chapter  Chapter 6
16 Pages

Lorentz transformation, II

ByJames H. Luscombe

This chapter shows that Lorentz transformations can be uniquely decomposed into the product of a boost and a rotation. It considers the rotations and boosts separately. Rotations about spatial axes can be represented as spacetime transformations using 4 × 4 real matrices with the (0, 0) element equal to unity. Such operations are passive transformations involving the mapping of coordinate axes. The operator for finite-angle rotations about an arbitrary axis can be developed through repeated applications of infinitesimal rotations. Rotations through a finite angle about the fixed axis can be realized from a succession of infinitesimal rotations about the same axis. Elementary boosts act as rotations where one of the axes affected is the time axis. Spatial rotations about coordinate axes affect the other two axes. For either elementary boosts or rotations two axes are involved.