The Mott Problem: a spherically symmetric emission that records as a straight track

James Norman Ibbotson

Published Nov 1, 2026• 0 citations

Abstract

An alpha-emitting nucleus is spherically symmetric and has no preferred axis. Quantum mechanics therefore describes the emitted alpha particle as an outgoing spherical wave of uniform angular amplitude, . Yet every cloud-chamber photograph of such an emission records a single straight track. This is Mott's problem (1929), the measurement problem in its sharpest experimental form: an apparent contradiction between a symmetry and a photograph. This paper (i) states the problem precisely, (ii) reproduces Mott's resolution quantitatively from CODATA constants — the alpha de Broglie wavelength, the angular tolerance set by the size of the recording atom, the resulting sideways wander over a finite track, and a direct numerical simulation of the joint alpha–atom amplitude that recovers the closed-form width, and (iii) examines a candidate interpretive model drawn from the Temporal Dynamics Framework and reports, on that model's own quantitative assumptions, that it adds no measurable prediction to Mott's result. This last outcome is recorded as a null, and a numerical target for any future derivation is fixed: rad for a 5.407 MeV alpha in hydrogen, equivalently a lateral wander of 1.86 m over a 10 cm track. No result here improves on Mott (1929); the solution is his. The contribution of this paper is a fully numerical restatement of that solution and an explicit, falsifiable target that fixes what any interpretive model would have to reproduce. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

DOI: 10.5281/zenodo.23848237

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