The Velocity Addition Rule of Special Relativity and Sagnac Effect

Subject: The Velocity Addition Rule of Special Relativity and Sagnac Effect
Date: Wed, 30 Jan 2008 06:27:19 EST

This well known rule is given as example (14.10) page 535, of J. B. Marion and S. T. Thornton, “Classical Dynamics” (HB, NY 1988, 3rd ed.). It is based on the Lorentz transform and is:

v = (v1 + v2) / (1 + (v1v2 / c squared))

It is developed in M. W. Evans et alii, “The Enigmatic Photon”, volume 4, pp. 92 ff. (see the _www.aias.us_ (http://www.aias.us) Omnia Opera).

It is seen that if

v1 = v2 = c

then

v = c

and if v1 = v2
v = v1 + v2

which is the “intuitive” or non-relativistic rule. Intuition does not work with a beam of light travelling at c because we have v2 = c and:

v = (v1 + c) / (1 + v1 / c) = c

As Dr Horst Eckardt pointed out yesterday, one cannot just add v1 to c. In the ECE explanation of the Sagnac effect this is not done, intead, the angular frequency cap omega is added to omega1. Everyday experience in interferometry shows that frequencies can add (interfere constructively) or subtract (interfere destructively). So the ECE explanation of the Sagnac effect seems to be the simplest one, and thus preferred by Ockham’s Razor.