechanical analogy is extended to general relativity. A variational principle for the trajectories of photons and particles is obtained which is applicable to a broad class of metrics. This permits us to cast the exact equations of motion for both massive and massless particles into the form of Newtonian mechanics. The new equations of motion are illustrated by applications to the Schwarzschild metric.
39 citations
TL;DR: In this paper, the authors give an exact solution of the five-dimensional relativity equations, and interpret it using the induced-matter formalism wherein geometry in 5D gives rise to matter in 4D.
Abstract: We give an exact solution of the five-dimensional relativity equations, and interpret it using the induced-matter formalism wherein geometry in 5D gives rise to matter in 4D. The solution represents oscillations of ordinary 3D space where the associated medium has the equation of state of the classical de Sitter vacuum. We outline implications for the inflationary universe model.
35 citations
TL;DR: In this paper, it was shown that the standard QCD Lagrangian can be represented as the sum of usual Palatini Lagrangians for Einstein general relativity and the Lagrangia of matter and some other fields where the tetrad fields and the metric are constructed from initial SU(3) Yang-Mills fields.
Abstract: It is shown that there exists such a collection of variables that the standard QCD Lagrangian can be represented as the sum of usual Palatini Lagrangian for Einstein general relativity and the Lagrangian of matter and some other fields where the tetrad fields and the metric are constructed from initial SU(3) Yang–Mills fields
22 citations
01 Jan 1996
TL;DR: K Gδdel as mentioned in this paper examined a nonexpanding but rotating solution of the Einstein field equations, in which causality is violated; this lead to an in-depth examination of the concepts of causality and time in curved space-times.
Abstract: K Gδdel published two seminal papers on general relativity theory and its application to the study of cosmology. The first examined a non-expanding but rotating solution of the Einstein field equations, in which causality is violated; this lead to an in-depth examination of the concepts of causality and time in curved space-times. The second examined properties of a family of rotating and expanding spatially homogeneous solutions of the Einstein equations, which was a forerunner of many studies of such cosmologies. Together they stimulated examination of themes that were fundamental in the development of the Hawking-Penrose singularity theorems and in studies of cosmological dynamics. I review these two papers, and the developments that resulted from them.
TL;DR: In this paper, the Ricci scalar is used as a criterion of the local instability in simple mechanical systems (systems with a natural Lagrange function) and the role of relativistic systems in general relativity is emphasized.
Abstract: Chaos is investigated in the context of general relativity and gravitation. We show how quantitative and global measures of chaos can be obtained from qualitative and local ones. After averaging---first, over all two-directions, and second, along the trajectory---the rate of separation of nearby trajectories (Lyapunov-like exponents) can be obtained. This gives us a tool to the invariant chaos description. The sign of the Ricci scalar serves as a criterion of the local instability in simple mechanical systems (systems with a natural Lagrange function). We also show how to reduce relativistic simple mechanical systems to the classical ones. Timelike and null geodesics in multi-black-hole cosmological spacetimes are considered. The role of relativistic systems in general relativity is emphasized. \textcopyright{} 1996 The American Physical Society.
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TL;DR: In this article, different topos-theoretical approaches to the problem of construction of General Theory of Relativity (GOR) have been studied, and a new theory of space-time, created in a purely logical manner, has been proposed.
Abstract: We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein theory of space-time. This is a new theory of space-time, created in a purely logical manner. Four possibitities are investigated: axiomatic approach to causal theory of space-time, the smooth toposes as a models of Theory of Relativity, Synthetic Theory of Relativity, and space-time as Grothendieck topos.
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TL;DR: In this paper, Chamseddine and Connes showed that the Dirac operator is covariant with respect to Lorentz and internal gauge transformations and must include Yukawa couplings.
Abstract: Connes has extended Einstein's principle of general relativity to noncommutative geometry. The new principle implies that the Dirac operator is covariant with respect to Lorentz and internal gauge transformations and the Dirac operator must include Yukawa couplings. It further implies that the action for the metric, the gauge potentials and the Higgs scalar is coded in the spectrum of the covariant Dirac operator. This ``universal'' action has been computed by Chamseddine & Connes, it is the coupled Einstein-Hilbert and Yang-Mills-Higgs action. This result is rederived and we discuss the physical consequences.
TL;DR: In this paper, the authors generalize Robertson's frame designed to discuss the experimental tests of Special Relativity and include parametrized post-Newtonian theories of gravitation in the new frame.
Abstract: We generalize Robertson's frame designed to discuss the experimental tests of Special Relativity. We include parametrized post-Newtonian theories of gravitation in the new frame. This generalization includes covariant equations for the motion of a test particle. We discuss the possibility of new tests such as tests of Special Relativity in astronomy.
TL;DR: In this article, it is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle and of the principle of general relativity are alternative programs, at least as long as only field equations of second order are considered.
Abstract: It is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle (in the version of the Mach-Einstein doctrine) and of the principle of general relativity are alternative programs. That means only the former or the latter can be realized—at least as long as only field equations of second order are considered. To demonstrate this we discuss two sufficiently wide classes of theories (Einstein-Grossmann and Einstein-Mayer theories, respectively) both embracing Einstein's theory of general relativity (GRT). GRT is shown to be just that “degenerate case” of the two classes which satisfies the principle of general relativity but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation.
TL;DR: The 8th Latin American Symposium on Relativity and Gravitation (LASG) as mentioned in this paper was held in Aguas de Lindoia, Brazil in July 1993, where 68 papers were devoted to mathematical aspects of quantum mechanics and general relativity.
Abstract: The book contains papers presented at the 8th Latin American Symposium on Relativity and Gravitation which was held in Aguas de Lindoia, Brazil in July 1993. The book is like a Turkish bazaar where there is something for everybody. Most of the 68 papers are devoted to mathematical aspects of quantum mechanics, quantum field theory and general relativity. The four plenary lectures were on cosmic strings and their observational consequences (by E P S Shellard), Clifford algebras, relativity and quantum mechanics (by P Lounesto), computational relativity (by R Matzner), and some notes on the use of computer algebra for the study of nakedly singular spacetimes (by K Lane). Shellard's review on cosmic strings is up to date, complete and very interesting. Matzner concentrates on important cosmological and astrophysical systems that can be analysed only numerically. The very important example of a fully relativistic two-black-hole collision and coalescence is thoroughly investigated. There are several other interesting papers but, unfortunately, the majority of papers are concerned with problems which are far away from the current mainstream of research in general relativity. Most of the authors have access to electronic mail and can easily get information on current theoretical problems and the main observational results. I do hope that the next conference will be more interesting resulting in a more valuable proceedings.
TL;DR: In this paper, it was shown that the Evans-Vigier modified electrodynamics is compatible with the Relativity Theory, and it was further shown that it is also compatible with quantum mechanics.
Abstract: It is shown that the Evans-Vigier modified electrodynamics is compatible with the Relativity Theory.
Journal Article•
TL;DR: In this paper, a new postulate based on the radar distance between freely falling particles and light signals is proposed, which is based upon the notion of the radar distances between the two objects and demands the approximate equality of the growth of radar distance for particle pairs of equal, small initial velocities.
Abstract: Efforts at providing a physical-axiomatic foundation of the space-time structure of the general theory of relativity have led, when based on simple empirical facts about freely falling particles and light signals, in a satisfying manner only to a Weyl space-time. By adding postulates based on quantum theory, however, the usual pseudo-Riemannian space-time can be reached. We present a newclassical postulate which provides the same results. It is based upon the notion of the radar distance between freely falling particles and demands the approximate equality of the growth of the radar distance for particle pairs of equal, small initial velocities. We show that given this, a property results, as found in earlier work by the author, that distinguishes between Weyl and Lorentz space-times. The property refers to a special metric and decides whether its metric connection has the given free-fall worldlines as geodesics or not. It consists in the vanishing of the mixed spatiotemporal componentsgi4 of this metric in suitable coordinates along the worldline of the freely falling observer, as the rest system of which the coordinates are constructed.
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Abstract: This paper focuses on the imposition of boundary conditions for numerical relativity simulations of black holes This issue is used to motivate the discussion of a new hyperbolic formulation of 3+1 general relativity The paper will appear in the Proceedings of the Les Houches School on Astrophysical Sources of Gravitational Radiation, 1995, edited by J-A Marck and J-P Lasota to be published by Springer-Verlag
01 Jan 1996
TL;DR: In this paper, the vierbein formalism for incorporating spinor fields in General Relativity has been studied and compared to those found in the standard formalism, and the Clifford algebra and spinor field equations are derived from an action principle.
Abstract: This lecture will focus on the vierbein formalism for incorporating spinor fields in General Relativity. The vierbein formalism is fundamentally related to the notion of local Lorentz invariance in the tangent space, and may be considered regardless of the presence of spinor fields. The field equations are derived from the action and compared to those found in the standard formalism. Finally, the Clifford algebra and spinor fields are embodied in the formalism, the field equations are obtained from an action principle and compared to the previous equations. Unlike the previous cases, when spinor matter is incorporated there is an ambiguity in the resulting field equations, depending on which fields are chosen to be independent dynamical variables. At present, there are no data to guideus to the correct version.
01 Jan 1996
01 Jan 1996
TL;DR: In this paper, the causal structure of Einstein's equations is described as a first-order system of balance laws, which is shown to be hyperbolic when the time coordinate is chosen in an invariant algebraic way (maximal slicing is recovered as a limiting case).
Abstract: The first lecture is devoted to the causal structure of Einstein’s evo lution equations They are written as a first-order system of balance laws, which is shown to be hyperbolic when the time coordinate is chosen in an invariant algebraic way (maximal slicing is recovered as a limiting case) The second lecture deals with first-order flux-conservative systems The propagation of characteristic fields in an inhomogeneous background is also considered, with a view on relativity applications
TL;DR: In the last two decades, theories explaining the same experiments as well as special relativity does, were developed by using different synchronization procedures All of them are ether-like theories Most authors believe these theories to be equivalent to special relativity, but no general proof was ever given.
Abstract: In the last two decades, theories explaining the same experiments as well as special relativity does, were developed by using different synchronization procedures All of them are ether-like theories Most authors believe these theories to be equivalent to special relativity, but no general proof was ever given By means of agedanken experiment on light aberration, we produce strong evidence that this is the case for experiments made in inertial systems