Proper velocity
In relativity, proper velocity (also known as celerity) 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. The two types of velocity, ordinary and proper, are very nearly equal at low speeds.