Objective uncertainty relation with classical background in a statistical model

We show within a statistical model of quantization reported in the previous work based on Hamilton-Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in velocity and position spaces satisfy a reciprocal uncertainty relation. The relation is objective (observation independent) and implies the standard quantum mechanical uncertainty relation. (C) 2012 Elsevier B.V. All rights reserved.