In reviewing comments and my posting, I realized i misrepresented my vision about gravitation redshift because I ignored my ideas about the contribution of the observer as mentioned at the end. The comments, especially by Grav alerted me to the errors. I am sorry. The proper perspective is as follows.

Gravitational frequency shift is complicated. The red or blue shift of light is determined by the observer. The frequency is a function of both the separation of the photons (wavelength) and the speed at which the arriving beam is traveling. Light sent down to earth from a nearby source is blue shifted to the observer. Gravitation is causing two things. It is speeding up the beam’s velocity and it is increasing the physical separation between the photons by pulling harder on the first than on the second. The speed increase applied to the beam is a greater factor than is the wavelength increase, so the photons arrive faster in seemingly shorter waves than when they started. The wavelength passage time – frequency - is shorter even though its length is longer.

Next consider two photons departing a source. The beam containing the two photons is continually slowed by the source gravitation. Thus the light is redshifted to an orbiting observer in logically opposite explanation of the blue shift discussed above. Extending the logic no further we have the localized redshift as applied in various theories. Beyond that, I first thought there would be further frequency shift by considering the ongoing gravitation, however small. But the issue is more complicated than that and requires considering the speed and wave length coincidentally with the gravitation of the source and of the recipient. In general the recipient can be considered to be similar to the source whether we and our sun receive light from another star, or we and our galaxy receive light from another galaxy.

Whatever the original separation of the two photons, the source gravitation is always closer to the second photon and slows it more at every time interval that it does to the first photon. However the first photon was gravitationally slowed first before the other existed so it started slower (Grav). Until some point in time the second photon will gain on the first. I don’t think we know when that point occurs. Since the beam velocity reduction exceeds the length change we may never know.

To bypass these issues consider the entire transmission. The frequency shift caused by slowing the beam near the source is exactly offset by accelerating the beam as it approaches the receiver. The second half of the path is a mirror image of the first half in regards to velocity. However, the physical separation is not mirrored. Throughout the transmission the first photon is attracted/pulled more by the receiver than is the second photon. Likewise the second photon is more pulled back by the source than is the first photon. The redshift over the entire transmission ignores velocity changes. Instead it is the wavelength difference of the pulls by each mass at every time interval. The result is most likely consistent throughout the transmission and thus is a linear summation.

A special perspective about redshift may apply to Quasars. The treatment above was explained as transmissions between similar bodies. We, as observers, do not have a nearby Quasar to serve with us as destination. Therefore Quasar redshift is mostly determined at the source. There is no offsetting acceleration of the beam. The result may be a continuous slowing of the beam throughout and a redshift due entirely to the slowing of transmission speed.