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From: lew@ihlpa.UUCP (Lew Mammel, Jr.)
Newsgroups: net.physics
Subject: Yet Another Redshift Derivation
Message-ID: <152@ihlpa.UUCP>
Date: Thu, 14-Mar-85 14:13:10 EST
Article-I.D.: ihlpa.152
Posted: Thu Mar 14 14:13:10 1985
Date-Received: Fri, 15-Mar-85 04:20:05 EST
Distribution: net
Organization: AT&T Bell Laboratories
Lines: 23

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