This web construction is about introducing unidirectional motion from a traveler perspective that works regardless of speed, space-time curvature, or mapframe-acceleration. It is powered by the 20th century discovery that time is a local variable, and that it is linked to a traveler's position through a space-time version of Pythagoras' theorem i.e. the local metric equation. The fact that time is local to the clock that's measuring it means that we can address the question of extended-simultaneity only as needed (with suitable caution) after the fact.
If we use this insight to describe motion with local traveler-centered (i.e. proper) variables, before the move to map-centered ones, good old three-vector velocities (proportional to momentum) and frame-invariant accelerations (albeit with frame-variant rates of momentum-change) become useful (especially for engineering problems) not only at high speeds but also in curved space-times (like that here on earth).
The focus here is not on fancy applications for these tools, but rather on introducing the concept of local time, and some of its applications, to introductory students in both high school and college physics courseswhen kinematics is first discussed. For the lion's share of students that are touched by physics courses, this might provide their physical intuition with a more solid conceptual-foundation from day one, even if the class moves immediately to a focus on applications of the Galilean-kinematic approximation.
This page on "metric-first kinematics" is only a stub at present. Look for more here soon.
To whet your whistle you might enjoy the summary below of a possible writeup, and the discussion of related student exercises below that. At the bottom you'll also find some more technical notes, for which some background in 4-vector analysis may come in handy. Extensive notes on use of this strategy with intro-physics classes are already available on the campus wiki for those with a campus ID.
Update: This working draft reflects downstream changes as we try to fashion a writeup for wide-accessibility e.g. in a journal like The Physics Teacher. Suggestions invited to that end.
Tip: How to insert objects like this "Table of contents" into your page.
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