Frank Wappler<p><span class="h-card"><a href="https://mathstodon.xyz/@RefurioAnachro" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>RefurioAnachro</span></a></span><br> &gt; &lt;em&gt; [...] acceleration doesn't even appear in the calculation [of arc length]. &lt;/em&gt;</p><p>Looking at textbook exercises, perhaps.<br>But there's dependence cmp.</p><p><a href="https://mathstodon.xyz/@MisterRelativity/109622725097842951" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">mathstodon.xyz/@MisterRelativi</span><span class="invisible">ty/109622725097842951</span></a></p><p>where Lorentzian distance<br>\[\ell[ \, p, q \, ] := \underset{(\gamma \in \Gamma_p^q)}{\text{Sup}}[ \, \{ \tau_{\gamma} \} \, ] \]<br>requires comparison of <a href="https://mathstodon.xyz/tags/durations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>durations</span></a> \(\tau_{\gamma}\)</p><p>In <a href="https://mathstodon.xyz/tags/SR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SR</span></a> you'd need to know + fix who remains a member of an <a href="https://mathstodon.xyz/tags/InertialSystem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>InertialSystem</span></a> ; but finding out is a hard problem in <a href="https://mathstodon.xyz/tags/GR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GR</span></a></p>