Reduced-order Abraham-Lorentz-Dirac equation and the consistency of classical electromagnetism

Abstract

It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is recognized that certain types of charge distribution are simply impossible, such as, for example, a point particle with finite charge and finite inertia. This is owing to the fact that negative inertial mass is an unphysical concept in classical physics. It remains useful to obtain an equation of motion for small charged objects that describes their motion to good approximation without requiring knowledge of the charge distribution within the object. We give a simple method to achieve this, leading to a reduced-order form of the Abraham-Lorentz-Dirac equation, essentially as proposed by Eliezer, Landau and Lifshitz, and derived by Ford and O'Connell.

8 pages, 1 figure; 2nd version has minor addition on impact of gravity; 3rd has added citations and better discussion of Ford and O'Connell

References in corpus (6)

• A Rigorous Derivation of Electromagnetic Self-force
• Aspects of electromagnetic radiation reaction in strong fields
• Radiation reaction of a classical quasi-rigid extended particle
• Absence of a consistent classical equation of motion for a mass-renormalized point charge
• The fields and self-force of a constantly accelerating spherical shell
• The non-existence of the self-accelerating dipole, and related questions

Cited by in corpus (8)

• Towards the nonlinear regime in extensions to GR: assessing possible options
• Vacuum friction on a rotating pair of atoms
• Tracking the radiation reaction energy when charged bodies accelerate
• Self-force of a rigid ideal fluid, and a charged sphere in hyperbolic motion
• Electromagnetic radiation and the self field of a spherical dipole oscillator
• Radiation Reaction as a Non-conservative Force
• Dynamics of spherical distributions of charge with small internal dipolar motion
• Newton like equations for the radiating particle: the non relativistic limit