dx*dp ~ h_ uncertainty of x h_ = lower limit of this product
dt*dE ~ h_ uncertainty of t h_ = also a lower limit of product
(dx/dt) < c c speed of light c = the upper limit of v (ratio)
The existance of an upper limit for the first derivative suggests (?)
that the second derivative (acceleration --> force) may also have an
upper limit. I never heard about this, except in the context that a
physical quantity can not change in zero time. What principles would
be violated by allowing too rapid change in v? (What kind of "inertia"
would prevent this? What kind of "Lenz law" would be ... ?)
Is there a formal limit for the second derivative of position with
respect of time somewhere ? (in general relativity? in QCD? ...).