Relativistic Analogue Hidden in Projectile Motion

Jae Hoon Lim, Dong Won Jung, U. Rae Kim, Sungwoong Cho, Jungil Lee

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)624-629
Number of pages6
JournalJournal of the Korean Physical Society
Issue number8
Publication statusPublished - 2020 Oct 1

Bibliographical note

Funding 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.

Publisher Copyright:
© 2020, The Korean Physical Society.


  • Four-velocity
  • Free falling
  • Lorentz transformation
  • Special relativity

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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