In relativity, proper velocity w of an object relative to an observer is the ratio between observer-measured displacement vector x {\displaystyle {\textbf {x}}} and proper time τ elapsed on the clocks of the traveling object: w = d x d τ {\displaystyle {\textbf {w}}={\frac {d{\textbf {x}}}{d\tau }}} It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer.
