The predicted doppler shift for classical theory is calculated by relativists using... W1=W(1+-v/c). Where W1 is observed doppler shifted wavelength and W is restframe wavelength.
So if v were 0.5c and W was 100 nm, then approaching blueshifted light would be 50 nm and receding would be 150 nm. Which is what relativists call a null result for classical theory ( ie, wavelength change is the same amount for both red and blueshifted in classical). Hence the well used argument that classical theory cannot correctly model the observed offset displacement in the spectra in the Ives Stillwell experiment.
This is incorrect. If v is+- 0.5 c then the total observed speed of the blueshifted light under classical theory is 1.5 c and for redshifted light it is 0.5 c.
Now if if one looks at the the redshifted lightspeed first: It is 1/2 the speed of the restframe light. If the restframe wavelength is 100 nm at c then at 1/2 c it will appear to be the same as 200 nm light at c ( thats the appearance of double the wavelength for half the frequency) And for the blueshifted light; 100 nm at 1.5c will appear to be the same as 66.66 nm of light at c in the spectrograph. In other words classical theory actually predicts that a restframe wavelength of 100 nm will have its observed wavelength stretched by 100 nm when receding at 0.5 c but ONLY compressed by approximately 33.33 nm when approaching.
On the linear scale this would give an offset, not a null result. And this is observed in Ives Stillwell.
(It is important to remember that the actual wavelength under the classical model doesnt change. But the frequency does, which makes it appear as if the wavelength has changed.)
