Let us consider the simplest case of a four-mirror Sagnac apparatus. Three of these mirrors are loop-forming mirrors (L in the figure). These exhibit no motion normal to the plane of the mirror, as Mr. Driscoll requires, as rw is an instantaneously tangential velocity vector at all times. The fourth, half-silvered, injection-retrieval mirror (I/R in the figure) will have its entire velocity vector normal to the face of the mirror at all times. If Mr. Driscoll’s statement is correct, then only this mirror will suffer any first-order Doppler effect. If we look at both paths of light, we see that each encounters this mirror coming and going, thus the effect of this mirror’s motion is identical to both paths, as far as Doppler is concerned. Ignoring the three loop-forming mirrors which, according to Mr. Driscoll’s statement, have no Doppler effect motion, and considering then only the relative velocity of the half-silvered mirror as a source and again as a detector, one path leaves this mirror as a receding source only to reach it as an approaching detector, with no net velocity between source and observer, while the other path leaves a forward moving source toward a receding detector, again with no net motion between source and observer. Thus there is nor first-order Doppler effect. In fact, the two figures illustrating this concept should be reminiscent to many of a single leg of the Michelson-Morley interferometer. And of course, Doppler played no role in the null-result of that experiment. If Mr. Driscoll perhaps meant to say that it is only the velocity component normal to the (alleged) wave front that is important, then the problem reduces to that analyzed in my previous letter, where there is no relative motion along this line, and thus, no first-order Doppler effect. One must also note that there is a Doppler effect due to motion tangential to the wave front, known as the transverse Doppler effect. In SRT this effect is attributed to time-dilation. In RCM it is due to the relative velocity between source and observer¹. Regardless of its nature, the effect has been verified experimentally, thus it is often convenient to separate motion into radial and transverse components for simplification of analysis.

[1] Renshaw, C. E., Galilean Electrodynamics, "The Radiation Continuum Model of Light and the Galilean Invariance of Maxwell’s Equations," Vol. 7, No. 1, January 1996.

Curt Renshaw

Questions? Comments?crenshaw@teleinc.com