lew@ihlpa.UUCP (Lew Mammel, Jr.) (03/14/85)
Here's another derivation using transformations of event coordinates. We start with the positions of two wavefronts in the "stationary" frame at time t=0: Event 1: ( x, ct ) = ( x', ct' ) = ( 0, 0 ) Event 2: ( x, ct ) = ( lambda, 0 ) ( x', ct' ) = gamma * ( lambda, -beta * lambda ) In the moving frame, we see that the leading wavefront was already at position (gamma * lambda) at time (-gamma * beta * lambda/c). Then at time t'=0 it is at: Event 3: ( x', ct' ) = ( gamma * ( 1 + beta ) * lambda, 0 ) But lo and behold: gamma * ( 1 + beta ) = 1/( gamma * ( 1 - beta ) ) in agreement with the previous result. Lew Mammel, Jr. ihnp4!ihlpa!lew