traveler point dynamics 2

Traveler-point dynamics employs a small set of variables distinct from one's reference frame coordinates, which help describe motion at any speed, in curved spacetimes, and in accelerated-frames. These variables are "minimally frame-variant" but not coordinate-free, so that all observers can agree on their values in physical units regardless of what "bookkeeper coordinate-system" they choose. One can also see them as "the quantities which Newtonian dynamics approximates", and as part of a "metric-first" [1] or "one-map two-clock" [2,3] approach to describing motion with 3-vectors from an engineering perspective in various spacetime settings.

In particular the metric-equation's synchrony-free [4] "traveler-point parameters" [5], namely proper-time, proper-velocity & proper-acceleration, are useful in curved spacetime because extended arrays of synchronized clocks (e.g. for local measurement of the denominator in Δx/Δt) may be hard to find. These same parameters can better prepare intro-physics students for their everyday world, as well as for the technological world e.g. of GPS systems where differential aging must be considered explicitly. The net frame-invariant proper-force [6], which is simply rest-mass times the proper-acceleration 3-vector [7], is not generally a rate of momentum-change, but is instead what is reported by accelerometers moving along with "the traveler" which e.g. are unable to see geometric forces like gravity and centrifugal.

Find a draft paper here [8] on possible use of one class-period e.g. for readers of The Physics Teacher. The objective is not to expand the introductory physics curriculum, for which there is little time in either high school or college, but simply to introduce Newton's 3-vector relationships as approximation to a set of more powerful 3-vector relationships, designed for use at any speed and (locally) in accelerated frames and gravitationally-curved spacetimes. Suggestions on how to make it better are invited.

Illustrations, problem examples, calculators, and simulators on this website, and on our more sprawling old google site, are in that sense not for mainstream content, but for students and educators interested in playing with the more extreme physics applications possible therewith.

References:

1. Edwin F. Taylor and John Archibald Wheeler (2000) Exploring Black Holes (original draft title" "Scouting Black Holes with Calculus") Addison-Wesley-Longman, NY; free 2017 2nd edition.
2. David G. Messerschmitt, “Relativistic timekeeping, motion, and gravity in distributed systems,” Proceedings of the IEEE, 105, 1511–1573 (2017) link.
3. P. Fraundorf (1996) "A one-map two-clock approach to teaching relativity in introductory physics" (arXiv:physics/9611011)
4. W. A. Shurcliff (1996) Special relativity: the central ideas (19 Appleton St, Cambridge MA 02138) archive tinyURL.
5. P. Fraundorf (2016/2017) "Traveler-point dynamics", hal-01503971 working draft on-line discussion.
6. P. Fraundorf (2016) "The proper-force 3-vector", HAL-01344268 current pdf.
7. P. Fraundorf and Matt Wentzel-Long (2019) "Parameterizing the proper-acceleration 3-vector", hal-02087094, working version.
8. Matt Wentzel-Long and P. Fraundorf (2019) "A class period on spacetime-smart 3-vectors with familiar approximates", laTeX draft with supplementary notes in an appendix (HAL-02196765), Word version in preparation for a physics education journal, introductory voicethread.