The pedagogical value of the four-dimensional picture I: Relativistic mechanics of point particles

We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of particles and fields are quite simple geometric objects as op...

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Bibliographic Details
Published inarXiv.org
Main Author Kosyakov, B P
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.05.2022
Subjects
Mechanics (physics)
Minkowski space
Physics - Classical Physics
Relativistic effects
Relativistic particles
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Summary:We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of particles and fields are quite simple geometric objects as opposed to their associated three-dimensional trajectories, and (ii) Newton's second law requires neither modification nor generalization, it should be only smoothly embedded in the four-dimensional geometry of Minkowski spacetime to yield the dynamical law for relativistic particles.
ISSN:2331-8422
DOI:10.48550/arxiv.2205.01186