Abstract
Even for the simplest physical situations the Lorentz-Dirac equation, solved as an initial value problem, gives unphysical ‘run-away’ solutions. Dirac’s method for avoiding these unphysical solutions generates solutions which exhibit unphysical acausal pre-acceleration. A careful examination of the application of the conservation of momentum in the derivation of the Abraham self-force reveals a fundamental error concerning the force acting on the particle. This error, originally made by Abraham (1903), has been repeated by subsequent investigators. When corrected, a new equation of motion results. A discussion of the general properties of the new equation of motion is given, and solutions for several important special cases are presented. The behaviour of these solutions is causal, physically reasonable, and easily understood.
Similar content being viewed by others
References
M. Abraham, “Prinzipien der Dynamik des Elektrons,”Ann, Phys. (Leipzig) 10, 105–179 (1903).
P. A. M. Dirac, “Classical theory of radiating electrons,”Proc. Roy. Soc. London A167, 148–169 (1938).
P. A. Hogan, “Electrodynamics without advanced fields or asymptotic conditions,”Nuovo Cimento 15B, 136–146 (1973).
J. D. Jackson,Classical Electrodynamics (Wiley, New York, 2nd edn., 1975).
F. Rohrlich,Classical Charged Particles (Addison-Wesley, Reading, Massachusetts, 1965).
E. G. P. Rowe, “Structure of the energy tensor in the classical electrodynamics of point particles,”Phys. Rev. D18, 3639–3654 (1978).
J. L. Synge,Relativity: The Special Theory (North-Holland, Amsterdam, 2nd edn., 1965).
C. Teitelboim, “Splitting of the Maxwell tensor: radiation reaction without advanced fields,”Phys. Rev. D 1, 1572–1582 (1970); Erratum:ibid.2, 1763 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oliver, M.A. Classical electrodynamics of a point particle. Found Phys Lett 11, 61–82 (1998). https://doi.org/10.1023/A:1022406820377
Received:
Issue Date:
DOI: https://doi.org/10.1023/A:1022406820377