The author of the paper (the owner of the Mrelativity website) is a well known crackpot, you can ignore what he's saying.
The IS experiment is brilliantly simple:
-the ions emit light DIRECTLY towards the receiver with frequency [latex]f_s[/latex]
-the light arrives redshifted at the receiver:
[latex]f_s=\gamma f_r (1-\frac{v}{c} cos \alpha_r)[/latex]
-the ions also emit light AWAY from the receiver, towards a mirror located at the opposite end from the receiver in the cathode tube that emitted the ions in the first place
-the light is reflected by the mirror and arrives at the receiver blueshifted:
[latex]f_s=\gamma f_b (1-\frac{v}{c} cos \alpha_b)=\gamma f_b (1+\frac{v}{c} cos \alpha_r)[/latex]
because [latex]\alpha_b=\pi-\alpha_r[/latex] (the beams are anti-parallel)
The experimenters measure [latex]f_r, f_b[/latex]. From the measurements, they determine the transverse Doppler effect as the part of the shift that is direction independent, by simply taking the average of the two measured frequencies:
[latex]\frac{f_r+f_b}{2}=\frac{f_s}{\gamma} [/latex]
It is a brilliant experiment. The person suggesting it was........Einstein.
51 years later (!), there was a DIRECT test of transverse Doppler effect:
Hasselkamp et al., Z. Physik A289 (1989), pg 151.
