Atomic Oscillations & Redshift in Sun and Earth

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Mickey1
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My question is very simple (and I assume it has been discussed before but I cant't find the topic):

An atom in the Sun emits a photon detected by an observer on Earth. Disregarding uncertainties and experimental problems relating to the movement of the atom (or assuming we could correct for it)

1 Should one expect:

differences in the oscillations of atoms in the Sun - from our observation point - so that a photon would leave the atom with a redshift – and then acquire additional redshift though its journey out of the Sun’s gravity field (also taking the lower gravity field of the observation point into account).

2 Alternative should we only expect:

one of these effects, perhaps being the same effect explained in two different ways?

The problem is also mentioned in K. Wilhelm, B. N. Dwivedi, On the gravitational redshift, Aug. 2014, Pages 8–13, accessed in arXiv:1307.0274.
 
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There is gravitational redshift. You can assign this to the point of production or the journey on the way to us - it doesn't make a difference. Both views, when treated consistently, lead to the same predictions for all measurements.

There is redshift and blueshift associated to the rotation of the Sun, you also have some thermal motion, but I guess these effects are not what the question is about.
 
mfb said:
There is gravitational redshift. You can assign this to the point of production or the journey on the way to us - it doesn't make a difference. Both views, when treated consistently, lead to the same predictions for all measurements.

There is redshift and blueshift associated to the rotation of the Sun, you also have some thermal motion, but I guess these effects are not what the question is about.

I take it then we should only expect one shift, i.e. any of the two, which you consider equivalent, and not two on top of each other.