  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.
