Minkowski interval
= Minkowski interval
{c}
{title2=$s^2=\eta_{\mu\nu}\Delta x^\mu\Delta x^\nu$}
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 $s^2=0$. https://farside.ph.utexas.edu/teaching/355/Surveyhtml/node136.html[Richard Fitzpatrick, University of Texas: Spacetime Interval, using the opposite sign convention]{ref}.