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

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.