English

Some minimally-variant map-based rules of motion at any speed

Physics Education 2008-02-03 v5 General Relativity and Quantum Cosmology Classical Physics

Abstract

We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the limit here, and consider motion on a ``map'' of landmarks and clocks fixed with respect to a single arbitrary inertial-reference frame. The metric equation connects a traveler-time with map-times, yielding simple integrals of constant proper-acceleration over space (energy), traveler-time (felt impulse), map-time (momentum), and time on the clocks of a chase-plane determined to see Galileo's original equations apply at high speed. Rules follow for applying frame-variant and proper forces in context of one frame. Their usefulness in curved spacetimes via the equivalence principle is maximized by using synchrony-free and/or frame-invariant forms for length, time, velocity, and acceleration. In context of any single system of locally inertial frames, the metric equation thus lets us express electric and magnetic effects with a single frame-invariant but velocity-dependent force, and to contrast such forces with gravity as well.

Keywords

Cite

@article{arxiv.physics/9704018,
  title  = {Some minimally-variant map-based rules of motion at any speed},
  author = {P. Fraundorf},
  journal= {arXiv preprint arXiv:physics/9704018},
  year   = {2008}
}

Comments

9 pages (1 table, 1 fig, 17 refs/context updated) RevTeX, cf. http://www.umsl.edu/~fraundor/a1toc.html

R2 v1 2026-07-22T19:16:42.692Z