Relativistic Particle Mechanics

Abstract

Newton’s mechanics is not Lorentz-invariant. According to the program of special relativity, therefore, a new mechanics had to be constructed, which is generally known as “relativistic” mechanics. This is not really a good name, since, as we have seen, Newton’s mechanics, too, is relativistic, but under the “wrong” (Galilean) transformation group. Still, Newton’s theory has excellently served astronomy (e.g., in foretelling eclipses and planetary motions in general), it has been used as the basic theory in the incredibly delicate operations of sending probes to Moon and Venus, 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.