Reply to "Comment on 'Absence of a consistent classical equation of motion for a mass-renormalized point charge'" (arXiv:2511.02865v1, 3 Nov 2025)

TL;DR

This paper reviews the derivation of the classical equation of motion for a point charge, addressing and refuting objections related to velocity jumps and delta functions in radiated fields.

Contribution

It clarifies the derivation of the Lorentz-Abraham-Dirac equation from extended charge models and counters specific objections about nonanalytic force points.

Findings

The derivation from extended charge models is valid as radius approaches zero.

Objections about velocity jumps causing delta functions are shown to be incorrect.

The classical equation of motion remains consistent despite nonanalytic force points.

Abstract

By means of a brief review of the derivation of the causal modified Lorentz-Abraham-Dirac classical equation of motion from the renormalization of the mass in the modified equation of motion of an extended charged sphere as its radius approaches zero, it is shown that Zin and Pylak's objection that the jumps in velocity allowed across transition intervals near nonanalytic points in time of the externally applied force produce delta functions in the radiated fields is incorrect.