  According to Einstein, the trajectory of a particle that is predicted by
special relativistic mechanics is well approximated by the trajectory predicted
by Newtonian mechanics if the particle speed is low, i.e., much less than the
speed of light. However, in this paper, it is shown with a counterexample
Hamiltonian dynamical system that Newtonian dynamics can eventually disagree
completely with relativistic dynamics even though the particle speed is low.
After the breakdown of the agreement, either the Newtonian description is no
longer correct or the relativistic description is no longer correct or both
descriptions are no longer correct for the low speed motion.
