The pedagogical value of the four-dimensional picture I: Relativistic mechanics of point particles

Abstract

We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of particles and fields are quite simple geometric objects as opposed to their associated three-dimensional trajectories, and (ii) Newton's second law requires neither modification nor generalization, it should be only smoothly embedded in the four-dimensional geometry of Minkowski spacetime to yield the dynamical law for relativistic particles.