The location of an event in spacetime is represented by the Herrmitian quaternion.

The Lorentz transformation is the orthogonal transformation :

Note that the Hermitian quaternion Q_e remains Hermitian.

Example of Lorentz transform. Observer A locates an event at time tA at the origin of a reference frame at rest. These event locations are described by the Hermitian Quaternion.

An observer B is traveling at velocity v with relative to frame A these events occur at the space time location relative to B.

We can now calculate with formula (16) the unimodular quaternion QL(v) that transforms Qa to Qb. that is, we seek a Lorentz transform that makes things traveling at velocity v appear at rest.

This result was first deduced by Silberstein.

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_{Rev 5/7/0 Copyright ©2000 George Raetz <bestwork.1@pcisys.net>}