Comparison of classical dynamical predictions for low-speed, weak-gravity, and low-speed weak-gravity chaotic systems.

There are three fundamental classical theories which can be used to study the motion of dynamical systems: Newtonian mechanics (NM), special-relativistic mechanics (SRM) and general-relativistic mechanics (GRM). It is conventionally believed that (i) the predictions of SRM are well approximated by those of NM in the low-speed limit, (ii) the predictions of GRM are well approximated by those of SRM in the weak-gravity limit, and (iii) the predictions of GRM are well approximated by those of NM in the low-speed weak-gravity limit. In my research project, numerically-accurate predictions of the theories were compared in the three limits for chaotic dynamical systems to check the validity of the conventional beliefs. The results of this study have overturned the conventional beliefs: for each limit, I showed that the two predictions can rapidly disagree completely. This new conceptual understanding of the relationships between the predictions of the theories for low-speed, weak-gravity, and low-speed weak-gravity chaotic dynamical systems implies that physicists and engineers must replace the theories they have conventionally been using to study these systems with the more general theories. In particular, NM must be replaced by SRM for low-speed systems, SRM must be replaced by GRM for weak-gravity systems, and NM must be replaced by GRM for low-speed weak-gravity systems. These paradigm shifts could potentially lead to new understanding and discoveries in these systems.