Properties of the Lorentz Coordinate Transformation

Abstract

The addition theorem of velocities is presented both for the collinear and for the general case of two arbitrary velocities; Fresnel drag coefficient of light in moving fluid is shown to be direct consequence of velocity addition theorem. Using addition theorem, speed of light is shown to be maximum observable body speed. The aberration of the line of sight of a focused light-ray emitted by a star for arbitrary relative velocity is obtained. We look again at the addition theorem of velocities from a more general perspective. The invariance of proper time under Lorentz coordinate transformations is demonstrated, using two different methods. This sets the stage for introduction of rapidity. The merits of rapidity are demonstrated by showing the additivity property of rapidity for collinear motion, akin to nonrelativistic velocity addition.