In [1] Bob Driscoll proposes that, at the half-silvered mirror, there is a Doppler effect due to the reflected beam, but not due to the transmitted beam. This proposal is false on several grounds. The source, half-silvered mirror and observing screen (or eyepiece) are all co-located on the Sagnac interferometer. So, in a coordinate frame co-rotating with the Sagnac interferometer, there is no relative motion among these components, and no Doppler effect at the entrance or exit points of the light beams.
However, even if such were not the case, Driscoll’s argument, that transmission and reflection are fundamentally different, would still be false. Transmission differs from reflection only in the path subsequently taken by the light: both processes involve extinction of the original photons and generation of new ones [2]. The wavelength of the photons "seen" (extinguished) by the half-silvered mirror is shifted for transmission by the same formula as for reflection. Given that the transmitted and reflected paths differ only in direction, the net effects over the two paths cannot differ in magnitude, contrary to what Mr. Driscoll suggests.
One also needs to question the following: If the entire Sagnac effect were really due to Doppler shifting at the entrance and exit of the apparatus, then why does the path ultimately taken by the light play any role in the calculations? At best, one would expect to see only rw dependencies.
Paul Wesley makes some very sound arguments, except that I question his analysis of the aether case [3]. The Sagnac experiment measures a change in fringe pattern due to a change in rw. Thus we could make the original fringe pattern measurement with the turntable operating at some arbitrary, even high, rw value. We then change the velocity to some new value and note that the shift in fringe pattern is given by the usual equation, with the exception that w is replaced by Dw. In this case, if we defined the velocity of light to be c with respect to the original rotating frame of the interferometer, we would get results consistent with Sagnac’s aether interpretation, except that the aether would now be defined as residing in the original rotating frame of the apparatus. The initial value of rw can of course be any value, so the frame of the aether could also assume any value, rotating or otherwise. This multiplicity of valid reference frames for the "fixed luminiferous aether" makes the very concept untena ble. Thus we are left either with the result that the optical path length change is the most likely interpretation, or that, if there is an aether, the Sagnac experiment is not a test of its presence or its properties with respect to light propagation.
[1] R.B. Driscoll, "Sagnac’s Experiment Misdescribed," Galilean Electrodynamics ….
[2] Fox, J.G., Am J Phys, "Evidence Against Emission Theories," 33, 1-17, (1965)
[3] J.P. Wesley, "The Sagnac Effect: Renshaw vs. Driscoll," Galilean Electrodynamics 8, 86 (1997)
Curt Renshaw
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