  In optical experiments involving a single photon that takes alternative paths
through an optical system and ultimately interferes with itself (e.g., Young's
double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer),
there exist fundamental connections between the linear and angular momenta of
the photon on the one hand, and the ability of an observer to determine the
photon's path through the system on the other hand. This paper examines the
arguments that relate the photon momenta (through the Heisenberg uncertainty
principle) to the "which path" (German: welcher Weg) question at the heart of
quantum mechanics. We show that the linear momenta imparted to apertures or
mirrors, or the angular momenta picked up by strategically placed wave-plates
in a system, could lead to an identification of the photon's path only at the
expense of destroying the corresponding interference effects. We also describe
a thought experiment involving the scattering of a circularly-polarized photon
from a pair of small particles kept at a fixed distance from one another. The
exchange of angular momentum between the photon and the scattering particle in
this instance appears to provide the "which path" information that must, of
necessity, wipe out the corresponding interference fringes, although the
fringe-wipe-out mechanism does not seem to involve the uncertainty principle in
any obvious way.
