Relativistic Analogue Hidden in Projectile Motion

Abstract

We present a four-vector analogue U-mu equivalent to (U-0, U) = (|V '|, V) that can be directly constructed from the velocity of a projectile. Here, V and V ' are the velocities of a projectile at heights h + H and h, respectively. In the non-relativistic regime, the mathematical structure of this four-vector analogue has an exact correspondence to the relativistic counterpart four-velocity u(mu) = gamma(1, beta)c of a massive particle. Based on this observation, we illustrate the design of an introductory laboratory experiment to investigate the Lorentz invariance and its covariant nature by measuring the velocity of a projectile. The experiment may help students to acquire a concrete perspective of Lorentz covariance through their own measurements and analyses of a free-fall motion.