Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams

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Scientific Paper
Title Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams
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Author(s) Calin Galeriu
Keywords classical electrodynamics, Minkowski space
Published 2003
Journal Apeiron
Volume 10
Number 1
No. of pages 14
Pages 1-14

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Abstract

This article presents intuitive, geometrical derivations of the relativistic addition of velocities, and of the elec-tromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional Minkowski diagrams. We calculate the relativistic addition of velocities by projecting the world-line of the particle on the spatio-temporal planes of the reference frames considered. We calculate the real component of the electromagnetic 4-force, in the proper reference frame of the source particle, from the Coulomb force generated by a charged particle at rest. We then obtain the imaginary component of the 4-force, in the same reference frame, from the requirement that the 4-force be orthogonal to the 4-velocity. The 4-force is then projected on a real 3 dimensional space to give the Lorentz force.