dorsal/arxiv
View SchemaSome minimally-variant map-based rules of motion at any speed
| Authors | P. Fraundorf |
|---|---|
| Categories | |
| ArXiv ID | physics/9704018 |
| URL | https://arxiv.org/abs/physics/9704018 |
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.
{
"annotation_id": "c56cfa7e-1e11-4479-811c-08dd02cd469d",
"date_created": "2026-03-02T18:01:20.647000Z",
"date_modified": "2026-03-02T18:01:20.647000Z",
"file_hash": "eb2f766d5e9c03ea2f70661e8c2a6cfaf839a5f0d08f872ba6d4d325bc4a2971",
"private": false,
"record": {
"abstract": "We take J. S. Bell\u0027s commendation of ``frame-dependent\u0027\u0027 perspectives to the\nlimit here, and consider motion on a ``map\u0027\u0027 of landmarks and clocks fixed with\nrespect to a single arbitrary inertial-reference frame. The metric equation\nconnects a traveler-time with map-times, yielding simple integrals of constant\nproper-acceleration over space (energy), traveler-time (felt impulse), map-time\n(momentum), and time on the clocks of a chase-plane determined to see Galileo\u0027s\noriginal equations apply at high speed. Rules follow for applying frame-variant\nand proper forces in context of one frame. Their usefulness in curved\nspacetimes via the equivalence principle is maximized by using synchrony-free\nand/or frame-invariant forms for length, time, velocity, and acceleration. In\ncontext of any single system of locally inertial frames, the metric equation\nthus lets us express electric and magnetic effects with a single\nframe-invariant but velocity-dependent force, and to contrast such forces with\ngravity as well.",
"arxiv_id": "physics/9704018",
"authors": [
"P. Fraundorf"
],
"categories": [
"physics.ed-ph",
"gr-qc",
"physics.class-ph"
],
"title": "Some minimally-variant map-based rules of motion at any speed",
"url": "https://arxiv.org/abs/physics/9704018"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a55c3ea0-2efa-4809-afea-d5fce31353a6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}