A 4-D transformation satisfied by all Four-Vectors ,

(1) |

(2) |

(3) |

(4) | |||

(5) |

Written explicitly, the transformation between and coordinate is

(6) | |||

(7) | |||

(8) | |||

(9) |

The Determinant of the upper left Matrix in (3) is

(10) |

A Lorentz transformation along the -axis can also be written

(11) |

(12) |

(13) | |||

(14) | |||

(15) |

**References**

Fraundorf, P. ``Accel-1D: Frame-Dependent Relativity at UM-StL.'' http://www.umsl.edu/~fraundor/a1toc.html.

Griffiths, D. J. *Introduction to Electrodynamics.* Englewood Cliffs, NJ: Prentice-Hall, pp. 412-414, 1981.

Morse, P. M. and Feshbach, H. ``The Lorentz Transformation, Four-Vectors, Spinors.'' §1.7 in
*Methods of Theoretical Physics, Part I.* New York: McGraw-Hill, pp. 93-107, 1953.

© 1996-9

1999-05-25