This was a waste of time.

 

Correct. I have no idea why you did it.

In Schwarzschild geometry, it holds that the deeper an atom sits in a gravitational potential well the smaller is the energy difference of atomic levels. This is an effect of space-time geometry and reflected in the frequency of photons observed in a frame of reference in which source and receiver are stationary. This is all that is captured by the usual equations.

 

The problem arises when one tries to locate (ascribe) the effect either to the atoms or to the photons, which needs to be decided in order to illustrate and understand what is going on.

 

 

But it's not a problem You have already chose to associate the shift with the atom, rather than the photon. What the physics says is there will be a relative frequency shift between the two. By saying the atoms are affected you have picked an interpretation, but you don't have to. What you can't do is say that both are affected.

 

It's like saying that if we are moving apart, that we must both be moving.