Traveler-point dynamics: A 3-vector bridge to curved spacetimes
Dynamique des points voyageurs
Résumé
Locally-defined parameters chosen to be minimally frame-variant can be useful for describing motion in accelerated frames and in curved spacetimes. In particular the metric-equation's synchrony-free ``traveler-point parameters'', namely scalar proper-time and the 3-vectors: proper-velocity and proper-force, are useful in curved spacetime because extended arrays of synchronized clocks (e.g. for local measurement of the denominator in $\Delta x / \Delta t$) may be hard to find. Combined with a recognition of improper (geometric) forces, these same parameters can better prepare intro-physics students for a world where Newton's approach is a only useful approximation. This strategy also suggests an ``accelerated-traveler perspective" on high speed travels that are exact at any speed in flat spacetime, and approximate in curved settings e.g. for computing gravitational trajectories at high speed.
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