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Abraham A. Ungar - One of the best experts on this subject based on the ideXlab platform.
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parametric realization of the Lorentz Transformation group in pseudo euclidean spaces
Journal of Geometry and Symmetry in Physics, 2015Co-Authors: Abraham A. UngarAbstract:Appears in: Journal of Geometry and Symmetry in Physics 38(2015), 39-108. Abstract. The Lorentz Transformation group SO(m,n), m,n ∈ N, is a group of Lorentz Transformations of order (m,n), that is, a group of special linear trans- formations in a pseudo-Euclidean space R m,n of signature (m,n) that leave the pseudo-Euclidean inner product invariant. A parametrization of SO(m,n) is pre- sented, givingriseto thecompositionlaw ofLorentzTransformationsoforder(m,n) in terms of parameter composition. The parameter composition, in turn, gives rise to a novel group-like structure that R m,n possesses, called a bi-gyrogroup. Bi-gyrogroups form a natural generalization of gyrogroups where the latter form a natural generalization of groups. Like the abstract gyrogroup, the abstract bi- gyrogroup can play a universal computational role which extends far beyond the domain of pseudo-Euclidean spaces.
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parametric realization of the Lorentz Transformation group in pseudo euclidean spaces
arXiv: Mathematical Physics, 2015Co-Authors: Abraham A. UngarAbstract:The Lorentz Transformation group $SO(m,n)$ is a group of Lorentz Transformations of order $(m,n)$, that is, a group of special linear Transformations in a pseudo-Euclidean space of signature $(m,n)$ that leave the pseudo-Euclidean inner product invariant. A parametrization of $SO(m,n)$ is presented, giving rise to the composition law of Lorentz Transformations of order $(m,n)$ in terms of parameter composition. The parameter composition, in turn, gives rise to a novel group-like structure called a bi-gyrogroup. Bi-gyrogroups form a natural generalization of gyrogroups where the latter form a natural generalization of groups. Like the abstract gyrogroup, the abstract bi-gyrogroup can play a universal computational role which extends far beyond the domain of pseudo-Euclidean spaces.
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the relativistic proper velocity Transformation group
Progress in Electromagnetics Research-pier, 2006Co-Authors: Abraham A. UngarAbstract:The Lorentz Transformation group of the special theory of relativity is commonly represented in terms of observer’s, or coordinate, time and coordinate relative velocities. The aim of this article is to uncover the representation of the Lorentz Transformation group in terms of traveler’s, or proper, time and proper relative velocities. Following a recent demonstration by M. Idemen, according to which the Lorentz Transformation group is inherent in Maxwell equations, our proper velocity Lorentz Transformation group may pave the way to uncover the proper time Maxwell equations.
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beyond the einstein addition law and its gyroscopic thomas precession the theory of gyrogroups and gyrovector spaces
2001Co-Authors: Abraham A. UngarAbstract:List of Figures. List of Tables. Preface. Acknowledgments. Introduction A.A. Ungar. 1. Thomas Precession: The Missing Link. 2. Gyrogroups: Modeled on Einstein's Addition. 3. The Einstein Gyrovector Space. 4. Hyperbolic Geometry of Gyrovector Spaces. 5. The Ungar Gyrovector Space. 6. The Mobius Gyrovector Space. 7. Gyrogeometry. 8. Gyrooperations -- The SL(2,C) Approach. 9. The Cocycle Form. 10. The Lorentz Group and its Abstraction. 11. The Lorentz Transformation Link. 12. Other Lorentz Groups. 13. References. About the Author. Topic Index. Author Index.
J. H. Field - One of the best experts on this subject based on the ideXlab platform.
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Translational invariance and the space-time Lorentz Transformation with arbitrary spatial coordinates
arXiv: General Physics, 2007Co-Authors: J. H. FieldAbstract:Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of the space-time Lorentz Transformation with arbitrary spatial coordinates shows that the spurious `length contraction' and `relativity of simultaneity' effects --the latter violating translational invariance-- result from the use of a different spatial coordinate system to describe each of two spatially separated clocks at rest in a common inertial frame
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clock rates clock settings and the physics of the space time Lorentz Transformation
arXiv: General Physics, 2006Co-Authors: J. H. FieldAbstract:A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz Transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious `relativity of simultaneity' and `length contraction' effects in special relativity is explained.
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derivation of the Lorentz force law the magnetic field concept and the faraday lenz and magnetic gauss laws using an invariant formulation of the Lorentz Transformation
Physica Scripta, 2006Co-Authors: J. H. FieldAbstract:It is demonstrated how the right-hand sides of the Lorentz Transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space–time and energy–momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday–Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampere law, due to the 4-vector character of the electromagnetic potential, is also pointed out.
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derivation of the Lorentz force law the magnetic field concept and the faraday lenz law using an invariant formulation of the Lorentz Transformation
arXiv: Classical Physics, 2004Co-Authors: J. H. FieldAbstract:It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. This formalism, making essential use of the 4-vector electromagnetic potential concept, provides a short derivation of the Lorentz force law of classical electrodynamics, the conventional definition of the magnetic field, in terms of spatial derivatives of the 4--vector potential and the Faraday-Lenz Law. An important distinction between the physical meanings of the space-time and energy-momentum 4--vectors is pointed out.
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derivation of the Lorentz force law and the magnetic field concept using an invariant formulation of the Lorentz Transformation
arXiv: Classical Physics, 2003Co-Authors: J. H. FieldAbstract:It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector electromagnetic potential plays a crucial role, of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field in terms spatial derivatives of the 4--vector potential. The time component of the relativistic generalisation of the Lorentz force law is discussed. An important physical distinction between the space-time and energy-momentum 4--vectors is also pointed out.
D Censor - One of the best experts on this subject based on the ideXlab platform.
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Quasi-Lorentz Transformation The need for a first-order quasi-Lorentz Transformation
2020Co-Authors: D CensorAbstract:Solving electromagnetic scattering problems involving non-uniformly moving objects requires an approximate but consistent extension of Einstein's Special Relativity theory which originally is valid for constant velocities only. For moderately varying velocities, a quasi-Lorentz Transformation is presented. The conditions for form-invariance of the Maxwell equations, the socalled "principle of relativity", are shown to hold for a broad class of motional modes and time scales. An example of scattering by a harmonically oscillating mirror is given. The present extended abstract is an overview of the full draft [1], where the derivations and formulas are given explicitly
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The Need for a First-Order Quasi Lorentz Transformation
2020Co-Authors: D CensorAbstract:Abstract. Solving electromagnetic scattering problems involving non-uniformly moving objects or media requires an approximate but consistent extension of Einstein's Special Relativity theory, originally valid for constant velocities only. For moderately varying velocities a quasi Lorentz Transformation is presented. The conditions for form-invariance of the Maxwell equations, the so-called "principle of relativity", are shown to hold for a broad class of motional modes and time scales. A simple example of scattering by a harmonically oscillating mirror is analyzed in detail. Application to generally orbiting objects is mentioned
Jeanluc Vay - One of the best experts on this subject based on the ideXlab platform.
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noninvariance of space and time scale ranges under a Lorentz Transformation and the implications for the study of relativistic interactions
Physical Review Letters, 2007Co-Authors: Jeanluc VayAbstract:We present an analysis which shows that the ranges of space and time scales spanned by a system are not invariant under Lorentz Transformation. This implies the existence of a frame of reference which minimizes an aggregate measure of the range of space and time scales. Such a frame is derived, for example, for the following cases: free electron laser, laser-plasma accelerator, and particle beams interacting with electron clouds. The implications for experimental, theoretical, and numerical studies are discussed. The most immediate relevance is the reduction by orders of magnitude in computer simulation run times for such systems.
Edward B Fomalont - One of the best experts on this subject based on the ideXlab platform.
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aberration and the fundamental speed of gravity in the jovian deflection experiment
Foundations of Physics, 2006Co-Authors: Sergei M Kopeikin, Edward B FomalontAbstract:We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7’ of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar’s radio wave is equivalent to comparison of the relativistic laws of the Lorentz Transformation for gravity and light. Because, according to Einstein, the Lorentz Transformation of gravity field variables must depend on a fundamental speed c, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. In particular, the v/c term beyond of the standard Einstein’s deflection, which we measured to 20% accuracy, is associated with the aberration of the null direction of the gravity force (“aberration of gravity”) caused by the Lorentz Transformation of the Christoffel symbols from the static frame of Jupiter to the moving frame of observer. General relativistic formulation of the experiment identifies the aberration of gravity with the retardation of gravity because the speed of gravitational waves in Einstein’s theory is equal to the speed of propagation of the gravity force. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual–Sanchez, and Carlip and show that their “speed of light” interpretations confuse the Lorentz Transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar. For this reason, the “speed of light” interpretations are not entirely consistent with a retarded Lienard–Wiechert solution of the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated with the aberration of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c beyond the Shapiro delay, thus, making their measurement highly desirable for deeper testing of general relativity in future astrometric experiments like Gaia, SIM, and SKA.
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aberration and the fundamental speed of gravity in the jovian deflection experiment
arXiv: Astrophysics, 2003Co-Authors: Sergei M Kopeikin, Edward B FomalontAbstract:We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7' of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar's radio wave is equivalent to comparison of the relativistic laws of the Lorentz Transformation for gravity and light. Because, according to Einstein, the Lorentz Transformation of gravity field variables must depend on a fundamental speed $c$, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual-Sanchez, and Carlip and show that their `speed of light' interpretations confuse the Lorentz Transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar.
