  Quantum mechanics has been argued to be a coarse-graining of some underlying
deterministic theory. Here we support this view by establishing a map between
certain solutions of the Schroedinger equation, and the corresponding solutions
of the irrotational Navier-Stokes equation for viscous fluid flow. As a
physical model for the fluid itself we propose the quantum probability fluid.
It turns out that the (state-dependent) viscosity of this fluid is proportional
to Planck's constant, while the volume density of entropy is proportional to
Boltzmann's constant. Stationary states have zero viscosity and a vanishing
time rate of entropy density. On the other hand, the nonzero viscosity of
nonstationary states provides an information-loss mechanism whereby a
deterministic theory (a classical fluid governed by the Navier-Stokes equation)
gives rise to an emergent theory (a quantum particle governed by the
Schroedinger equation).
