Proper length of a string
= Proper length of a string
{title2=$L(t)=\int\sqrt{h_{\sigma\sigma}}\,d\sigma$}
On a spacelike constant-target-time slice, integrate the induced spatial line element to obtain the geometric string length. It depends on the embedding and is distinct from the fundamental <string length> $\ell_s=\sqrt{\alpha'}$. For transverse local motion, energy additionally includes the local Lorentz factor; the geometric length alone does not determine the total energy.