  We show that the Schroedinger equation is a lift of Newton's law of motion on
the space of probability measures, where derivatives are taken w.r.t. the
Wasserstein Riemannian metric. Here the potential is the sum of the total
classical potential energy of the extended system and its Fisher information.
The precise relation is established via a well known ('Madelung') transform
which is shown to be a symplectic submersion of the standard symplectic
structure of complex valued functions into the canonical symplectic space over
the Wasserstein space. All computations are conducted in the framework of
Otto's formal Riemannian calculus for optimal transportation of probability
measures
