Does the Mott problem extend to Geiger counters?

TL;DR

This paper investigates whether ionization physics in Geiger counters can explain wavefunction collapse, proposing an experiment that supports the idea of near-singular ionization mechanisms similar to cloud chambers, with implications for quantum measurement.

Contribution

It extends the Mott problem analysis to Geiger counters and proposes an experiment to test ionization mechanisms underlying wavefunction collapse.

Findings

Experimental results support the near-singular-ionization hypothesis.

The proposed experiment demonstrates measurable count rate variations.

Supports the idea that ionization physics may explain quantum measurement phenomena.

Abstract

The Mott problem is a simpler version of the quantum measurement problem that asks: Is there a microscopic physical mechanism - based (explicitly or implicitly) only on Schroedinger's equation - that explains why a single alpha particle emitted in a spherically symmetric s-wave nuclear decay produces a manifestly non-spherically-symmetric single track in a cloud chamber? I attempt here to generalize earlier work that formulated such a mechanism. The key ingredient there was identification of sites at which the cross section for ionization by a passing charged particle is near singular at ionization threshold. This near singularity arose from a Penning-like process involving molecular polarization in sub-critical vapor clusters. Here, I argue that the same Mott problem question should be asked about Geiger counters. I then define a simple experiment to determine if ionization physics similar to the cloud chamber case takes place in the mica window of a Geiger counter and explains the collimation of wavefunctions that are spherically symmetric outside the counter into linear tracks inside. The experiment measures the count rate from a radioactive point source as a function of source-window separation. I have performed a proof of concept of this experiment; results are reported here and support the near-singular-ionization picture. These results are significant in their own right, but also because they may shed light on physical mechanisms underlying the full quantum measurement problem. I illustrate this for the Stern-Gerlach experiment and a particular realization of superconducting qubits. I conclude by detailing further work required to flesh out these results more rigorously.