Abstract

According to Einstein, if the speed of a particle remains low, i.e., much less than the speed of light, then the dynamical prediction of special relativistic mechanics remains very well approximated by the prediction of Newtonian mechanics for the same parameter(s) and initial conditions. However, in this paper, it is shown with two counterexample Hamiltonian dynamical systems that, contrary to Einstein's claim, Newtonian dynamics can eventually disagree completely with relativistic dynamics, even though the particle speed is low. This result points to a new possibility of testing the two theories in the domain of low speed.

This paper is aka "Einstein's Mistake on the Connection of Newtonian Mechanics to Special Relativistic Mechanics".