@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

Frank Wappler (@[email protected])

Finally, a generalization of equality (5/7) by Lorentzian distance: \(\newcommand{\ef}{\varepsilon_{(A\, \Phi)}}\) \(\newcommand{\es}{\varepsilon_{(A\, \Psi)}}\) \(\newcommand{\ep}{\varepsilon_{(A\, P)}}\) \(a_A:=c\,\text{lim}\left[\sqrt{\frac{\begin{vmatrix}0&1&1&1\\1&0&\ell^2[\ef,\ep]&\ell^2[\ef,\es]\\1&\ell^2[\ef,\ep]&0&\ell^2[\ep,\es]\\1&\ell^2[\ef,\es]&\ell^2[\ep,\es]&0\end{vmatrix}}{\ell^2[\ef,\ep]\,\ell^2[\ef,\es]\,\ell^2[\ep,\es]}}\right]\) (7/7) #Relativity #TeachRelativity #SpaceTime

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