The Theory of Special Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Euler Equations ◽  
Lorentz Transformation ◽  
Electromagnetic Force ◽  
Momentum Tensor ◽  
Perfect Fluids ◽  
Dimensional Spacetime ◽  
Tensor Formulation ◽  
Basic Equations

This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, space and time are not separate entities. They are combined into a four-dimensional spacetime continuum, which is most clearly demonstrated in the formulation of the theory of special relativity due to Hermann Minkowski. The chapter then defines vectors and tensors with respect to the Lorentz transformation, leading to a tensor formulation of Maxwell's equations, of the electromagnetic force acting on charges and currents, and of the energy-momentum of the electromagnetic field and its conservation law. It also introduces the energy-momentum tensor of matter and discusses the basic equations of the hydrodynamics of perfect fluids (the Euler equations).

scholarly journals The relativistic foundations of synchrotron radiation

2017 ◽  
Vol 24 (4) ◽  
pp. 898-901 ◽  
Author(s):  
Giorgio Margaritondo ◽  
Johann Rafelski
Keyword(s):  
Electromagnetic Field ◽  
Synchrotron Radiation ◽  
Special Relativity ◽  
Reference Frame ◽  
Lorentz Transformation ◽  
Doppler Shift ◽  
Time Dilation ◽  
Common Belief ◽  
Research Discipline ◽  
Radiation Properties

Special relativity (SR) determines the properties of synchrotron radiation, but the corresponding mechanisms are frequently misunderstood. Time dilation is often invoked among the causes, whereas its role would violate the principles of SR. Here it is shown that the correct explanation of the synchrotron radiation properties is provided by a combination of the Doppler shift, not dependent on time dilation effects, contrary to a common belief, and of the Lorentz transformation into the particle reference frame of the electromagnetic field of the emission-inducing device, also with no contribution from time dilation. Concluding, the reader is reminded that much, if not all, of our argument has been available since the inception of SR, a research discipline of its own standing.

scholarly journals A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1259 ◽  
Author(s):  
Abraham A. Ungar
Keyword(s):  
Special Relativity ◽  
Symmetry Group ◽  
Lorentz Transformation ◽  
Lorentz Group ◽  
Transformation Group ◽  
Relativity Theory ◽  
Symmetry Violation ◽  
3 Dimensional ◽  
Dimensional Spacetime ◽  
The Common

A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

Analysis of Vibration Caused by Electromagnetic Force on Stator End-Winding of Large Dry Submersible Motor

2013 ◽  
Vol 416-417 ◽  
pp. 428-432
Author(s):  
Li Shan ◽  
Xiao Wei Cheng ◽  
Yong Fang ◽  
Xiao Hua Bao
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Transition State ◽  
Electromagnetic Force ◽  
Radial Displacement ◽  
Radial Direction ◽  
Axial Direction ◽  
Axial Displacement ◽  
Force Density ◽  
Submersible Motor

This paper investigates the vibration which caused by electromagnetic on the stator end-winding of the large dry submersible motor. Firstly, the electromagnetic field which included transition state and steady state is researched by 3-D FEM. Secondly, the electromagnetic force which lead to vibrations of end-winding is calculated by numerical method, it can be obtained that where endured the largest force density along the slant part of end-winding. Finally, the radial displacement and the axial displacement of the slant part which caused by vibrations is studied, the analysis results show that the axial displacement is larger than the amplitude of radial displacement. It indicates that the slant part of end-winding will be more easily damaged at axial direction than radial direction.

scholarly journals $$ T\overline{T} $$-like flows in non-linear electrodynamic theories and S-duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
H. Babaei-Aghbolagh ◽  
Komeil Babaei Velni ◽  
Davood Mahdavian Yekta ◽  
H. Mohammadzadeh
Keyword(s):  
Type Theory ◽  
Free Action ◽  
Momentum Tensor ◽  
Flow Equation ◽  
Supersymmetric Model ◽  
Deformation Problem ◽  
Dimensional Spacetime ◽  
Non Linear ◽  
The Relationship ◽  
Simple Integration

Abstract We investigate the $$ T\overline{T} $$ T T ¯ -like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$ T T ¯ operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$ T T ¯ deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$ T T ¯ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$ T T ¯ operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$ N = 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$ T T ¯ operator and quadratic form of the energy-momentum tensor in D = 4.

scholarly journals THE LOCALLY COVARIANT DIRAC FIELD

2010 ◽  
Vol 22 (04) ◽  
pp. 381-430 ◽  
Author(s):  
KO SANDERS
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Covariant Quantum ◽  
Dimensional Spacetime ◽  
Stress Energy ◽  
Hadamard States ◽  
Stress Energy Momentum Tensor

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

scholarly journals Special Relativity sans Lorentz Transformation (OR) Perceptional Relativity

2021 ◽  
Author(s):  
Sebastin Patrick Asokan
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Inertial Frames ◽  
Impossible Task

Abstract This paper shows that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a simple and straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in paradoxical Lorentz Transformation. This paper also proves that Lorentz Transformation has failed in its attempt to do the impossible task of establishing t' ≠ t to explain the constancy of the speed of light in all inertial frames without contradicting the interchangeability of frames demanded by the First Postulate of the Special Theory of Relativity. This paper also points out the misconceptions regarding the claimed experimental verifications of Lorentz Transformation's predictions in the Hafele–Keating experiment and μ meson experiment. This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.

An Synergistic Dynamic 2D FEM Model of an Active Magnetic Bearing with Three Electromagnets

2014 ◽  
Vol 214 ◽  
pp. 106-112 ◽  
Author(s):  
Adam Krzysztof Pilat
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Electromagnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Comsol Multiphysics ◽  
Mesh Deformation ◽  
Arbitrary Lagrangian Eulerian ◽  
Fem Model ◽  
Mathematical Formulas

This elaboration presents a dynamic model of an Active Magnetic Bearing (AMB) developed in COMSOL Multiphysics. The electromagnetic field is calculated on the basis of Partial Differential Equations (PDEs). The calculated electromagnetic force is applied to the rotor, which is free to move. The Arbitrary Lagrangian-Eulerian (ALE) method for mesh deformation is applied to achieve rotor motion on the bearing plane. The planar rotor motion is described by a set of Ordinary Differential Equations (ODEs) solved in parallel to the electromagnetic field calculations. To enable rotor levitation, three local PD controllers are applied. The mathematical formulas of the control action are coded in the form of COMSOL equations and embedded into the rotor motion ODEs.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

Numerical Simulation of Electromagnetic Field in the Cold Crucible

2013 ◽  
Author(s):  
Jinlong Zhang ◽  
Pengfei Li
Keyword(s):  
Heat Transfer ◽  
Electromagnetic Field ◽  
Induction Heating ◽  
Electromagnetic Force ◽  
Power Efficiency ◽  
Cooling Water ◽  
Joule Heat ◽  
Cold Crucible ◽  
Primary Problem ◽  
Frequency Power

SNPTRD was planning to employ cold crucible induction heating technique to investigate the corium pool heat transfer, using the UO2 and ZrO2 mixture as the simulated corium pool. Compared with the actual situation, the primary problem of the cold crucible induction heating was the additional introduction of electromagnetic field. To investigate the cold crucible applicability in simulating the corium pool heat transfer, the distribution of joule heat inside cold crucible and the magnitude of electromagnetic force were carried out. To be more suitable for heat transfer test research, the shape of cold crucible was changed to hemisphere, and the cooling water channels were set horizontally. The simulation results indicated that joule heat distribution would be more uniform with lower frequency power but considering power efficiency, there was only one best frequency. The magnitude of electromagnetic force can be ignored compared to the gravity on the natural convection research.

Sign in / Sign up

Export Citation Format

Share Document