How Do Gravitational Fields Affect Photon Energy Levels?

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Photons emitted from stars in strong gravitational fields experience greater redshift compared to those from weaker fields, due to the influence of gravity on their energy levels. The discussion raises questions about whether photons entering a high gravitational field would initially be blueshifted before being redshifted upon exiting, potentially canceling the effects. It is suggested that as a star's mass increases, the entire system could appear blueshifted, complicating the measurement of redshift. However, gravitational redshift is consistently observed, indicating that the energy levels of photons differ based on the gravitational context. The key takeaway is that while photons may have the same energy at their source, their observed energy varies depending on the gravitational field they traverse.
MikeGomez
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A photon emitted from a star with a large mass (strong gravitational field) will be redshifted more than a comparable photon emitted from a star with a weaker gravitational field (comparable meaning the two photons would otherwise be expected to have exactly the same values in both cases, i.e. third to second energy level of Hydrogen, or whatever).

What I don't understand is that it seems as though the two photons from the two stars are assumed to have the save energy levels at their source. But how exactly can that occur? When a photon of a given energy level enters the system with a high gravitational field, would it not be blue shifted as it entered, and then redshifted as it exits? In that way the redshift and blueshift would cancel and the entire gravitational redshift phenomenon would be hidden from us outside observers when we make the energy measurements. This is how I see it viewing gravity as a conservative force.

Also as a star forms and increases its mass, doesn't everything is the entire system become more blueshifted under its own increasing gravitation? This would mean that all matter and energy in a larger mass system would be more blueshifted than a lower mass system, assuming they have the same size. Again, it seems as though photons emitted would be redshifted while exiting, and since they began blueshifted, the two effects would cancel and we outside observers wouldn't measure a difference.

But of course we do measure gravitational redshift, so what am I missing about the nature of star systems and their relative redshift/blueshift effects?
 
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As far as the atoms producing the photons are concerned (in their own frames) the frequency / energy is the same. But, to an observer in another frame, the energies will be different.
 
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