Resolution of a paradox in classical electrodynamics

Fabrizio Pinto
Phys. Rev. D 73, 104020 – Published 15 May 2006

Abstract

It is an early result of electrostatics in curved space that the gravitational mass of a charge distribution changes by an amount equal to Ues/c2, where Ues is the internal electrostatic potential energy and c is the speed of light, if the system is supported at rest by external forces. This fact, independently rediscovered in recent years in the case of a simple dipole, confirms a very reasonable expectation grounded in the mass-energy equivalency equation. However, it is an unsolved paradox of classical electrodynamics that the renormalized mass of an accelerated dipole calculated from the self-forces due to the distortion of the Coulomb field differs in general from that expected from the energy correction, Ues/c2, unless the acceleration is transversal to the orientation of the dipole. Here we show that this apparent paradox disappears for any dipole orientation if the self-force is evaluated by means of Whittaker’s exact solution for the field of the single charge in a homogeneous gravitational field described in the Rindler metric. The discussion is supported by computer algebra results, diagrams of the electric fields distorted by gravitation, and a brief analysis of the prospects for realistic experimentation. The gravitational correction to dipole-dipole interactions is also discussed.

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  • Received 9 April 2006

DOI:https://doi.org/10.1103/PhysRevD.73.104020

©2006 American Physical Society

Authors & Affiliations

Fabrizio Pinto*

  • InterStellar Technologies Corporation, 115 N Fifth Avenue, Monrovia, California 91016, USA

  • *Electronic address: fabrizio.pinto@interstellartechcorp.com

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Vol. 73, Iss. 10 — 15 May 2006

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