We
derive the addition of velocities in special relativity from the Minkowski’s
space-time diagram. We only need to draw some world lines on the diagram,
measure the lengths and divide the two lengths for obtaining the velocity. We
also give the theoretical background for this method. This method is so simple
that it is worth for undergraduate students to acquire the addition of
velocities in special relativity.
References
[1]
Mermin, N.D. (1997) An Introduction to Space-Time. American Journal of Physics, 65, 476-486. https://doi.org/10.1119/1.18574
[2]
Dray, T. (2017) The Geometry of Relativity. American Journal of Physics, 85, 683-691. https://doi.org/10.1119/1.4997027
[3]
Saletan, E.J. (1997) Minkowski Diagram in Momentum Space. American Journal of Physics, 65, 799-800. https://doi.org/10.1119/1.18651
[4]
Bokor, N. (2011) Analysing Collisions Using Minkowski Diagram in Momentum Space. European Journal of Physics, 32, 773-782. https://doi.org/10.1088/0143-0807/32/3/013
[5]
Ogura, A. (2018) Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity. World Journal of Mechanics, 8, 353-361. https://doi.org/10.4236/wjm.2018.89026
[6]
Ogura, A. (2019) Elastic Collisions in Minkowski Momentum Space with Lorents Transformations. World Journal of Mechanics, 9, 267-284. https://doi.org/10.4236/wjm.2019.912018
[7]
Paredes, A., Prado, X. and Mira, J. (2022) Relativistic Velocity Addition from the Geometry of Momentum Space. European Journal of Physics, 43, 045601. https://doi.org/10.1088/1361-6404/ac41d7
[8]
Synge, J.L. (1956) Relativity: The Special Theory. North-Holland Pub. Co., Amsterdam, 126-130.
[9]
Brehme, R.W. (1969) Geometrization of the Relativistic Velocity Addition Formula. American Journal of Physics, 37, 360-363. https://doi.org/10.1119/1.1975576
[10]
Kocik, J. (2012) Geometric Diagram for Relativistic Addition of Velocities. American Journal of Physics, 80, 737-739. https://doi.org/10.1119/1.4730931
[11]
Machotka, R. (2018) Euclidian Model of Space and Time. Journal of Modern Physics, 9, 1215-1249. https://doi.org/10.4236/jmp.2018.96073
[12]
Takeuchi, T. (2010) An Illustrated Guide to Relativity. Cambridge University Press, Cambridge, 110-111. https://doi.org/10.1017/CBO9780511779121
