Showing papers on "Special relativity (alternative formulations) published in 2007"
TL;DR: KimKimberly, Magueijo, and Medeiros as discussed by the authors studied the nature of kinematical and dynamical laws in Minkowski spacetime from a new perspective: the canonical phase space approach.
Abstract: In this paper we have studied the nature of kinematical and dynamical laws in $\ensuremath{\kappa}$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\ensuremath{\kappa}$-Minkowski phase space algebra that yields the $\ensuremath{\kappa}$-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $\ensuremath{\kappa}$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not $\ensuremath{\kappa}$-Minkowski) phase space algebra and special relativity Lorentz transformation (and not $\ensuremath{\kappa}$-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical $\ensuremath{\kappa}$-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the $\ensuremath{\kappa}$-particle.
132 citations
124 citations
TL;DR: Within the standard model extension, simultaneous limits on Lorentz violation for electrons (5 coefficients) and photons (8) at levels down to 10(-16), improved by factors between 3 and 50 compared to previous work.
Abstract: We report relativity tests based on data from two simultaneous Michelson-Morley experiments, spanning a period of more than 1 yr. Both were actively rotated on turntables. One (in Berlin, Germany) uses optical Fabry-Perot resonators made of fused silica; the other (in Perth, Australia) uses microwave whispering-gallery sapphire resonators. Within the standard model extension, we obtain simultaneous limits on Lorentz violation for electrons (5 coefficients) and photons (8) at levels down to ${10}^{\ensuremath{-}16}$, improved by factors between 3 and 50 compared to previous work.
123 citations
TL;DR: These simulations illustrate that the concept of "thermal equilibrium" extends naturally to special relativity only if a many-particle system is spatially confined and make evident that "temperature" can be statistically defined and measured in an observer frame independent way.
Abstract: There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Juttner function as well as modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Juttner distribution. Moreover, our simulations illustrate that the concept of "thermal equilibrium" extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that "temperature" can be statistically defined and measured in an observer frame independent way.
103 citations
TL;DR: In this paper, the authors show that there is a one-to-one dual correspondence between Snyder's quantized space-time model in de Sitter space of momenta and the dS special relativity on dS-spacetime of radius R with Beltrami coordinates.
Abstract: Between Snyder's quantized space-time model in de Sitter space of momenta and the dS special relativity on dS-spacetime of radius R with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with the Planck length lP, R (3/Λ)1/2 should be a fundamental constant. They lead to a dimensionless constant g ~ lPR−1 = (Gc−3Λ/3)1/2 ~ 10−61. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local dS-invariance characterized by g. A simple model of dS-gravity with a gauge-like action on umbilical manifolds may show these characteristics. It can pass the observation tests and support the duality.
70 citations
01 Jan 2007
TL;DR: This chapter discusses the development of models of Specrel in first-order logic, and describes the motivation for special relativistic kinematics in place of Newtonian kinematic.
Abstract: 2 Special relativity 4 2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Axiomatization Specrel of special relativity in first-order logic 15 2.4 Characteristic differences between Newtonian and special relativistic kinematics . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Explicit description of all models of Specrel, basic logical investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Observer-independent geometries in relativity theory; duality and definability theory of logic . . . . . . . . . . . . . . . . . 47 2.7 Conceptual analysis and “reverse relativity” . . . . . . . . . . 59
64 citations
TL;DR: Real Time Relativity as discussed by the authors is a computer program that allows users to move at relativistic speeds through a simulated world populated with planets, clocks, and buildings, with the goal of teaching special relativity to first year students.
Abstract: “Real Time Relativity” is a computer program that lets users move at relativistic speeds through a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year students.
54 citations
TL;DR: Hilbert as discussed by the authors was the first to discover the correct form of the law of warpage (i.e., the form that obeys his relativity principle) in space-time.
Abstract: Remarkably, Einstein was not the first to discover the correct form of the law of warpage [of space-time, i.e. the gravitational field equations], the form that obeys his relativity principle. Recognition for the first discovery must go to Hilbert. In autumn 1915, even as Einstein was struggling toward the right law, making mathematical mistake after mistake, Hilbert was mulling over the things he had learned from Einstein’s summer visit to Göttingen. While he was on an autumn vacation on the island of Rugen in the Baltic the key idea came to him, and within a few weeks he had the right law–derived not by the arduous trial-and-error path of Einstein, but by an elegant, succinct mathematical route. Hilbert presented his derivation and the resulting law at a meeting of the Royal Academy of Sciences in Göttingen on 20 November 1915, just five days before Einstein’s presentation of the same law at the Prussian Academy meeting in Berlin. 2
48 citations
01 Nov 2007
TL;DR: In this article, the problem of computing initial data for the Cauchy problem of 3+1 general relativity is addressed, where the main task is to solve the constraint equations.
Abstract: This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York, is presented. Two standard methods, the conformal transverse-traceless one and the conformal thin sandwich, are discussed and illustrated by some simple examples. Finally a short review regarding initial data for binary systems (black holes and neutron stars) is given.
42 citations
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TL;DR: In this article, the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories, including the universal light cone principle of special relativity and the equivalence principle.
Abstract: This paper concerns relational first principles from which the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories. This was accompanied by a number of results and conjectures about matter theories and general features of physics -- such as gauge theory, the universal light cone principle of special relativity and the equivalence principle -- being likewise picked out. I have previously shown that many of these matter results and conjectures are contingent on further unrelational simplicity assumptions. In this paper, I point out 1) that the exhaustive procedure in these cases with matter fields is slower than it was previously held to be. 2) While the example of equivalence principle violating matter theory that I previously showed how to accommodate on relational premises has a number of pathological features, in this paper I point out that there is another closely related equivalence principle violating theory that also follows from those premises and is less pathological. This example being known as an `Einstein--aether theory', it also serves for 3) illustrating limitations on the conjectured emergence of the universal light cone special relativity principle.
TL;DR: In this article, the anomalous quartic gauge couplings were derived using a general non-forward dispersion relation for the elastic scattering amplitude of two longitudinally polarized vector bosons.
Abstract: We derive one loop constraints on the anomalous quartic gauge couplings using a general non-forward dispersion relation for the elastic scattering amplitude of two longitudinally polarized vector bosons. We show that for exactly chiral theories more stringent bounds can be obtained by the assumption that the underlying theory satisfies the causality principle of Special Relativity.
TL;DR: In this article, the authors show that the correct bound on the Standard Model Extension photon-sector parameter is in fact $2.2\times 10^{-7} = 0.
Abstract: In an earlier paper [1] (hep-ph/0408006), the bound on the Standard Model Extension photon-sector parameter $\tilde{\kappa}_{tr}$ [2] (hep-ph/0205211) set by the heavy-ion storage-ring experiment of Saathoff et al. [3] was incorrectly reported. We show that the correct bound on $\tilde{\kappa}_{tr}$ which resulted from this experiment is in fact $2.2\times 10^{-7}$.
TL;DR: There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation.
Abstract: There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length l
P
and the scale R = (3/Λ)1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = l
P
/R ∼ 10−61.
TL;DR: In this paper, it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients.
Abstract: In this paper two things are done. First it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited.
Book•
01 Jan 2007
TL;DR: In this paper, the geometrical structure of space-time and the transformation of the Electromagnetic Field were discussed. And the results of General Relativity were discussed as well.
Abstract: Space and Time Before Einstein.- In Search of the Ether.- Space and Time in Special Relativity.- Geometric Structure of Space-Time.- Transformation of the Electromagnetic Field.- Energy and Momentum.- Covariant Formulation.- Inertia and Gravity.- Results of General Relativity.
Book•
26 Nov 2007
TL;DR: In this article, Westwell-Roper discusses the ontology and methodology in Relativity, and how Euclidean geometry has misled metaphysics and how to make things have happened.
Abstract: Preface Introduction Part I. Ontology and Methodology in Relativity: 1. On learning from the mistakes of Positivists 2. What ontology can be about with Andrew Westwell-Roper 3. Special relativity is not based on causality 3. Simultaneity and convention in special relativity 5. Motion and change of distance Part II. Variable Curvature and General Relativity: 6. How Euclidean geometry has misled metaphysics 7. What can geometry explain? 8. Is curvature intrinsic to physical space? 9. Holes in the hole argument Part III. Time and Causation: 10. Can time be finite? 11. How to make things have happened Bibliography Index.
TL;DR: Real Time Relativity as mentioned in this paper is a computer program that allows students to fly at relativistic speeds through a simulated world populated with planets, clocks, and buildings, with the goal of teaching special relativity to first year university students.
Abstract: Real Time Relativity is a computer program that lets students fly at relativistic speeds though a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year university students.
TL;DR: A long history of attempts to reduce an apparently complex reality to a few elementary building blocks from which everything else is constructed has been made to reduce the complexity of the world as mentioned in this paper.
Abstract: Ever since antiquity, attempts have been made to reduce an apparently complex reality to a few elementary building blocks from which everything else is constructed. This project – now called reductionism – has a long history of failures. One example is the 200-year-long attempt to describe all physical processes in terms of mechanics, such as James Clerk Maxwell's mechanical models of the electromagnetic field. Another is Hermann Weyl's failed attempt to unify electromagnetism and gravity in a single theory shortly after Einstein had introduced special relativity.
TL;DR: Using only ideas from Galilean relativity, the covariance of the relationship between work and kinetic energy as we move from one inertial reference frame to another is considered in this paper.
Abstract: As the topic of relativity is developed in a first-year physics class, there seems to be a tendency to move as quickly as possible to the fascinating ideas set forth in Einstein's special theory of relativity1 In this paper we linger a little with the Galilean side of relativity and discuss an intriguing problem and its solution to illustrate a sometimes omitted issue in relativity Using only ideas from Galilean relativity, we will consider the covariance of the relationship between work and kinetic energy as we move from one inertial reference frame to another
TL;DR: In this article, the authors provide a history of how the equation E=mc2 arose, establish what "mass" means in the context of this relation, and present some aspects of how it can be understood.
Abstract: First I provide some history of how the equation E=mc2 arose, establish what “mass” means in the context of this relation, and present some aspects of how the relation can be understood. Then I address the question, Does E=mc2 mean that one can “convert mass into energy” and vice versa?
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TL;DR: The authors argued that special relativity is neither paradoxical nor correct (in the absolute sense of the nineteenth century) but the most natural and expected description of the real space-time around us valid for all practical purposes.
Abstract: Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince the audience of this teaching that Newtonian physics is natural but incorrect and special relativity is its paradoxical but correct amendment. I argue in this article in favor of logical instead of historical trend in teaching of relativity and that special relativity is neither paradoxical nor correct (in the absolute sense of the nineteenth century) but the most natural and expected description of the real space-time around us valid for all practical purposes. This last circumstance constitutes a profound mystery of modern physics better known as the cosmological constant problem.
01 Jan 2007
TL;DR: In this paper, it was shown that the relativistic length contraction and the twin paradox can not be confirmed if the physical bodies involved in these effects were three-dimensional objects.
Abstract: The main purpose of this paper is to demonstrate that the analysis of the kinematical effects of special relativity holds the key to answering the question of the dimensionality of the world. It is shown that these effects and the experiments which confirmed them would be impossible if the world were three-dimensional. Section 2 shows that relativity of simultaneity, conventionality of simultaneity, and the existence of accelerated observers in special relativity would be impossible if the world were three-dimensional. Section 3 deals with the dimensionality of physical objects and demonstrates that the relativistic length contraction and the twin paradox would be impossible if the physical bodies involved in these relativistic effects were three-dimensional objects.
03 Dec 2007
TL;DR: In this paper, the kinematics of a spinless particle in a de Sitter spacetime are studied. And the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics.
Abstract: In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincare special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics.
TL;DR: In this paper, it was shown that the continuous group of transformations between the frames of noninertial particles following trajectories that satisfy Hamilton's equations is given by the Hamilton group Ha(3)=SO(3)⊗sH(3), where H(3 is the Weyl-Heisenberg group that is parametrized by rates of change of position, momentum, and energy, i.e., velocity, force and power.
Abstract: The group E(3)=SO(3)⊗sT(3), that is the homogeneous subgroup of the Galilei group parametrized by rotation angles and velocities, defines the continuous group of transformations between the frames of inertial particles in Newtonian mechanics. We show in this paper that the continuous group of transformations between the frames of noninertial particles following trajectories that satisfy Hamilton’s equations is given by the Hamilton group Ha(3)=SO(3)⊗sH(3), where H(3) is the Weyl-Heisenberg group that is parametrized by rates of change of position, momentum, and energy, i.e., velocity, force, and power. The group E(3) is the inertial special case of the Hamilton group.
TL;DR: In this paper, the persistence problem of shock fronts in perfect fluids is also a continuation problem for a pseudo-Riemannian metric of reduced regularity, which is solved by considerations on a Cauchy problem which combines a well-known formulation of the Einstein-Euler equations as a first-order symmetric hyperbolic system and Rankine-Hugoniot-type jump conditions for the fluid variables with an extra (non-) jump condition for the first derivatives of the metric.
Abstract: For general relativity, the persistence problem of shock fronts in perfect fluids is also a continuation problem for a pseudo-Riemannian metric of reduced regularity. In this paper, the problem is solved by considerations on a Cauchy problem which combines a well-known formulation of the Einstein–Euler equations as a first-order symmetric hyperbolic system and Rankine–Hugoniot-type jump conditions for the fluid variables with an extra (non-)jump condition for the first derivatives of the metric. This ansatz corresponds to the use of space-time coordinates which are natural in the sense of Israel and harmonic at the same time. As in non-relativistic settings, the shock front must satisfy a Kreiss–Lopatinski condition in order for the persistence result to apply. The paper also shows that under standard assumptions on the fluid's equation of state, this condition actually holds for all meaningful shock data.