Showing papers on "Special relativity (alternative formulations) published in 2001"
Book•
01 Jan 2001
TL;DR: In this paper, the authors present an overview of special and general relativity from absolute space and time to influenceable spacetime: an overview is given, including the Lorentz transformation, the Schwarzschild metric, and the full field equations de Sitter space.
Abstract: INTRODUCTION 1. From absolute space and time to influenceable spacetime: an overview PART I: SPECIAL RELATIVITY 2. Foundations of special relativity the Lorentz transformation 3. Relativistic kinematics 4. Relativistic optics 5. Spacetime and four-vectors 6. Relativistic particle mechanics 7. Four-tensors electromagnetism in vacuum PART II: GENERAL RELATIVITY 8. Curved spaces and the basic ideas of general relativity 9. Static and stationary spacetimes 10. Geodesics, curvature tensor, and vacuum field equations 11. The Schwarzschild metric 12. Black holes and Kruskal space 13. An exact plane gravitational wave 14. The full field equations de Sitter space 15. Linearized general relativity PART III: COSMOLOGY 16. Cosmological spacetimes 17. Light propagation in FRW universes 18. Dynamics of FRW universes
621 citations
TL;DR: In this article, the authors proposed to modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer, by taking dispersion relations such that the speed of light goes to infinity for finite momentum but infinite energy.
Abstract: It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at the Planck scale the world may be non-relativistic.
172 citations
TL;DR: This article investigated student understanding of the concept of time in special relativity and found that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames.
Abstract: This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of relativity was probed. The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist.
103 citations
TL;DR: In this paper, it was shown that any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. The authors interpreted this fact as the impossibility of time machines.
Abstract: Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).
32 citations
TL;DR: In this paper, two new methods to determine Wigner's angle in special relativity are presented, the first one consists in calculating the angle between the compositions of the two non-collinear velocities and the second one introduces a generalization in the complex plane of the addition law of parallel velocity.
Abstract: Two new methods to determine Wigner's angle in special relativity are presented. The first one consists in calculating the angle between the compositions ⊕ and ⊕ of the two non-collinear velocities and . In another method we introduce a generalization in the complex plane of Einstein's addition law of parallel velocities.
29 citations
TL;DR: In this paper, an affine superpotential is derived which comprises the energy and angular-momentum content of exact solutions of the Kerr-AdS solution of GR with a (induced) cosmological constant.
Abstract: On the basis of the ``on shell'' Noether identities of the metric-affine gauge approach of gravity, an affine superpotential is derived which comprises the energy- and angular-momentum content of exact solutions. In the special case of general relativity (GR) or its teleparallel equivalent, the Komar or Freud complex, respectively, are recovered. Applying this to the spontaneously broken anti--de Sitter gauge model of McDowell and Mansouri with an induced Euler term automatically yields the correct mass and spin of the Kerr-AdS solution of GR with a (induced) cosmological constant without the factor two discrepancy of the Komar formula.
28 citations
Dissertation•
01 Jan 2001
TL;DR: In this article, an investigation of student underststanding of basic concepts in special relation is presented, based on a case study conducted by the University of Edinburgh.
Abstract: AN INVESTIGATION OF STUDENT UNDERSTANDING OF BASIC CONCEPTS IN SPECIAL RELATIVITY
22 citations
TL;DR: In this paper, the Lorentz transformation is reformulated as a symmetry property of space-time: spacetime exchange invariance, and the additional hypothesis of spatial homogeneity is then sufficient to derive the LRT without reference to the traditional form of the Principle of Special Relativity.
Abstract: Special relativity is reformulated as a symmetry property of space-time: space-time exchange invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dynamical application, the laws of electrodynamics and magnetodynamics are derived from those of electrostatics and magnetostatics respectively. The four-vector nature of the electromagnetic potential plays a crucial role in the last two derivations.
20 citations
18 citations
01 Jan 2001
TL;DR: This paper presented the author's theory of cosmology and physics, which is a sequel to his study Relativity, gravitation and world structure (1935), but can well be read independently from the earlier volume.
Abstract: This book is a presentation of the author ’s theory of cosmology and physics. It is a sequel to his study Relativity, gravitation and world structure (1935), but can well be read independently from the earlier volume. It is a fascinating treatise, centered around a brilliant idea, excellently presented and showing unusual skill in the elaboration of some of the details. Even though the reviewer could not agree with all parts of the book, his admiration never slackened for the scope of the work and the wealth of results obtained by the author with the help of only a handful of collaborators.
TL;DR: In this paper, a plane wave solution to noncommuting photodynamics exhibits violaton of Lorentz invariance (special relativity) in the sense that it can be realized in actual physical situations.
Abstract: Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
TL;DR: In the dynamic interpretation of the Lorentz and Poincare theory as discussed by the authors, a balance of forces holding together elementary particles is destroyed near the event horizon, and all matter would be converted into zero rest mass particles which could explain the gamma ray bursters.
Abstract: In the dynamic interpretation of relatively by Lorentz and Poincare, Lorentz invariance results from real physical contractions of measuring rods and slower going clocks in absolute motion against an ether. As it was shown by Thirring, this different interpretation of special relativity can be extended to general relativity, replacing the non-Euclidean with a Euclidean geometry, but where rods are contracted and clocks slowed down. In this dynamic interpretation of the special, (and by implication of the general) theory of relativity, there is a balance of forces which might be destroyed near the Planck energy, reached in approaching the event horizon. In gravitational collapse, the event horizon appears first at the center of the collapsing body, thereafter moving radially outward. If the balance of forces holding together elementary particles is destroyed near the event horizon, all matter would be converted into zero rest mass particles which could explain the large energy release of gamma ray bursters.
TL;DR: In this paper, the authors re-elaborate on the recent basic result that the action of any multilayer is equivalent to a proper Lorentz transformation, and propose simple optical measurements that can serve as an analogue computer for simulating special relativity.
Abstract: We re-elaborate on the recent basic result that the action of any multilayer is equivalent to a proper Lorentz transformation. As a consequence, we propose simple optical measurements that can serve as an analogue computer for simulating special relativity. Special attention is paid to the question of the Wigner rotation, showing that it can be easily observed in multilayers.
TL;DR: In this article, the nonassociative axiomatics of the relativistic law of composition of velocities in special relativity are presented, and for the first time the canomical unary operations are considered.
Abstract: The nonassociative axiomatics of the relativistic law of composition of velocities in special relativity is presented. For the first time the canomical unary operations are considered.
TL;DR: In this article, a generalization of the procedure for general relativity is presented, based on the quadratic space geometry corresponding to space-time and action and the philosophical principles of general relativity theory.
Abstract: General Relativity is derived from the quadratic space geometry corresponding to space-time and action and the philosophical principles of Einstein's general relativity theory. The formulation allows a systematic generalization of the procedure.
03 Jan 2001
TL;DR: A new general structure of Lorentz Transformations, in the form of General Lettz Transformation model (GLT-model), has been derived in this paper, where the free parameters of GLT model have been identified in a gravitational field, and it can be employed both in Special and General Relativity.
Abstract: A new general structure of Lorentz Transformations, in the form of General Lorentz Transformation model (GLT-model), has been derived This structure includes both Lorentz-Einstein and Galilean Transformations as its particular (special) realizations Since the free parameters of GLT-model have been identified in a gravitational field, GLT-model can be employed both in Special and General Relativity Consequently, the possibilities of an unification of Einstein’s Special and General Theories of Relativity, as well as an unification of electromagnetic and gravitational fields are opened If GLT-model is correct then there exist four new observation phenomena (a length and time neutrality, and a length dilation and a time contraction) Besides, the well-known phenomena (a length contraction, and a time dilation) are also the constituents of GLT-model It means that there is a symmetry in GLT-model, where the center of this symmetry is represented by a length and a time neutrality A time and a length neutra
TL;DR: In this paper, it was shown that some of the plane symmetric homogeneous models in Rosen's bimetric relativity are singular, i.e., they are not singular in the plane.
Abstract: It is established that some of the plane symmetric homogeneous models in Rosen's bimetric relativity are singular.
TL;DR: A pedagogical cosmology illustrating general relativity concepts, without requiring general or special relativity, is presented in this paper, where the existence of a global time scale, proper vs coordinate variables, the variation of light speed in an expanding universe, the look-back paradox, the horizon, the red shift, the age of the universe, and the dynamics of universe.
Abstract: A pedagogical cosmology illustrates general relativity concepts, without requiring general or special relativity. Topics examined are the existence of a global time scale, proper vs coordinate variables, the variation of light speed in an expanding universe, the look-back paradox, the horizon, the red shift, the age of the universe, and the dynamics of the universe. An Appendix is devoted to space and time in general relativity, but can be skipped by readers unfamiliar with general relativity.
TL;DR: In this paper, a plane wave solution to noncommuting photodynamics exhibits violaton of Lorentz invariance (special relativity) in the sense that it can be realized in actual physical situations.
Abstract: Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
TL;DR: In this paper, a topology can be defined in the four-dimensional space-time of special relativity so as to obtain a topological semigroup for time, which allows the possibility of an intrinsic asymmetry in the time evolution of physical systems.
Abstract: We show that a topology can be defined in the four-dimensional space–time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space–time elements as well as the key properties of special relativity are still the same as in the standard theory. However, the new topological structure allows the possibility of an intrinsic asymmetry in the time evolution of physical systems.
Posted Content•
TL;DR: In this paper, the authors found that the resolution can be obtained by defining standards and units properly, and that the mathematical method to change the units of General Relativity has been discussed in general almost 40 years ago by Dicke.
Abstract: General Relativity is considered to be so far the best gravitation theory. However it is quite hard to use in real situations. The root of these difficulties lays in the non-linearity of the theory. Our aim was not to linearize the theory, but find the source of non-linearity and get rid of it. We found that the resolution can be obtained by defining standards and units properly. We also found that the mathematical method to change the units of General Relativity has been discussed in general almost 40 years ago by Dicke. Linear Relativity can be founded by choosing the right function for his transformation and reinterpret his results.
Posted Content•
TL;DR: In this article, the authors report on the construction of a nonlinear distributional geometry and its applications to general relativity with a special focus on the distributional description of impulsive gravitational waves.
Abstract: This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive gravitational waves
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TL;DR: In this article, the Thomas rotation is introduced and investigated in the context of a typical introductory course on special relativity, in a way that is appropriate for, and completely accessible to, undergraduate students.
Abstract: We review why the Thomas rotation is a crucial facet of special relativity, that is just as fundamental, and just as "unintuitive" and "paradoxical", as such traditional effects as length contraction, time dilation, and the ambiguity of simultaneity. We show how this phenomenon can be quite naturally introduced and investigated in the context of a typical introductory course on special relativity, in a way that is appropriate for, and completely accessible to, undergraduate students. We also demonstrate, in a more advanced section aimed at the graduate student studying the Dirac equation and relativistic quantum field theory, that careful consideration of the Thomas rotation will become vital as modern experiments in particle physics continue to move from unpolarized to polarized cross-sections.
TL;DR: In this article, it was shown that sending signals to a particular union of space-like separated regions cannot cause causality paradoxes and that the relative phase of quantum superposition of a particle in two separate locations can be measured locally.
Abstract: Two recent works suggest a possibility of sending signals to a space-like separated region, contrary to the spirit of special relativity. In the first work [J. Grunhaus, S. Popescu, and D. Rohrlich, Phys. Rev. A 53, 3781 (1996)] it has been shown that sending signals to particular union of space-like separated region cannot cause causality paradoxes. Another work [Y. Aharonov and L. Vaidman, Phys. Rev. A 61, 052108 (2000)] showed that the relative phase of quantum superposition of a particle in two separate locations can be measured locally. Together with the possibility of changing the relative phase in a nonlocal way using potential effect we, apparently, have a method of sending signals to space-like separated regions. These arguments are critically analyzed in this paper.