In the classical definition, velocity is the time derivative of the particles position curve (trajectory). The Uncertainty principle restricts the particles velocity from ever being zero. Doesn't this imply that a particles path is restricted to paths that do not have a zero time derivative at any point?. (ie implying that the path cannot reverse directions among other things). If this is true, does it place restrictions on the Path Integral Formulation, where all possible paths are assumed to be possible, but not likely? Or am I a victim of classical thinking once again?