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I note there are many question about gravitational redshift and I realize that my question might be buried in one of those but I can’t see it.

I am thinking about two different processes in relation to gravitational redshift:

  1. The photon on its way out from the Sun’s gravity field is experience gravitational redshift

  2. The atom is subject to gravity induced effects which slows down the atom’s processes implying that the photon is red-shifted already at emission.

Are both correct and valid ?

I read in http://www.einstein-online.info/spotlights/redshift_white_dwarfs that: A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. It is, therefore, perhaps best regarded as a test of that principle rather than as a test of general relativity.

My follow-up question is: Are both examples of the principle of equivalence or is the second version different from the first (and perhaps in need of the full general theory of relativity for its explanation)?

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Both are equally derived from the gravitational redshift. In #2 the light is further redshifted if it escapes the earth. In #1, the same is true, on the Suns surface (the sun's light comes from near the surface), there is a redshift at which it is emitted, and when it escapes from the Sun it is further redshifted. The whole thing in both cases just depends on the difference in gravitational potential, that is,

Fractional redshift = $\Delta \nu/\nu$ = - $\Delta \phi$/$c^2$

If emitted at the Sun and received at the earth take both potentials into account (from the Sun there is a semi random Doppler from the velocities of the emitting particles in the high temperature surface, much less in white dwarfs)

One point on that article you referenced. It was written by an astronomer/astrophysicist. The tricky part is the particle theory of light, which was really a Newtonian idea. Well, we know there is some truth that light can act like particles, but also that it is a wave, and the true theory is quantum electrodynamics (QED). In the particle theory of light, to have light have inertial mass you postulate that it is proportional to freq which you postulate is proportional to energy, so there is a frequency, mass and energy equivalence. The important assumption is best stated that energy and mass are equivalent because in modern terminology light has no mass, it is massless, but carries energy, thus that equivalence is needed.

Best way to derive the equations is to use General Relativity. For cosmological redshift you have to use the cosmological model of the theory.

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  • $\begingroup$ Would you say that both processes are test of the same principle or is it possibly the case that the redshifted escaping photon is a test of the equivalence principle and the first, the inter-atom processes being slowed down is more directly a test of relativity? $\endgroup$ Aug 13, 2017 at 15:19
  • $\begingroup$ It's the same effect in slightly different circumstances. In both cases it's a gravitational redshift derived from General Relativity which reflects the Principle of Equivalence. Those are not two different effects. Btw, keep in mind it's a very small effect (i mean the slowing of time or redshift in a weak gravitational field like earth's or even regular stars. You can calculate it from the equation) $\endgroup$
    – Bob Bee
    Aug 13, 2017 at 18:59
  • $\begingroup$ A late comment. I have perhaps been asking too much about the type of interactions rather than their sum. Can I double-check about the total redshift from radiation from the Sun (assuming the earth gravity field is zero or taking properly into account): is it the sum of the two effects we would see (the internal atom’s slower oscillations in the Sun’s gravity field, and the redshift during the photon’s path out of the Sun’s field) or is what see only the effect of one (disregarding the measurement problems). I assume the two are the same size. $\endgroup$ Nov 25, 2017 at 14:44
  • $\begingroup$ Mikael: the size of both is small, right offhand I do not know which is bigger, or even if they are the same order of magnitude. You would just sum the two. I've read about something similar, but not the same, where the calculations to sunc the time kept at the standard clock (in Paris I think) and that measured at the GPS satellites had to account for all the small differences between different points. Any such metrology calculations and syncs are complicated, but are well understood and done nowadays. $\endgroup$
    – Bob Bee
    Nov 26, 2017 at 5:03
  • $\begingroup$ Bob Bee: Could you comment on Wilhelm’s article in arXiv:1307.0274v2 where one gets the impression that there is still disagreement about the redshift at least in some aspect.: “Even after the prediction of the gravitational 3 redshift by Einstein (ref 15) for over a century and the many observational confirmations mentioned in Section I, there appears to be no consensus on the physical process(es) causing the shift.” $\endgroup$ Dec 1, 2017 at 14:38

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