Editing Four-velocity (section)

=== Definition of the four-velocity ===

The four-velocity is the tangent four-vector of a [[timelike curve|timelike]] [[world line]].
The four-velocity <math>\mathbf{U}</math> at any point of world line <math>\mathbf{X}(\tau)</math> is defined as:
<math display="block">\mathbf{U} = \frac{d\mathbf{X}}{d \tau}</math>
where <math>\mathbf{X}</math> is the [[four-position]] and <math>\tau</math> is the [[proper time]].<ref>{{cite book | last1 = McComb | first1 = W. D. | title=Dynamics and relativity | date=1999 | publisher=Oxford University Press | location = Oxford [etc.] | isbn=0-19-850112-9 | pages=230}}</ref>

The four-velocity defined here using the proper time of an object does not exist for world lines for massless objects such as photons travelling at the speed of light; nor is it defined for [[tachyon]]ic world lines, where the tangent vector is [[spacelike]].