  We discuss a force arising from zero-temperature quantum fluctuations in a
weakly interacting Bose-Einstein condensate (BEC). We argue that there is a
drag force on an object moving at speeds well below Landau's critical velocity,
and motivate our argument by an analogy to the Casimir force in an
electromagnetic vacuum. We sketch the calculation of this force for an object
described by a general potential. We comment about the relevance of our results
to the stability of superfluid flow, arguing that this effect is consistent
with the observation of persistent currents and that this effect introduces new
experimental observables. Finally, we describe a new hydryodynamic boundary
condition for superfluid flow that takes into account the scattering of quantum
fluctuations off a rough surface.
