The clock on earth runs slower because it is in a higher gravitational field. If the change in the rate of time passage due to gravitational difference is disregarded, then there would be no difference in the rate of passage of time. But that is not a meaningful comparison, since that is to disregard the reason why they are recording a different rate of time passage.

@ThomasLeeAbshierND I think the OP is interested in time dilation effects from the fact that the Earth clock is moving relative to the frame of the GPS satellite. i.e. Trying to look at effects of SR and not GR

@AaronStevens, I think you are right. Without that qualification, the question cannot be answered. Good insight!

@ThomasLeeAbshierND I have been in chat with the OP discussing various aspects of SR (although I wish I could claim excellent insight). I can say with pretty good confidence this is what they mean. But we can wait for the clarification if you would like.

@AaronStevens, since you have put so much effort into it, go ahead and answer it.

@ThomasLeeAbshierND The OP wanted other perspectives, so I do not think an answer from me would suffice. Plus, I am not 100% sure on how to treat what a frame moving with the GPS would observe since that reference frame is not inertial. Although if you treat it as inertial then I would say we can only have time dilation.

Hello

@AaronStevens, yes, this is a tricky question. It seems as though the standard answer in SR analysis is that two inertial frames observing the passage of time in the other always see the other as going slower. This is not intuitive, nor satisfying. Is this the standard SR perspective as you see it? (The added complication of neither the earth nor the satellite being inertial frames makes this question impossible to answer from any method I understand.)

Yes, and this is the issue the OP is having with SR as well. The resolution (as I see it) is that you have to pick an inertial reference frame first, and then work out everything in that reference frame. SR technically does not say "both clocks tick slower", since that assumes there is some absolute reference frame with an absolute time

I think a somewhat analogous scenario to what the OP is getting at would be a rotating turn table with one observer in the middle and one on the edge. Then the question is "does the observer on the edge observe the clock in the center as dilated?" The outer observer is still not in an inertial frame of reference, but at least the observer in the center is not accelerating now

@AaronStevens, I read through your chat with Zane - you covered the issue well. I didn't intend to imply an absolute frame, only that from the perspective of two inertial frames in relative motion, that they both observe time passing slower in the other. I think this is what you were saying.

Yes exactly. I wasn't saying you said any of that, I was just discussing the usual objection. You looked at all of the chat? It is a lot of chatting haha. And then Albert randomly showed up and it turned more into a conspiracy theory type discussion.

I think the simplification of the earth-satellite problem to the center and outer rim of a rotating record is reasonably accurate. But, I think the fact that the satellite and outer edge of the record frames are both non-inertial/accelerating frames takes this problem out of the realm of SR. Maybe GR could calculate the time dilation effect associated with angular acceleration?

You mentioned that the clocks on a satellite are adjusted to a higher clock rate to compensate for the SR effects of the satellite's orbital motion. I wonder if this was done empirically or by calculation from SR theory? I know when they did the famous around the world atomic clock in an airplane experiment (compared to the one left at home), they included a GR compensation as well as an SR compensation to compare the expected theoretical and experimental values of the two atomic clocks.

Yeah I haven't looked too much into the details of the calculations.

brighthub.com/science/space/articles/32969.aspx

Check out the diagram on the right with the rotating clock

Aaron, thanks for the link. The diagram, its author, and other answers to this question, clearly believe that orbital velocity may be considered the same as relative velocity between inertial frames. The idea that SR can be applied to a frame under acceleration seems to counter the assumptions underlying the derivation of SR. I had not considered using a line integral to determine the total relative velocity. This will require more research.

@ThomasLeeAbshierND I didn't send the link :)

Aaron, you are right - I didn't realize that Zane had jumped in the chat! Hello @ZaneScheepers, thanks for the link. I read through it. I understand the issue and objections you are having with the twin paradox.

That problem has been bothering people for decades. I have seen people attempt to solve the twin paradox using the argument that there is a GR domain at the turn-around due to the acceleration and deceleration, which makes the two twins go through asymmetrical space-time domains to explain why the spaceship twin ages more rapidly. I've never seen a resolution attempted before using a line integral.

Hi Tomas. Yes I've never come across this argument either, but it struck me as an obvious argument. It's just difficult getting people to understand it.

I think the wikipedia article on the twin paradox does a good job at covering a bunch of different view points :en.wikipedia.org/wiki/Twin_paradox