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Four-velocity

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.



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