A notion of length for quantum mechanical trajectories is introduced within the realm of stochastic mechanics. Using a stochastic calculus of variation, one shows that the geodesic dynamics is not the free one, but the quantum evolution in the time-dependent quadratic potential associated with the Wiener process in stochastic mechanics. The length for the free evolution is also examined.

• Received 23 May 1983

DOI:https://doi.org/10.1103/PhysRevLett.52.2107