Newtonian and special-relativistic predictions for the trajectory of a slow-moving dissipative dynamical system

摘要

We show that the trajectories predicted by Newtonian mechanics and special relativistic mechanics from the same parameters and initial conditions for a slow-moving dissipative dynamical system will rapidly disagree completely if the trajectories are chaotic or transiently chaotic. There is no breakdown of agreement if the trajectories are non-chaotic, in contrast to the slow breakdown of agreement between non-chaotic Newtonian and relativistic trajectories for a slow-moving non-dissipative dynamical system studied previously. We argue that, once the two trajectory predictions are completely different for a slow-moving dissipative dynamical system, special relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly study its trajectory.