Note 1 to entry: The proper length ${\ell }_{\text{AB}}$ is the largest of the local lengths, i.e., distances ${d^{\prime }}_{\mathrm{AB}}$ measured synchronously (${t^{\prime }}_{\text{A}}={t^{\prime }}_{\text{B}}$) between the begin A and the end B of the rod in any other frame S′. For inertial frame S′, ${\ell }_{\mathrm{AB}}\text{=}\text{γ}{d^{\prime }}_{\mathrm{AB}}$.

Note 2 to entry: The proper length is a Lorentz scalar.

Note 3 to entry: The coherent SI unit of proper length is metre, m.