The Grain and the Runaway: Abraham–Lorentz at the Counting Grain
Year: 2026
Type: preprint
Abstract: AF-1 evaluated the classical electron's pathology timescale — the Abraham–Lorentz τ₀ = 6.266425×10⁻²⁴ s — and charged its F2 against any construction that places a counting grain at the frame's τ_cell = 2.216789×10⁻²⁴ s: if the grain fails to remove the runaway at order τ₀, the correlation dies. This paper runs that construction in four dresses of the grain derivative. Three dresses fail by their own numbers — the runaway survives every one-sided grain (retarded, forward, backward-implicit), with growth rates printed. The fourth dress — the derivative as a symmetric average over one grain — kills the runaway completely: the characteristic equation has no root with positive real part, only a single neutral oscillatory pair at ω = 2.013415×10²⁴ rad/s. The same dress does not kill pre-acceleration: the response window compresses from τ₀ to τ_cell/2 = 1.108394×10⁻²⁴ s, a factor 5.6536 — sub-grain, below the resolution of the frame that owns the grain, but not zero. The construction is graded exactly there: a grain can cure the runaway or preserve strict causality at this order — the symmetric grain does the first and rents the second at half a cell.
Author: Aldred, William Alexander
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225432708