Classical Electromagnetism via Relativity

Rosser, W. G. V.

doi:10.1007/978-1-4899-6559-2

Cited by 73 publications

(125 citation statements)

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“…8: "This law does not depend on the inertial reference frame in which q, u, E, and B are measured." The same assertions about the form of the Lorentz force law in two inertial frames can be found in [23], Eqs. (6.42) and (6.43).…”

Section: Jackson's Paradox the 3d Quantities And Their Apparentsupporting

confidence: 61%

“…There, this form invariance of the Lorentz force, together with the AT of the 3D force F (26) and the AT of the 3D velocity u, Eqs. (1.26)-(1.28) in [23], are used to derive the AT for the 3D E and B. However the above discussion clearly shows that the 3D quantities in S ′ are not obtained by the LT from the corresponding 3D quantities in S than by the use of the AT.…”

Section: Jackson's Paradox the 3d Quantities And Their Apparentmentioning

confidence: 93%

“…It is generally accepted, e.g., [1,3,23], that the "relativistic" equations of motion have the same form in two relatively moving inertial frames S and S ′ F = dp/dt, p =mγ u u F ′ = dp…”

Section: Jackson's Paradox the 3d Quantities And Their Apparentmentioning

confidence: 99%

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Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

Ivezić

2006

Found Phys

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In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N s , N t and M s , M t respectively are given. The torques N s , N t (the angular momentums M s , M t ), taken together, contain the same physical information as the bivector N (the bivector M ). The usual approaches that deal with the 3D quantities E, B, F, L, N, etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.

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Section: Jackson's Paradox the 3d Quantities And Their Apparentsupporting

confidence: 61%

Section: Jackson's Paradox the 3d Quantities And Their Apparentmentioning

confidence: 93%

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Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

Ivezić

2006

Found Phys

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“…To quote e.g. Rosser [21]: "Now if the co-ordinates and time are transformed using the Galilean transformations, Maxwell's equations do not obey the principle of relativity. [...] If the Galilean transformations were assumed to be correct, Maxwell's equations could only be hold in the one reference frame and should have been possible to identify this absolute system by electrical and optical experiments.…”

Section: Discussionmentioning

confidence: 99%

Radiation by Moving Charges

Tsang¹

1998

Classical Electrodynamics

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It is generally accepted that in order to describe the dynamics of relativistic particles in the laboratory (lab) frame it is sufficient to take into account the relativistic dependence of the particles momenta on the velocity. This solution of the dynamics problem in the lab frame makes no reference to Lorentz transformations. For this reason they are not discussed in particle tracking calculations in accelerator and plasma physics. It is generally believed that the electrodynamics problem can be treated within the same "single inertial frame" description without reference to Lorentz transformations. In particular, in order to evaluate radiation fields arising from charged particles in motion we need to know their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newton's second law "corrected" for the relativistic dependence of momentum on velocity. It is assumed in all standard derivations that one can perform identification of the trajectories in the source part of the usual Maxwell's equations with the trajectories x(t) measured (or calculated by using the corrected Newton's second law) in the lab frame. This way of coupling fields and particles is considered since more than a century as the relativistically correct procedure. We argue that this procedure needs to be changed, and we demonstrate the following, completely counterintuitive statement: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. In order to find the trajectory of a particle in the lab frame consistent with the usual Maxwell's equations, one needs to solve the dynamics equation in manifestly covariant form by using the coordinate-independent proper time τ to parameterize the particle world-line in space-time. We show that there is a difference between "true" particle trajectory x(t) calculated or measured in the conventional way, and covariant particle trajectory x cov (t) calculated by projecting the world line to the lab frame (t(τ), x 1 (τ), x 2 (τ), x 3 (τ)) and using the lab time t to parameterize the trajectory curve. In other words, for a relativistic motion accelerated along a curved trajectory, the results of conventional particle tracking differ from those of covariant particle tracking. The difference is only due to a choice of convention, but only x cov (t) is consistent with the usual Maxwell's equations. This essential point has never received attention in the physical community. As a result, a correction of the conventional synchrotron-cyclotron radiation theory is required.

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“…Among the four different approaches that he mentions, one particular approach is based on applying Lorentz-Einstein transformations of spacetime coordinates and fields to a stationary point charge. 3 He considers that this method is fairly simple mathematically, but it doesn't fit into the classical theory of electromagnetism.…”

Section: Introductionmentioning

confidence: 99%