Test of a theory of the Mott quantum-measurement problem
Abstract
The Mott problem asks: Is there a microphysical mechanism - based only on Schroedinger's equation - that explains why an alpha particle emitted in a spherically symmetric nuclear decay produces a non-spherically-symmetric single track in a cloud chamber? This is a variant of the more general quantum measurement problem. Earlier, I proposed such a mechanism, drawing on quantum-mechanical Coulomb scattering and the thermal behavior of supersaturated vapors. I found that the probability that a track originates at distance R from the decay source is proportional to 1/R^2, with a proportionality constant that I expressed in terms of more fundamental parameters but was unable to estimate at the time. I tested the 1/R^2 law opportunistically using cloud chamber video from the Internet. Here, I draw on chemical physics to independently estimate the proportionality constant. The estimate is within a factor 1-2 of a value extracted directly from the data.
Keywords
Cite
@article{arxiv.2209.05344,
title = {Test of a theory of the Mott quantum-measurement problem},
author = {Jonathan F. Schonfeld},
journal= {arXiv preprint arXiv:2209.05344},
year = {2025}
}
Comments
Updated to take into account factor K (see Equation 3.18), which greatly enhances accuracy of estimate that the paper is all about. Modified title and abstract accordingly. Also corrected sign error in Equation (2.1). Inserted factor S (Equation 3.7), and estimated its impact; clarified some other language