Relativistic Particle Mechanics

Abstract

Newton’s mechanics is not Lorentz-invariant. According to the program of special relativity, therefore, it was necessary to construct a new mechanics-even before any serious empirical deficiencies of the old mechanics had become apparent. The new mechanics is known as “relativistic” mechanics. This is not really a good name,¹ since, as we have seen, Newton’s mechanics, too, is relativistic, but under the “wrong” (Galilean) transformation group. Newton’s theory has excellently served astronomy (e.g., in foretelling eclipses and orbital motions in general), it has been used as the basic theory in the incredibly delicate operations of sending probes to the Moon and some of the planets, and it has proved itself reliable in countless terrestrial applications. Thus it cannot be entirely wrong. Before the twentieth century, in fact, only a single case of irreducible failure was known, namely the excessive advance of the perihelion of the planet Mercury, by about 43 seconds (!) of arc per century. Since the advent of modern particle accelerators, however, vast discrepancies with Newton’s laws have been uncovered, whereas the new mechanics consistently gave correct descriptions. (Of course, Newton’s mechanics has undergone two “corrections,” one due to relativity and one due to quantum theory. We are here concerned exclusively with the former.)