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 single spherically symmetric s-wave nuclear decay produces a manifestly nonspherically 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 subcritical 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 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 reported here and support the near-singular-ionization picture. These results are significant in their own right, and they may shed light on physical mechanisms underlying instances of 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.
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 single spherically symmetric s-wave nuclear decay produces a manifestly nonspherically 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 subcritical 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 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 reported here and support the near-singular-ionization picture. These results are significant in their own right, and they may shed light on physical mechanisms underlying instances of 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.
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.
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.
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.
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).
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.