Can you explain where the kinematic term comes from? Also, is SR not applicable here due to an accelerating reference frame?

@AaronStevens: Can you explain where the kinematic term comes from? The kinematic term is the leading term of the Taylor series for $\gamma=(1-v^2/c^2)^{-1/2}$. Also, is SR not applicable here due to an accelerating reference frame? This is the leading-order result from general relativity, not an SR result. (It also is not true that SR cannot handle accelerated frames -- it can.) For a detailed derivation, see N. Ashby, “Relativity in the Global Positioning System,” Living Reviews in Relativity (open access).

I know SR can handle accelerating frames. I just didn't know if you can apply SR within an accelerated frame. Also, your conclusion is opposite of what the other answer here says.

@AaronStevens: Also, your conclusion is opposite of what the other answer here says. No, my answer and WillO's agree on the direction of the effect. I know SR can handle accelerating frames. I just didn't know if you can apply SR within an accelerated frame. I'm not clear on what distinction you're trying to make here. In any case, there is no frame of reference being discussed in my answer. This is simply a leading-order approximation to the integral of the line element, $\int ds$.

You say that according to the GPS, the Earth's clock ticks faster. WillO says it will tick slower. And the frames I am talking about is what reference frame we are choosing to work in. See my comment on WillO's answer.

You say that according to the GPS, the Earth's clock ticks faster. There is no "according to" involved here. There is a difference in the long-term trend of the two clock rates. In reality, the earth clock ticks slower. If you bring down the satellite on a parachute and reunite it with the earth clock, the satellite's clock will show more time having passed. (If we get rid of the gravitational term, the effect is reversed in sign.) There are no frames of reference involved. GR does not have (global) frames of reference. The entire concept is absent from the foundations of GR.

Hi.

I know that there are no global frames of reference. That doesn't mean there are no frames of reference. In any case, I have been chatting with the OP for the past couple of days about SR. The OP believes hshowing that the GPS see the Earth clock as ticking faster proves that SR is invalid and that there is in fact an absolute/global frame of reference

This is why I've been focusing on SR. The OP thinks that GPS temporal corrections proves relativity wrong.

And why I've been focusing specifically on what an observer moving with the satellite would observe. Would they see a faster or slower time on Earth? Not talking about if you parachuted the satellite to Earth

The OP is after the typical SR example that we observe clocks moving relative to us to be ticking slower, but he wants to use this example where the observer is with the satellite looking at a clock on Earth

There is not much point in discussing what the OP may or may not think, since the OP isn't here. If the OP believes in silly kook stuff, that's irrelevant.

Well can you at least explain how you and WillO are saying the same thing, since they seem different to me.

"And why I've been focusing specifically on what an observer moving with the satellite would observe. Would they see a faster or slower time on Earth?" The word "see" is a sign of conceptual confusion here.

This stuff about what an observer "sees" only means anything if you define it in one of two ways. Either (1) it is about optical observation (which is a way of transmitting signals), or (2) it refers to something like the Einstein synchronization convention, which is the underlying operational definition for the SR concepts like Minkowski coordinates.

> Well can you at least explain how you and WillO are saying the same thing, since they seem different to me.

I think I did explain that, in the comment beginning with 'There is no "according to"...'

Sorry, I need to get some work done. Hope this was helpfyl. Bye.

Thanks for taking the time. It seems like the OPs question is more concerned with GR rather than SR like they intended to.

If we omit gravitational time dilatiib, from the pow of the co-moving with satellite observer the clock on Earth will appear ticking gamma times faster. Look for te

Transverse doppler effect in wikipedia. Rotating observer always measures blueshift of frequency of the source

If I may, what I think Ben is trying to say is that if we take two synchronised clocks and put one on a GPS satellite, we will find that after a year, they won't be synchronised. The lower gravitational effecient of the satellite would cause it's clock to be ahead of ours but, if we disregard this effect and only focus on velocity time dilation, the satellites clock would be behind the earthbound clock.

SR tells us that if you we're on the satellite, and we disregard the GR effect, that you would see the earth clock ticking slower. This is counter to what is actually happening.

@Albert I don't think Doppler shifts are relevant for this discussion.

@Albert You have to recognize that the blue shift in that scenario also involves length contraction effects, even though it is a transverse Doppler effect, because of when the light has to be emitted for it to reach the observer.

Amount of relativistic Doppler effect does not depend on distance between emitter/receiver. It can be one inch or one light year, that's doesn't matter. Transverse Doppler effect is only due to time dilation.

Doppler effect only affects what we see with our eyes. In relativity we mean see, after taking light delay into account. So technically we shouldn't discuss Doppler shift in relativity

@Albert You keep citing the Wikipedia article. "The source would be time-dilated relative to the receiver, but the redshift implied by this time dilation would be offset by a blueshift due to the longitudinal component of the relative motion between the receiver and the apparent position of the source."

This is dealing with figure 2a

I'm not really sure what your position is. Are you saying SR is wrong? You just keep talking about Doppler shifts, but every time (in the other chat) I try to ask you questions you just start throwing stuff at me. I really just don't understand where you are coming from.