Comment on "Absence of a consistent classical equation of motion for a mass-renormalized point charge"

TL;DR

This paper critiques a proposed classical equation of motion for a point charge, arguing that it leads to infinite energy due to velocity jumps, thus questioning the validity of the point-particle limit in that context.

Contribution

It clarifies that the point-particle limit used in the discussed equation results in infinite energy, challenging the validity of the proposed motion in certain regimes.

Findings

Velocity jumps cause infinite electromagnetic energy

Point-particle limit is physically inconsistent

Critique of Yaghjian's equation of motion

Abstract

Here we comment on the paper by Arthur D. Yaghjian, Phys. Rev. E 78, 046606 (2008) (arXiv:0805.0142). The author provides an equation of motion for a point charged particle in a certain regime of system parameters (on the other hand, claiming that in a different regime the classical equation of motion does not exist). The solutions of this equation (in the regime where it exists) presented in the paper show instantaneous jumps in the particle's velocity. We show that such jumps, in the case of a point particle, would generate infinite energy in the radiated electromagnetic field. Therefore, we claim that the point-particle limit used by the author is incorrect.