4.1 Article

Relativistic velocity addition from the geometry of momentum space

期刊

EUROPEAN JOURNAL OF PHYSICS
卷 43, 期 4, 页码 -

出版社

IOP Publishing Ltd
DOI: 10.1088/1361-6404/ac41d7

关键词

special relativity; education in physics; geometrical methods

资金

  1. MCIN/AEI [PID2020-118613GB-I00]
  2. Conselleria de Educacion, Universidade e Formacion Profesional [ED431B 2018/57, ED431B 2021/22]
  3. Ministerio de Economia, Industria y Competitividad, Spain [FIS2017-83762-P]
  4. Xunta de Galicia

向作者/读者索取更多资源

This article presents the geometrization of the addition of velocities in special relativity using Minkowski diagrams in momentum space. It provides graphical solutions for collinear velocities and generalizes the concept to non-collinear velocities in higher dimensions. Interactive applets are also offered to enhance students' understanding of the subtleties of special relativity.
With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe three ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1 + 1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1 + 2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

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