Benefits of clock-specific assertions about elapsed time.
You intentionally avoid reinforcing “sloppy time-think”, thus taking this special opportunity to teach “space-time smart, from the start”.
The introductory physics equations take on clear (well-defined, unambiguous) meaning in space-time.
This approach is extensible, since traveling clock times, & proper accelerations, are then quantified naturally at any speed via Minkowski’s space-time version of Pythagoras’ theorem, i.e. the metric equation (c dtau)2 = (c dt)2 - ds2. [cf. an accelerated twin plot]
A part-per-billion error in this flat-space metric equation in turn then gives gravity from curved space-time on earth! Edwin Taylor’s workshop on Scouting Black Holes with Calculus explores more extreme cases of this same curvature.
