  Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a
simplified version of a variational principle within Nelson stochastic
mechanics that produces the von Neumann wave packet reduction after a position
measurement. This stochastic control problem parallels, with a different
kinematics, the problem of the Schroedinger bridge. This gives a profound
meaning to what was observed by Schroedinger in 1931 concerning Schroedinger
bridges: "Merkwuerdige Analogien zur Quantenmechanik, die mir sehr des
Hindenkens wert erscheinen".
