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prime axiom

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point O: origin point of emitted photo, in Galaxy GlxO

point R: receiving point of photon, in Galaxy GlxR

GlxO, O ---------->----------------R, GlxR

Suppose:

Observer O (ObserO) at GlxO: is moving away from point O at speed RS, relative to GlxO

Observer R (ObserR) at GlxR: is moving away from point O at speed RS, relative to GlxO

So, we have that ObserO and ObserR are in the same reference frame, relative to GlxO.

So, as ObserO is moving away from point O, ObserO sees the emitted photon red-shifted by amount FRS.

When photon arrives to ObserR, ObserR would also see the same amount of red-shift in the photon's frequency, FRS, because they are in the same frame of reference, relative to GlxO.

That makes perfect sense.

For General Relativity however, the standard convention, for explaining gravitational red-shifting, and the measuring of a photon's energy before and after its emission, seems to use the exact same principles as those used to explain red-shifting by the doppler effect in Special Relativity.

The exact same scenario as above, with different observers measuring different energies in different frames of reference, is used. The result is the same, that there is no energy lost by the photon, just different measurements due to different reference frames.

Great.

However, it seems that one thing is forgotten. That this photon is actually traveling through a gravitational field from point O to point R.

We know that photons are effected by gravitational fields, and that they bend around heavy objects in space.

Question:

Lets say GlxO is relatively more massive than GlxR. Then the gravity well of GlxO would be relatively deeper than the gravity well of GlxR.

If point O begins at a point, in a gravity well of GlxO, that is relatively deeper than the gravity well of point R, would the frequency of the photon be measured the same for the same observers, ObserO and ObserR?

It seems to me, that if you take into account the photon's path, through curved space due to gravitational fields, that the 2 observers would measure different frequencies, since both observers are traveling in 2 different gravitational fields, and would be measuring the photon's energy, having been gravitationally red-shifted by 2 different fields.

Thanks for the view. All replies welcome.

Mike F.