 Minkowski interval

The squared interval between two events in Minkowski spacetime is the quadratic form of their coordinate difference under the Minkowski metric. In signature $(-,+,+,+)$ it is $-c^2\Delta t^2+|\Delta \mathbf{x}{|}^2$. Lorentz transformations preserve this quadratic form; timelike, spacelike and null separation correspond to negative, positive and zero values.

The opposite metric signature $(+,-,-,-)$ reverses the sign of the Minkowski interval, giving $c^2\Delta t^2-|\Delta \mathbf{x}{|}^2$; the physical classification and proper time stay the same. State the convention before using a sign to identify a separation. With the mostly-plus convention here, a straight clock segment has $s^2=-c^2\Delta {\tau }^2$, while a light signal has $s^2=0$. ^[ref].