Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams: Difference between revisions
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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. | 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. | ||
[[Category:Scientific Paper]] | [[Category:Scientific Paper|addition velocities electromagnetic interaction geometrical derivations using d minkowski diagrams]] | ||
[[Category:Relativity]] | [[Category:Relativity|addition velocities electromagnetic interaction geometrical derivations using d minkowski diagrams]] | ||
Latest revision as of 22:15, 1 January 2017
| Scientific Paper | |
|---|---|
| Title | Addition of Velocities and Electromagnetic Interaction: Geometrical Derivations Using 3D Minkowski Diagrams |
| Read in full | Link to paper |
| Author(s) | Calin Galeriu |
| Keywords | classical electrodynamics, Minkowski space |
| Published | 2003 |
| Journal | Apeiron |
| Volume | 10 |
| Number | 1 |
| No. of pages | 14 |
| Pages | 1-14 |
Read the full paper here
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.