The Four-velocity reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

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

A four-velocity always has norm 1 and points forwards in time.

Equivalent formulation of the four-velocity vector

In a set of unit which c isn't equal to 1 but to its MKS value, the formulating of the four-velocity alters a bit, mainly on notations.

The Lorentz factor is defined as

With these notatations, we can define velocity as the derivative of space-time vector with respect to the proper time of the moving body:

One should note that its norm is equal to c.

See also: four-vector, four-acceleration, four-momentum, four-force.

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