Here's my question first: If radio waves are transmitted from earth, are they actually redshifted, or is it that they appear redshifted when measured by an identical clock in space? Here's where I'm coming from. I'm trying to reconcile things I know. I think I know that (1) clocks further from earth will run faster, as proven experimentally, (2) the GPS clocks in the satellites were pre-adjusted (slowed) so that the frequency at earth will appear correct. So I could explain these by the clocks themselves in all cases running faster at higher potential, but radio waves being fixed as they move through different potentials. Conversely, if I have both effects, the GPS thing doesn't make sense: The clocks on the spacecraft will run faster than their setting on the ground, but if I also have the waves blueshift as they come down, I'd be "double booking" the effect. I'm fairly certain the corrections to GPS were only one application of the redshift equation, not the equation squared. Does my question make sense?