= Proper time
{title2=$\tau$}
{wiki}
Proper time is the time measured by a clock following a timelike worldline. With metric signature $(-,+,+,+)$ and units $c=1$,
$$
d\tau^2=-ds^2
$$
along that worldline.
Restoring the <speed of light>, the same <metric signature> gives $d\tau=\sqrt{-ds^2}/c=dt\sqrt{1-|\mathbf v|^2/c^2}$ for a future-directed <timelike curve>. Integrating along a clock's <world line> gives its elapsed <proper time>, even when its <velocity> varies. For uniform motion this becomes the <time dilation> formula; it is not generally the square root of the interval between endpoints of a curved <world line>.
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