Einstein was Wrong Newtonian Dynamics Can Disagree Completely with Relativistic Dynamics at.pdfVIP

EINSTEIN WAS WRONG: NEWTONIAN DYNAMICS CAN DISAGREE COMPLETELY WITH RELATIVISTIC DYNAMICS AT LOW SPEED Boon Leong Lan School of Engineering and Science, Monash University, 2 Jalan Kolej, 46150 Petaling Jaya, Selangor, Malaysia ABSTRACT 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. According to Einstein (1): ‘Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter v are not very small as compared with the velocity of light. … for other motions [v very small compared with the velocity of light] the variations from the laws of classical mechanics are too small to make themselves evident in practice.’ In other words, according to Einstein (1,2), and also others (3-6) later, if the speed of a particle v is much less than the speed of light c, then the dynamical prediction of special relativistic