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arXiv:2201.13249 · Open Physics

Measured distribution of cloud chamber tracks from radioactive decay: A new empirical approach to investigating the quantum measurement problem

Jonathan Schonfeld

Published Jan 1, 2022• 4 citations
arXivHTMLPDF

Abstract

Abstract Using publically available video of a cloud chamber with a very small radioactive source, I measure the spatial distribution of where tracks start, and consider possible implications. This is directly relevant to the quantum measurement problem and its possible resolution, and appears never to have been done before. The raw data are relatively uncontrolled, leading to caveats that should guide future, more tailored experiments. Track distributions from decays in cloud chambers represent a previously unappreciated way to probe the foundations of quantum mechanics, and a novel case of wavefunctions with macroscopic signatures.

DOI
10.1515/phys-2022-0009

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Abstract Using publically available video of a cloud chamber with a very small radioactive source, I measure the spatial distribution of where tracks start, and consider possible implications. This is directly relevant to the quantum measurement problem and its possible resolution, and appears never to have been done before. The raw data are relatively uncontrolled, leading to caveats that should guide future, more tailored experiments. Track distributions from decays in cloud chambers represent a previously unappreciated way to probe the foundations of quantum mechanics, and a novel case of wavefunctions with macroscopic signatures.
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.
Abstract In a cloud chamber, the quantum measurement problem amounts to explaining the first droplet in a charged-particle track; subsequent droplets are explained by Mott’s 1929 wave-theoretic argument about collision-induced wavefunction collimation. I formulate a mechanism for how the first droplet in a cloud chamber track arises, making no reference to quantum measurement axioms. I look specifically at tracks of charged particles emitted in the simplest slow decays, because I can reason about rather than guess the form that wave packets take. The first visible droplet occurs when a randomly occurring, barely-subcritical vapor droplet is pushed past criticality by ionization triggered by the faint wavefunction of the emitted charged particle. This is possible because potential energy incurred when an ionized vapor molecule polarizes the other molecules in a droplet can balance the excitation energy needed for the emitted charged particle to create the ion in the first place. This degeneracy is a singular condition for Coulombic scattering, leading to infinite or near-infinite ionization cross sections, and from there to an emergent Born rule in position space, but not an operator projection as in the projection postulate. Analogous mechanisms may explain canonical quantum measurement behavior in detectors such as ionization chambers, proportional counters, photomultiplier tubes or bubble chambers. This work is important because attempts to understand canonical quantum measurement behavior and its limitations have become urgent in view of worldwide investment in quantum computing and in searches for super-rare processes (e.g., proton decay).
In a cloud chamber, the quantum measurement problem amounts to explaining the first droplet in a charged-particle track; subsequent droplets are explained by Mott's 1929 wave-theoretic argument about collision-induced wavefunction collimation. I formulate a mechanism for how the first droplet in a cloud chamber track arises, making no reference to quantum measurement axioms. I look specifically at tracks of charged particles emitted in the simplest slow decays, because I can reason about rather than guess the form that wave packets take. The first visible droplet occurs when a randomly occurring, barely-subcritical vapor droplet is pushed past criticality by ionization triggered by the faint wavefunction of the emitted charged particle. This is possible because potential energy incurred when an ionized vapor molecule polarizes the other molecules in a droplet can balance the excitation energy needed for the emitted charged particle to create the ion in the first place. This degeneracy is a singular condition for Coulombic scattering, leading to infinite or near-infinite ionization cross sections, and from there to an emergent Born rule in position space, but not an operator projection as in the projection postulate. Analogous mechanisms may explain canonical quantum measurement behavior in detectors such as ionization chambers, proportional counters, photomultiplier tubes or bubble chambers. This work is important because attempts to understand canonical quantum measurement behavior and its limitations have become urgent in view of worldwide investment in quantum computing and in searches for super-rare process (e.g., proton decay).
I review and augment my work of the last few years on the physical origins and limitations of canonical quantum measurement behavior. Central to this work is a detailed analysis of the microstructure of real measurement devices. Particular attention is paid to the Mott problem, which addresses a simpler version of canonical quantum measurement behavior: It asks why an Alpha particle emitted in nuclear decay produces one and only one track in a cloud chamber. My analysis - entirely consistent with unitarity - leads to an emergent, approximate Born rule supported by experiment, with possible breakdown at very small probability density. I argue that a similar picture applies to other measurement scenarios, including Geiger counters, the Stern-Gerlach experiment and superconducting qubits.
I extend earlier work that derived a Born rule for nuclear-decay cloud chamber tracks (Mott problem) without invoking quantum measurement axioms. The key ingredient there was the identification of sites at which the cross section for ionization by a passing charged particle is singular at ionization threshold. This singularity arose from a Penning-like process involving molecular polarization in sub-critical vapor clusters. In the present paper, I propose a simple experiment to determine if similar ionization physics takes place in the mica window of a Geiger counter and drives the collimation of spherically-symmetric wavefunctions outside the counter tube into ion 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 consistent with the singular-ionization picture. I consider implications for the Stern-Gerlach experiment and superconducting qubits. I detail further work required to flesh out these results more rigorously.
An experimentalist trying to work his way through the impressive body of literature in quantum measurement theory rapidly notices that the theory, at least hitherto, does not make any predictions for experiments aimed at its own test. Rather one has the impression that most experiments discussed in the context of that theory serve more the purpose of trying to demonstrate its internal consistency. An early example is the beautiful paper by Mott (1929) where he presents the wave mechanical analysis of a seemingly particle-like phenomenon, the α-ray tracks in a cloud chamber.