In
special relativity,
four-velocity is a
four-vector that replaces classical
velocity. The four-velocity of the four-vector a is defined as
- <math>U_a ={da\over d\tau_a}={da_0 \over d\tau_a}{da\over da_0}=\gamma_a {da_0\over d\tau_a}={1\over\sqrt{1-{a_1^2 +a_2^2 +a_3^2 \over a_0^2}}} {da \over da_0}.</math>
A four-velocity always has length 1 and points forwards in time.
See also: four-vector, four-acceleration, four-momentum, four-force.