For example, from QM, the energy lost by a light beam of intensity I, wavelength l, over a time T, when incident on an electron in free space is given by:
l – lambdao ~ 2v lambdao / mc2 sin2 theta/2
Where v is the velocity of the electron.
The resultant Doppler shift is:
l – lambdao ~ 2W lambdao / mc2 sin2 theta/2
where W is the total energy removed from the incident light beam.
This can also be calculated by the Einstein-DeBroglie relations, E = hv and p = hv/c. To do this calculation, we only need the Compton shift for a light beam of incident frequency f, scattered from an electron, moving with some momentum p. If we suppose that the electron momentum is in the direction of the incident light beam, for simplicities sake, the change of the wavelength is then equal to:
l – lambdao = 2(h + lambdao p) / sqrt m2 c2 + p2 – p
We can also obtain the correct QM frequency shift by setting W = hv, where W is the total energy, v is the frequency, and h is of course the Planck’s constant.
If the redshift relation as expressed by Hubble has any variations or exceptions, the entire Hubble expression must be re-evaluated. I have previously mentioned, that the gravitational redshifting mechanism as derived by MTW in their book “Gravitation”, shows an additional exception to the Hubble expression for redshifting.
I suggest, as I have in the past, that the Hubble expression is an egregious error, as there are a great many effects which can cause redshifting.
If the Hubble expression is wrong, clearly the concept of an “expanding universe”, as implied by the Hubble expression, must also be an error.