@RefurioAnachro
> <em> [...] acceleration doesn't even appear in the calculation [of arc length]. </em>
Looking at textbook exercises, perhaps.
But there's dependence cmp.
https://mathstodon.xyz/@MisterRelativity/109622725097842951
where Lorentzian distance
\[\ell[ \, p, q \, ] := \underset{(\gamma \in \Gamma_p^q)}{\text{Sup}}[ \, \{ \tau_{\gamma} \} \, ] \]
requires comparison of #durations \(\tau_{\gamma}\)
In #SR you'd need to know + fix who remains a member of an #InertialSystem ; but finding out is a hard problem in #GR