Note 1 to entry: The proper distance $D_{\text{AB}}$ is the largest of the Euclidean distances ${d^{\prime }}_{\text{AB}}$ in all other frames S′ where ${t^{\prime }}_{\text{A}}\ne {t^{\prime }}_{\text{B}}$. For inertial frame S′, $D_{\text{AB}}={\gamma }^{\prime }{D^{\prime }}_{\text{AB}}$ where ${\gamma }^{\prime }$ is the Lorentz factor corresponding to the speed between frames S and S′.

Note 2 to entry: For events A and B separated by an infinitesimally small squared space-time interval, the proper distance $D_{\text{AB}}$ is the largest of the Euclidean distances ${d^{\prime }}_{\text{AB}}$ in all frames S′ and $D_{\text{AB}}={\gamma }^{\prime }{d^{\prime }}_{\text{AB}}$.

Note 3 to entry: The proper distance is a Lorentz scalar.

Note 4 to entry: The coherent SI unit of proper distance is metre, m.