The field of a moving charge

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Radiation ◽  
Lorentz Transformation ◽  
World Line ◽  
Uniform Motion ◽  
Special Cases ◽  
Inertial Frames ◽  
A Charge

This chapter begins the study of electromagnetic radiation by calculating the field created by a single moving charge, first when in uniform motion, and then when it is accelerated. It reveals the potential created by a charge in uniform motion starting from the Coulomb expression for the potential in the frame where it is at rest, and then by making a Lorentz transformation. The chapter then follows the exact reasoning for any type of motion by introducing inertial frames tangent to the charge world line. In this way, it obtains the retarded Liénard–Wiechert potential created by a charge in any type of motion. After studying some special cases of the field of a moving charge, the chapter defines the asymptotic, radiation, part of the field.

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.

The Lorentz transformation

2021 ◽  
pp. 80-88
Author(s):  
Geoffrey Brooker
Keyword(s):  
Lorentz Transformation ◽  
Speed Of Light ◽  
Inertial Frames

“The Lorentz transformation” derives the Lorentz transformation by an unusual route, from application of simple postulates: space is uniform and isotropic; inertial frames exist; physics is invariant under a change between inertial frames. The speed of light is an invariant, but this property is input last.

Interacting charges II

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Radiation ◽  
Mechanical Energy ◽  
Equation Of Motion ◽  
Coupling Constant ◽  
General Study ◽  
A Charge

This chapter continues the discussion from the previous chapter. The motion of a charge (m,q) in the field of another charge (m′,q′) and in its own field can now be studied in the lowest orders of the velocities directly using the equation of motion obtained in the preceding chapter. However, the features of this motion are revealed more easily by deriving them from the Darwin Lagrangian. This allows for a rigorous establishment of a balance between the energy radiated by the system and the mechanical energy lost by the system. The chapter concludes this general study of the electromagnetic radiation of a system of charges by outlining the ‘post-Minkowski’ approach based on iteration in the ‘coupling constant’ qq′ rather than in the velocities.

Moving dipoles and the relativity of simultaneity

2019 ◽  
Vol 97 (2) ◽  
pp. 125-132
Author(s):  
Francis Redfern
Keyword(s):  
Lorentz Transformation ◽  
Rest Frame ◽  
Charge Carriers ◽  
Current Loop ◽  
Linear Charge ◽  
Linear Charge Density ◽  
Net Charge ◽  
The Wire ◽  
A Charge ◽  
A Current

An observer moving parallel to a current-carrying wire detects an electric field due to the Lorentz transformation directed either toward or away from the wire, depending on the relative motion of observer and current. The accepted interpretation of this situation as viewed from the observer’s rest frame is that there is a net linear charge density on the wire. The Lorentz contraction of the separation of fixed ions and charge carriers is different due to their different speeds in the observer’s frame. The idea that a net charge exists on a wire in a reference frame moving parallel to the wire leads to the expectation that there is a charge separation seen on a moving current loop, resulting in paradoxes, such as that proposed by Mansuripur. I argue that the apparent charge on a current-carrying wire is due to a misinterpretation of the Lorentz transformation and is a consequence of the relativity of simultaneity. Given this insight, the nature of the fields of moving dipoles and the nature of the magnetization–polarization tensor are investigated.

scholarly journals On the fields and equations of motion of point particles

1946 ◽  
Vol 185 (1002) ◽  
pp. 250-268 ◽  
Keyword(s):  
Stress Tensor ◽  
World Line ◽  
Equations Of Motion ◽  
Mean Field ◽  
Point Particle ◽  
Point Particles ◽  
Symmetric Field ◽  
The World ◽  
Actual Field ◽  
A Charge

The investigation covers point particles possessing a charge, dipole and higher multipole moments interacting with fields of any spin satisfying the generalized wave equation (8). It is shown that the radiation field defined as the retarded minus the advanced field and all its derivatives is always finite at all points including those on the world line of the point particles. The symmetric field, defined as half the sum of the retarded and advanced fields, is shown to contain apart expressible as an integral along the world line from minus to plus infinity, which is continuous and finite everywhere. This integral vanishes if X = 0. The modified symmetric field is defined as the symmetric field minus this integral. The actual field is expressed as a sum of the modified symmetric field plus the modified mean field defined as half the sum of the Ingoing and outgoing fields plus the integral just mentioned. It is proved that the part of the stress tensor of the field quadratic in the modified symmetric field plays no part in determining the equations of motion of the point particle. Being conserved by itself, it can always be subtracted away, thus defining a new stress tensor which is free from all the highest singularities in the usual stress tensor. The equations of motion of the particle are shown to depend only on the usual ‘mixed terms’ in the inflow with the modified mean field substituted for the ingoing field. The formulation for several particles is given.

Matter Determinants in Background Fields Using Random Walk World Line Loops on the Lattice

2003 ◽  
Vol 18 (22) ◽  
pp. 1499-1515 ◽  
Author(s):  
Michael G. Schmidt ◽  
Ion-Olimpiu Stamatescu
Keyword(s):  
Random Walk ◽  
World Line ◽  
Background Field ◽  
Analytic Solutions ◽  
Special Cases ◽  
Background Fields ◽  
The Continuum

The continuum World Line Formalism permits a transparent discussion of bosonic and fermionic determinants in some background field. For general, nontrivial backgrounds numerical evaluations must be envisaged. In this work we implement this formalism on the lattice by using statistically generated random walk world line loops. We illustrate the method by applying it to special cases and discuss the results in comparison with known analytic solutions in continuum.

Path integral for spinning particle subjected to the constant electromagnetic field

2015 ◽  
Vol 30 (25) ◽  
pp. 1550124
Author(s):  
A. Merdaci ◽  
N. Boudiaf ◽  
L. Chetouani
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Transformation ◽  
Path Integral ◽  
Dirac Particle ◽  
Wave Functions ◽  
Integral Approach ◽  
Spinning Particle ◽  
Constant Electromagnetic Field ◽  
Special Cases ◽  
Electromagnetic Tensor

The problem of the Dirac particle submitted to a wave [Formula: see text] of a four-dimensional constant electromagnetic tensor is solved with the path integral approach via the use of Lorentz transformation and with an adequate choice for the velocity of the mobile referential.We show that the supersymmetric action associated to the pair [Formula: see text] can be determined from that associated to the pair [Formula: see text] and from that associated to the pair [Formula: see text] following simple relations.The wave functions and the energy spectrums are thus exactly determined and tested. Special cases are considered as well.

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

2021 ◽  
Author(s):  
SEBASTIN PATRICK ASOKAN
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Fast Moving ◽  
Inertial Frame ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Slowing Down ◽  
Inertial Frames

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 shows that the premise that each inertial frame has its unique time, which Lorentz Transformation introduced to explain the constancy of the speed of light in all inertial frames is incompatible with the interchangeability of the frames, an essential requisite of 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 hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity instead of Time Dilation. This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.

scholarly journals Direct calculation of length contraction and clock retardation

2015 ◽  
pp. 49-58 ◽  
Author(s):  
D.V. Redzic
Keyword(s):  
Electromagnetic Field ◽  
Causal Effect ◽  
Direct Calculation ◽  
Equation Of Motion ◽  
Uniform Motion ◽  
Correct Equation ◽  
Length Contraction ◽  
Inertial Frames ◽  
Electromagnetic Models ◽  
Dynamical Change

For simple electromagnetic models of a rod and a clock, a change of shape of a rod and of the rate of clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle in electromagnetic field and the universal boostability assumption. Thus it is demonstrated that, for the simple system considered, the length contraction and clock retardation can be interpreted as dynamical cause-and-effect phenomena, and not as kinematical effects as usually construed in conventional presentations of Special Relativity. It is argued that the perspective relativistic change of an object (corresponding to observations from two inertial frames), while certainly being an a causal effect, has a dynamical content in the sense that it is tantamount to an actual dynamical change of the object in one frame.

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