We present a four-vector analogue Uμ ≡ (U0, 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 uμ = γ(1, β)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.
Bibliographical noteFunding Information:
As members of the Korea Pragmatist Organization for Physics Education (KPOP&), the authors thank the remaining members of KPOP& for useful discussions. This work is supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) under Contract Nos. NRF-2020R1A2C3009918 (U-R.K., D.W.J., S.C., and J.L.), NRF-2017R1E1A1A01074699 (D.W.J. and J.L.), NRF-2018R1D1A1B07047812 (D. W.J.), NRF-2020R1A2C3009918 (J.H.L.), and NRF-2019R1A6A3A01096460 (U-R.K.). This work is supported in part by the National Research Foundation of Korea (NRF) under the BK21+ program at Korea University, Initiative for Creative and Independent Scientists.
© 2020, The Korean Physical Society.
- Free falling
- Lorentz transformation
- Special relativity
ASJC Scopus subject areas
- Physics and Astronomy(all)