The energy and momentum viewed from a frame moving with velocity is give by

(3.16) |

where , and and are the components of perpendicular and parallel to , respectively.

Since and are related, we can define a single ``rapidity'' parameter, , as

Using the properties of the hyperbolic functions we have

We can thus write

(3.19) |

Other 4-vectors, such as the space-time coordinates of events transform in the same way.

We see that the Lorentz transformation may be regarded as a rotation through an imaginary angle in the - plane.

2004-03-18