[Forked off from this thread to allow for discussion of more basic principles of QM] Time derivatives limit the mechanism for evolution in a system. Since quantum particles jump rather than move through space, a rate of change of position per unit time is meaningless. Indeterminacy arises in this conflict between trying to force a particle to move through space when it wants to jump. IE. It won't have a range of velocities so you're just dividing by zero to get the position.