A one-map two-clock approach to teaching relativity in introductory physics

Abstract

This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler using only distances measured with respect to a single ``map'' frame. When this is done, the relativistic equations for momentum, energy, constant acceleration, and force take on forms strikingly similar to their Newtonian counterparts. Thus high-school and college students not ready for Lorentz transforms may solve relativistic versions of any single-frame Newtonian problems they have mastered. We further show that multi-frame calculations (like the velocity-addition rule) acquire simplicity and/or utility not found using coordinate-velocity alone.