How do we observe redshifted light from distant stars if the effect is not intrinsic to photons? Derek from Vertasium says that wavelength and energy are not intrinsic properties of photons; they are properties of the photon-observer system. An observer in freefall in space will not observe photons redshifted as does an observer in an accelerated rocket, nor will an observer in freefall see gravitationally redshifted photons as observed by observers conducting the Pound-Rebka type experiment. So my question is, how do we observe gravitationally redshifted wavelengths of light from distant stars? Aren't we essentially in freefall at the earth (ignoring the marginal blue shift effect of photons entering earth's gravitational influence)?
I am concerned with gravitational redshift, not redshift due to the expansion of the universe.
Example: Observer f1 is in freefall above a planet, and observes non-redshifted photons emitted from the surface, while an observer at the top of a building observes photons emitted from the surface as redshifted.
Now let us place another freefall observer f2, a distance of 0.1 lightyear farther away from the surface than observer f1. Presumably this second freefall observer observes the emitted photons from the surface as not redshifted, the same as f1. Let us continue to place freefall observers farther and farther away from the surface, to infinity.
-freefall observer f1 at 0 distance from the planet observes 0 redshift.
-freefall observer f2 at 0.5ly distance from the planet observes 0 redshift.
-freefall observer f3 at 10.0ly distance from the planet observes 0 redshift.
-freefall observer f4 at infinite distance from the planet does observe redshift.
 A: Given an event in spacetime with light going through it, you can make that light seem to have any wavelength by choosing the right freefalling observer. Remember that freefalling observers at the same event can still have different velocities. For your example of a star, at any point in space, there is a freefalling observer that sees the starlight with the wavelength(s) it had for an observer comoving with the star surface at the point of emission, but every other freefalling observer sees something different. It is not true that if any observer is in freefall it sees the light "as it was emitted." In particular, there is no reason to believe that we on Earth will just happen to have the right velocity (i.e. "be the right freefalling observer") to see starlight with the gravitational redshift cancelled out. Indeed, as you get further from a star, the freefalling observer that sees light "as it was emitted" needs to be going faster and faster towards the star.
This line of thinking does highlight another issue with measuring gravitational redshift from stars, which is that we will generally have some velocity with respect to the star (in GR this statement is technically nonsense and needs some interpretation), and the resulting Doppler shift alters the measurement (again, technically gravitational and Doppler shifts are not even really separate, so perhaps its more like "the prediction for gravitational redshift depends on our velocity relative to the star"). This needs to be accounted for. We can look at this article about an influential early measurement (cited by Wikipedia here) for an example of how this was done in the case of the Sirius binary. In this case, we have a binary star system where one member exhibits low gravitational redshift (due to being a less-dense main-sequence star), and the other exhibits comparatively higher redshift (due to being a white dwarf, which are much denser). The redshift of the light from either member depends on the relative velocity between us and the star, but the difference in those redshifts does not, since the stars are in a system together (though we still have to account for their relative velocity of a few km/s). That differential measurement was what was predicted, measured, and tested.
A: For gravitational redshift in particular, we are approximately a stationary observer at infinity with respect to the distant star's emitted photons. So we observe the redshift because of our location in the gravitational potential  well of the star compared to the potential location where the photon was emitted. A free falling observer with respect to the star would be an observer falling into the star on a collision course.  This observer would not observe the redshift.  Another observer who would not observe the redshift is a stationary one standing directly on the surface of the star (somehow) who is stationary with respect to the emitted light and at the same potential level.
