Variant forms of Eliezer's Theorem
Abstract
Over 60 years ago, Eliezer proved the surprising result that an electron moving radially according to the LorentzDirac equation in the Coulomb field of a proton will not be attracted to a collision with the proton as expected. Instead, it is repelled from the proton with proper acceleration increasing asymptotically with proper time. Proponents of the LorentzDirac equation sometimes try to explain this away by speculation that the electron must approach so closely to the proton that the field strength would be beyond the domain of validity of the classical LorentzDirac equation and therefore require a quantummechanical analysis. This note proves some variants of Eliezer's result which apply to *bounded*, compactly supported, spherically symmetric fields, and thus call into question such speculation. However, these variants do require the additional hypothesis (not required by Eliezer) that the electron is unaccelerated before entering the fieldi.e., that "preacceleration" is impossible. Though these results may not appear in the literature, the methods of proof are well known. The motivation for writing down careful proofs was continued skepticism by proponents of the LorentzDirac equation.
 Publication:

arXiv eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.mathph/0505042
 arXiv:
 arXiv:mathph/0505042
 Bibcode:
 2005math.ph...5042P
 Keywords:

 Mathematical Physics
 EPrint:
 10 pages, LaTeX, no figures