= Timelike separation
{title2=$s^2<0$}
Two distinct <spacetime events> have <timelike separation> when their displacement has negative <Minkowski interval> in <metric signature> $(-,+,+,+)$, equivalently $c|\Delta t|>|\Delta\mathbf x|$. A massive observer can connect them along a straight <timelike curve>. If the later <spacetime event> has $\Delta t>0$, every <Lorentz transformation> in the <orthochronous Lorentz group> keeps it later. The elapsed <proper time> on the straight inertial segment is $\sqrt{-s^2}/c$.
In the <light-second> units of the <Minkowski spacetime> example, $O$ to $A$ has $s^2=(-4^2+3^2)\,\mathrm{ls}^2=-7\,\mathrm{ls}^2$. Its straight moving clock therefore records $\sqrt7\,\mathrm s$, approximately $2.646\,\mathrm s$, while the coordinate time difference is $4\,\mathrm s$. Coordinate time and <proper time> answer different questions.
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