  We apply the formalism of quantum measurement theory to the idealized
measurement of the position of a particle with an optical interferometer,
finding that the backaction of counting entangled photons systematically
collapses the particle's wavefunction toward a narrow Gaussian wavepacket at
the location $x_\mathrm{est}$ determined by the measurement without appeal to
environmental decoherence or other spontaneous collapse mechanism. Further, the
variance in the particle's position, as calculated from the post-measurement
wavefunction agrees precisely with shot-noise limited uncertainty of the
measured $x_\mathrm{est}$. Both the identification of the absolute square of
the particle's initial wavefunction as the probability density for
$x_\mathrm{est}$ and the de Broglie hypothesis emerge as consequences of
interpreting the intensity of the optical field as proportional to the
probability of detecting a photon. Linear momentum information that is encoded
in the particle's initial wavefunction survives the measurement, and the
pre-measurement expectation values are preserved in the ensemble average.
