Traveler-point dynamics: A 3-vector bridge to curved spacetimes

Dynamique des points voyageurs

Phil Fraundorf (1)

1 University of Missouri [St. Louis]

Locally-defined ``flat-patch" parameters, chosen to be minimally frame-variant, can be useful for describing the perspective of a {\em single observer} in accelerated frames and in curved spacetimes. In particular the metric-equation's scalar proper-time, and the 3-vectors proper-velocity and proper-acceleration, are useful because they don't rely on extended arrays of synchronized clocks, which may be hard to find. This use of an observer's ``proper reference frame" is where diverse metric definitions of extended-simultaneity converge to agree on a set of locally-approximate ``geometric" (i.e. connection-coefficient) forces, which in turn further prepare intro-physics students for ``flat-patch" engineering in curved spacetimes. Newton's approximation to gravity is the oldest example of this. The strategy also opens the door to engineering nomograms that allow one to track {\em arbitrary} local and extended radar time trajectories from the perspective of accelerated and curved-spacetime travelers, as well as real-time single-traveler trajectories that are exact at any speed in flat spacetime, and approximate around gravitating masses.

Mots clés: proper time; proper velocity; proper acceleration; proper force

Domaines: Enseignement de la physique [physics.ed-ph]

Phil Fraundorf. Traveler-point dynamics: A 3-vector bridge to curved spacetimes. 2023. ⟨hal-01503971v5⟩