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I construct perforated, "take-away" fractals that support short-distance power-law scaling with complex exponents for Dirac (spin-1/2) propagators. The construction relies on a fortuitous ansatz for Dirac boundary conditions at the surfaces of spherical voids in a three-dimensional embedding space, and requires that boundary conditions vary from void to void and are distributed statistically. The appropriate distribution can ensure that nonzero charges (but not dipoles, which drive nontrivial power-law scaling) induced in voids cancel out in spatial averaging., Comment: To be published in Fractals (World Scientific)

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., Comment: Accepted by Open Physics (De Gruyter)

The Mott problem 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 non-spherically-symmetric single track in a cloud chamber? This is a variant of the more general quantum measurement problem. Earlier, we proposed such a mechanism, drawing on quantum-mechanical Coulomb scattering and the thermal behavior of supersaturated vapors. Our analysis implied that, in a large enough sample, the probability that a track originates at distance R from the decay source is proportional to 1/R^2, with a proportionality constant which we expressed in terms of more fundamental parameters involving diverse physical processes, but were unable to estimate at the time. More recently, we tested the 1/R^2 law opportunistically using pedagogical cloud chamber video posted on the Internet. In the present paper, we draw on the chemical physics literature for an independent estimate of the proportionality constant. The estimate is rough, but within about 1.7 orders of magnitude (factor of 50) of a rough value that we derive directly from the video data. Given the crudeness of the experimental data, the roughness of the numerical estimates, and the extreme spread of concentrations involved (air molecules vs. subcritical vapor clusters of specific sizes), we view this level of agreement as significant, at this stage in the theory's development.

For single-particle nonrelativistic quantum mechanics, a Gamow state is an eigenfunction of the Hamiltonian with complex eigenvalue. Gamow states are not normalizable; they depend on time via the usual multiplier exp(-iEt) supplemented by a cutoff at an expanding wavefront. Gamow states have been used to extend nuclear shell models; they are to metastable states as normalizable eigenfunctions are to bound states. In this paper we generalize Gamow states to decays with multiple outgoing particles. We derive the exact form of the expanding wavefront, even for relativistic outgoing particles. In the non-relativistic limit we derive the exact form of the multi-particle Gamow state contribution to the system propagator (Green's function).

Using publicly available video of a diffusion 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. Aspects of the results may suggest a modification to Born's rule at very small wavefunction, with possibly profound implications for the detection of extremely rare events such as proton decay, but other explanations are not ruled out. Speculatively, I introduce two candidate small-wavefunction Born rule modifications, a hard cutoff, and an offset model with a stronger underlying physical rationale. 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., Comment: Accepted for publication by Open Physics (De Gruyter)

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)., Comment: This paper has been accepted by "Foundations of Physics"

I argue that the marquis characteristics of the quantum-mechanical double-slit experiment (point detection, random distribution, Born rule) can be explained using Schroedinger's equation alone, if one takes into account that, for any atom in a detector, there is a small but nonzero gap between its excitation energy and the excitation energies of all other relevant atoms in the detector (isolated-levels assumption). To illustrate the point I introduce a toy model of a detector. The form of the model follows common practice in quantum optics and cavity QED. Each detector atom can be resonantly excited by the incoming particle, and then emit a detection signature (e.g. bright flash of light) or dissipate its energy thermally. Different atoms have slightly different resonant energies per the isolated-levels assumption, and the projectile preferentially excites the atom with the closest energy match. The toy model permits one easily to estimate the probability that any atom is resonantly excited, and also that a detection signature is produced before being overtaken by thermal dissipation. The end-to-end detection probability is the product of these two probabilities, and is proportional to the absolute square of the incoming wavefunction at the atom in question, i.e. the Born rule. I consider how closely a published neutron-interference experiment conforms to the picture developed here; I show how this paper's analysis steers clear of creating a scenario with local hidden variables; I show how the analysis steers clear of the irreversibility implicit in the projection postulate; and I discuss possible experimental tests of this paper's ideas. Hopefully, this is a significant step toward realizing the program of solving the measurement problem within unitary quantum mechanics envisioned by Landsman, among others., Comment: This paper has been peer reviewed and accepted for publication by Studies in History and Philosophy of Modern Physics (Elsevier)

In a single-particle detection experiment, a wavefront impinges on a detector but observers only see a point response. The extent of the wavefront becomes evident only in statistical accumulation of many independent detections, with probability given by the Born rule. Drawing on concepts from quantum optics, we analyze a simple model to reverse-engineer how this behavior can come about in terms of wave mechanics alone without a measurement axiom. The model detector consists of many molecules, each of which can be resonantly excited by the incoming particle and then emit a detection signature (e.g., localized flash of light). Different molecules have different resonant energies because local conditions (proximity of other molecules, Doppler shifts, etc.) vary. The detector is thus a quasi-continuum, and the incoming particle preferentially excites the molecule that it matches most closely in energy. (In actuality, molecules can be so numerous that many could closely match the incoming particle in energy; but in that case only one will be the first, and there will be nothing left for the others by the time the first match resonates and then emits. The model does not explicitly take into account the temporal advance of the particle wave packet through the detector medium.) The excited molecule can emit a detection signature, but that process competes with fluctuation-driven dephasing. We estimate the probability that a given molecule is resonantly excited, and we also estimate the probability that a detection signature is produced before being overwhelmed by fluctuations in the detector medium. The product of these two probabilities is proportional to the absolute-square of the incoming wavefunction at the molecule in question, i.e. the Born rule. We discuss ways to probe these mechanisms experimentally, and check the model with numbers from a neutron interference experiment.

In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform media, either by simulating random samples or by expanding in spherical harmonics and analyzing Bessel functions. We introduce a simple regulator that applies to unbounded media, enabling trivial derivation and analysis of lifetimes via elementary Fourier techniques. The regulator can be interpreted as a correlation length for atomic positions; the regularized system describes localized regions of enhanced radiative activity in otherwise quiescent surroundings.

We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling at short distance follows almost immediately. Similar techniques provide easy constructions of objects with fractional Brownian short-distance behavior for phase screens and other applications., Comment: This article has been accepted for publication by the journal Fractals (World Scientific Publishing). Acceptance dated November 17, 2016

We explicitly construct fractals of dimension 4-epsilon on which dimensional regularization approximates scalar-field-only quantum-field-theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to nonscalar fields, and speculate about implications for quantum gravity., Comment: This article has been accepted for publication by European Physical Journal C. Acceptance date November 17, 2016