On conceptual issues in classical electrodynamics: Prospects and problems of an action-at-a-distance interpretation

Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous intercharge force. Problems discussed include small angle Rutherford scattering, Jackson's recent "torque paradox" and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossibility of stable circular motion with retarded fields in either classical electromagnetism or Newtonian gravitation is demonstrated.

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Action at a Distance and Self-Consistency of Classical Electrodynamics

The Enigmatic Photon ◽

10.1007/978-94-010-9842-7_11 ◽

1998 ◽

pp. 261-304 ◽

Cited By ~ 1

Author(s):

A. E. Chubykalo ◽

R. Smirnov-Rueda

Keyword(s):

Classical Electrodynamics ◽

Action At A Distance ◽

Self Consistency

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Relativistic analysis of application of Helmholtz theorem to classical electrodynamics

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v7i1.1740 ◽

2015 ◽

Vol 7 (1) ◽

pp. 1297-1308

Author(s):

Andrew Chubykalo ◽

R. Alvarado-Flores ◽

A. Espinoza

Keyword(s):

Special Relativity ◽

Gauge Transformation ◽

Classical Electrodynamics ◽

Invariant Solutions ◽

Helmholtz Theorem ◽

Action At A Distance ◽

The Relationship ◽

Relativistic Analysis

In this work we discuss the relationship between the instantaneous-action-at-a-distance solutions of Maxwellâ€™s equations obtained using Helmholtz theorem and the Lorentzâ€™s invariant solutions of the same equations obtained using Special Relativity postulates. We show that Special Relativity postulates are not consistent with Helmholtzâ€™s theorem in the presence of charges and currents, but in the vacuum, without charges and currents, Helmholtzâ€™s theorem and Special Relativity agree because the instantaneous-action-at-a-distance solutions can be eliminated using a gauge transformation.

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Instantaneous Action‐at‐a‐Distance Formulation of Classical Electrodynamics

Journal of Mathematical Physics ◽

10.1063/1.1664973 ◽

1969 ◽

Vol 10 (8) ◽

pp. 1349-1362 ◽

Cited By ~ 15

Author(s):

Frederick James Kennedy

Keyword(s):

Classical Electrodynamics ◽

Action At A Distance

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On the removal of divergences in electrodynamics: a global point of view

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0115 ◽

1993 ◽

Vol 442 (1915) ◽

pp. 469-484 ◽

Cited By ~ 8

Keyword(s):

Charged Particle ◽

Quantum Electrodynamics ◽

Large Scale ◽

Point Of View ◽

The Other ◽

Classical Electrodynamics ◽

Theoretical Mass ◽

Quantum Version ◽

Action At A Distance ◽

The Universe

This paper explores the implications of Dirac’s seminal work on the concept of self-energy of a charged particle in classical electrodynamics. To avoid the notion of divergent acceleration through self-action, Dirac offered an alternative that involved the existence of preacceleration and an apparent departure from the inherent causality of special relativity. It is argued that Dirac’s solution appears naturally in the electrodynamics described by action at a distance. In this framework the notion of self-action is replaced by that of the response of the universe on the large scale. Provided the universe has the correct large-scale structure, there are no divergent integrals either in the classical or the quantum version of electrodynamics. The price one has to pay involves replacing the purely local Lorentz invariant picture by a global cosmological one. On the other hand the price of standard renormalizable quantum electrodynamics is that of the theoretical mass of the electron is infinitely negative, a requirement that Dirac regarded as absurd, far worse than the loss of local invariance in favour of global invariance, the position adopted here.

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NECESSITY OF SIMULTANEOUS CO-EXISTENCE OF INSTANTANEOUS AND RETARDED INTERACTIONS IN CLASSICAL ELECTRODYNAMICS

International Journal of Modern Physics A ◽

10.1142/s0217751x99001755 ◽

1999 ◽

Vol 14 (24) ◽

pp. 3789-3798 ◽

Cited By ~ 8

Author(s):

ANDREW E. CHUBYKALO ◽

STOYAN J. VLAEV

Keyword(s):

Electromagnetic Field ◽

Maxwell Equations ◽

Direct Interaction ◽

Classical Electrodynamics ◽

Constant Acceleration ◽

Action At A Distance ◽

A Charge ◽

Accelerated Charge

We consider the electromagnetic field of a charge moving with a constant acceleration along an axis. We find that this field obtained from the Liénard–Wiechert potentials does not satisfy Maxwell equations if one considers exclusively a retarded interaction. We show that if and only if one takes into account both retarded interaction and direct interaction (so-called "instantaneous action at a distance") the field produced by an accelerated charge satisfies Maxwell equations.

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