Why does time dilation only affect GPS satellites in one direction?

[JesseM]

Firstly, the 'twins issue' is due to a coordinate acceleration (i.e., a change of inertial frames); proper acceleration is not a requirement, I think. The satellite clock undergoes a continuous coordinate acceleration and is hence similar to the twins scenario.

You may know this already, but just to avoid confusion, coordinate acceleration in an inertial SR frame is always associated with proper acceleration and vice versa, in inertial frames you can't have one without the other (this is no longer true in non-inertial frames of course). A clock moving in a circle in flat SR spacetime (as opposed to one orbiting in GR due to spacetime curvature) would be experiencing proper acceleration, it would measure a nonzero reading on its accelerometer (the 'centrifugal force').

 

[cfrogue]

Firstly, the 'twins issue' is due to a coordinate acceleration (i.e., a change of inertial frames); proper acceleration is not a requirement, I think. The satellite clock undergoes a continuous coordinate acceleration and is hence similar to the twins scenario.

Secondly, I thought your referenced Eq. (24) has been fully explained in this thread. Be that as it may, Eq. (28) and what follows directly below it explains it. It calculates the proper time of the orbiting clock, which by definition, is coordinate choice independent. What more is there to say?

Einstein solved the twins by considering both twins and proving they come up with the same result. So, he showed both directions are necessary.


No, I have not seen this integral done from both directions.

Is only one preferred frame necessary under SR and GR?

Under this context, I could sit inside one frame and predict all events in the universe.

Is this your claim?

 

[JesseM]

Now place an infinite number of clocks on towers as you specify and make the orbit of the satellite follow this path.

What does the integral tell you?

Same thing, that the orbiting clock elapses less time over the course of an entire orbit. It would also be true in all frames that for two clocks on nearby towers, if the first read a time t1 when the orbiting clock passed it and the second read a time t2 (and the two tower clocks were synchronized in their mutual rest frame), then the time T elapsed on the orbiting clock between passing these two tower clocks would be less than (t2 - t1). But keep in mind, this is not inconsistent with the idea that there might be some inertial frame where both of these tower clocks were ticking slower than the orbiting clock during the time between the two passings...in this frame, the explanation for the fact that T < (t2 - t1) would be that the two tower clocks were out-of-sync (the relativity of simultaneity), with the second tower clock ahead of the first tower clock at the moment the orbiting clock was passing the first one, so even though the second tower clock ticked forward by less than the orbiting clock during the time it took for the orbiting clock to get from the first to the second, it could still be true that T < (t2 - t1).

Can you please answer the question I asked in my last post?

And so would you agree that the GPS calculations don't contradict the idea of reciprocal time dilation in different frames, they just doesn't address it one way or another?

 

[JesseM]

Einstein solved the twins by considering both twins and proving they come up with the same result. So, he showed both directions are necessary.

No, such a calculation is just an exercise to show that different frames give the same predictions about local events (something that is already guaranteed if you assume Lorentz-symmetric laws); once you accept this, if predicting local events is all you are interested in, then only one frame is necessary.

Is only one preferred frame necessary under SR and GR?

If you just want to make predictions about local events, only one frame is necessary. But any frame will give the same predictions about local events, so no frame is "preferred".

Under this context, I could sit inside one frame and predict all events in the universe.

Yup, in relativity you only need one coordinate system to predict all local events in the universe.

 

[Jorrie]

You may know this already, but just to avoid confusion, coordinate acceleration in an inertial SR frame is always associated with proper acceleration and vice versa, in inertial frames you can't have one without the other (this is no longer true in non-inertial frames of course). A clock moving in a circle in flat SR spacetime (as opposed to one orbiting in GR due to spacetime curvature) would be experiencing proper acceleration, it would measure a nonzero reading on its accelerometer (the 'centrifugal force').

Yup, I agree.

IMO, using three purely inertial clocks, one can demonstrate coordinate independent relativistic time dilation without invoking acceleration as part of the test. I do not wish to dilute this thread by debating it here, but unless already beaten to death in this forum, maybe we can devote another thread to it.

 

[Ich]

Come to think of it Pervect, the best approach might be to begin with defining the metric in the weak field limit for an Earth sized planet, in Riemann normal coordinates.

Definitely not, as long as you're not at the Earth's core.
FWIW, https://www.physicsforums.com/showthread.php?p=1600272#post1600272"'s another version of pervect's calculation. It's easiest to use the complete Schwarzschild solution (it's not that difficult) and then approximate from flat space, not the center.

 

[cfrogue]

Yup, I agree.

IMO, using three purely inertial clocks, one can demonstrate coordinate independent relativistic time dilation without invoking acceleration as part of the test. I do not wish to dilute this thread by debating it here, but unless already beaten to death in this forum, maybe we can devote another thread to it.

Can you do this please?

I do not think another thread is necessary.

 

[cfrogue]

Yup, in relativity you only need one coordinate system to predict all local events in the universe.

I am OK with this, but I would assume switching to another frame should produce a similar pattern and thus reciprocal time dilation even though there exists gravity and orbital considerations.

However, can both directions conclude the satellite clock will follow the adjustments consistent with the experimental evidence?

More specifically, when only the satellite is considered compared to Earth based clocks, will it conclude time dilation is absolute for relative v to the Earth and will the Earth when calculating the satellite conclude exactly the same thing?

 

[yuiop]

More specifically, when only the satellite is considered compared to Earth based clocks, will it conclude time dilation is absolute for relative v to the Earth and will the Earth when calculating the satellite conclude exactly the same thing?

The time dilation of the satellite clock is not a function of v relative to the Earth. If the satellite was in a high geosynchronous orbit it would have no velocity relative to the surface of the Earth but it would still have a velocity based time dilation component due to its velocity relative to the space that the Earth is rotating with respect to. Even though the geosynchronous satellite appears motionless from the point on the surface of the Earth immediately below the satellite, the satellite obviously has orbital velocity otherwise it would not remain in orbit.

 

[cfrogue]

The time dilation of the satellite clock is not a function of v relative to the Earth. If the satellite was in a high geosynchronous orbit it would have no velocity relative to the surface of the Earth but it would still have a velocity based time dilation component due to its velocity relative to the space that the Earth is rotating with respect to. Even though the geosynchronous satellite appears motionless from the point on the surface of the Earth immediately below the satellite, the satellite obviously has orbital velocity otherwise it would not remain in orbit.

So what is it a function of?

 

[JesseM]

cfrogue, did you read post #93? Can you please answer the question I asked at the end of that post, and also tell me if you understand the reasoning about why different frames can disagree about whether the orbiting clock or the two tower clocks are ticking slower, but still agree on the time T that elapses between passing the two tower clocks, and the times t1 and t2 that each tower clock reads when the orbiting clock passes it?

 

[cfrogue]

cfrogue, did you read post #93? Can you please answer the question I asked at the end of that post, and also tell me if you understand the reasoning about why different frames can disagree about whether the orbiting clock or the two tower clocks are ticking slower, but still agree on the time T that elapses between passing the two tower clocks, and the times t1 and t2 that each tower clock reads when the orbiting clock passes it?

Well, let me ask this question. Can you repost #93 in terms of orbital distance please?

This means, use the logic of #93 with a low orbit and a high orbit.

I think I would understand it better that way.

 

[JesseM]

Well, let me ask this question. Can you repost #93 in terms of orbital distance please?

This means, use the logic of #93 with a low orbit and a high orbit.

I think I would understand it better that way.

I don't understand. What scenario do you want to analyze? In that post I talked about an orbiting clock passing two clocks on towers attached to the ground--do you still want to have tower clocks? And the logic of post 93 was specifically based on the fact that the orbiting clock passed right next to two tower clocks in succession so the times could be compared locally--if you have two clocks at different heights, how can you make a local comparison of their readings? One would need to change heights to meet the other at some point, or else they could send radio signals with each tick and each clock could compare its own rate of ticking with the rate it was receiving signals from the other.

Also, the question at the end of post 93 had nothing to do with this particular scenario anyway (it was just a repost of a question I asked you earlier which you didn't answer), so can you please answer that?

 

[cfrogue]

I don't understand. What scenario do you want to analyze? In that post I talked about an orbiting clock passing two clocks on towers attached to the ground--do you still want to have tower clocks? And the logic of post 93 was specifically based on the fact that the orbiting clock passed right next to two tower clocks in succession so the times could be compared locally--if you have two clocks at different heights, how can you make a local comparison of their readings? One would need to change heights to meet the other at some point, or else they could send radio signals with each tick and each clock could compare its own rate of ticking with the rate it was receiving signals from the other.

Also, the question at the end of post 93 had nothing to do with this particular scenario anyway (it was just a repost of a question I asked you earlier which you didn't answer), so can you please answer that?

I will answer your question. But I must understand it first.

Please put #93 in the context of several orbits and distance to Earth to see if the logic works.
Then please explain the logic to me.

 

[JesseM]

I will answer your question. But I must understand it first.

But the question at the end of post 93 had nothing to do with the the scenario I was talking about in the earlier part of the post, so you don't need to understand anything about that scenario to answer it. The question at the end of post 93 was just asking whether, since you already agreed "reciprocal time dilation" involves comparing multiple frames, then since the GPS system does all its calculation in one frame, it in no way contradicts the idea of reciprocal time dilation, it just doesn't address comparisons between frames in the first place. Do you agree or disagree that a calculation that's confined to just one frame cannot possibly in itself contradict a claim about what happens when you compare multiple frames?

Please put #93 in the context of several orbits and distance to Earth to see if the logic works.

You already asked me to consider different orbits, and I said I didn't know what scenario you wanted me to consider, which is why I asked these questions:

I don't understand. What scenario do you want to analyze? In that post I talked about an orbiting clock passing two clocks on towers attached to the ground--do you still want to have tower clocks? And the logic of post 93 was specifically based on the fact that the orbiting clock passed right next to two tower clocks in succession so the times could be compared locally--if you have two clocks at different heights, how can you make a local comparison of their readings? One would need to change heights to meet the other at some point, or else they could send radio signals with each tick and each clock could compare its own rate of ticking with the rate it was receiving signals from the other.

If you give me a specific well-defined scenario to analyze, I can "see if the logic works", but I can't if you won't even answer my questions about what scenario you're imagining!

 

[cfrogue]

But the question at the end of post 93 had nothing to do with the the scenario I was talking about in the earlier part of the post, so you don't need to understand anything about that scenario to answer it. The question at the end of post 93 was just asking whether, since you already agreed "reciprocal time dilation" involves comparing multiple frames, then since the GPS system does all its calculation in one frame, it in no way contradicts the idea of reciprocal time dilation, it just doesn't address comparisons between frames in the first place. Do you agree or disagree that a calculation that's confined to just one frame cannot possibly in itself contradict a claim about what happens when you compare multiple frames?

Let's see.
The a posteriori logic of the experimental evidence proves a non reciprocal time dilation relationship between the satellite and the Earth based clocks.


I have been asking for a priori proofs to demonstate a consistency with the mainstream experimental evidence.

Do you have this for all directions?

 

[JesseM]

Let's see.
The a posteriori logic of the experimental evidence proves a non reciprocal time dilation relationship between the satellite and the Earth based clocks.

SR does not say anything about a reciprocity between total times elapsed on clocks over an extended period! For example, in the twin paradox there is only one objective truth about which clock has elapsed less time between meetings. The only "reciprocity" is between the instantaneous rate of ticking of different clocks when this rate is calculated in two different frames--one frame can say that clock A is ticking slower then clock B at the moment clock B shows a particular time, another frame can say clock A is ticking faster than clock B at the moment clock B shows that time.

Do you disagree?

I have been asking for a priori proofs to demonstate a consistency with the mainstream experimental evidence.

Do you have this for all directions?

There are general proofs that you can apply the same relativistic laws in different coordinate systems and they must make identical predictions about local events.

 

[cfrogue]

SR does not say anything about a reciprocity between total times elapsed on clocks over an extended period! For example, in the twin paradox there is only one objective truth about which clock has elapsed less time between meetings. The only "reciprocity" is between the instantaneous rate of ticking of different clocks when this rate is calculated in two different frames--one frame can say that clock A is ticking slower then clock B at the moment clock B shows a particular time, another frame can say clock A is ticking faster than clock B at the moment clock B shows that time.

Do you disagree?

Of course I do.

I can solve the normal twins paradox with an integral both ways and it is eazy.

I will conclude the traveling twin is younger in both cases.

This is different.

I suggest you listen and separate theory from logic and make sure they both match.

 

[JesseM]

Of course I do.

What part of it do you disagree with? Your comments below suggest you didn't read what I was saying very carefully, or didn't understand it.

I can solve the normal twins paradox with an integral both ways and it is eazy.

I will conclude the traveling twin is younger in both cases.

Uh, yes, that was exactly my point. Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock. Similarly, if you calculate the instantaneous rate of ticking for orbiting vs. ground clocks in different frames you can find a reciprocal relationship, but all frames will agree on which clock elapses more time over the course of an entire orbit. In both cases, "reciprocal time dilation" only applies to instantaneous ticking rates, not to elapsed times. Therefore, the fact that the GPS clock objectively elapses less time over an entire orbit does not imply a failure of "reciprocal time dilation". Again, do you disagree with any of these statements? If so, quote the first one you specifically disagree with.

 

[cfrogue]

What part of it do you disagree with? Your comments below suggest you didn't read what I was saying very carefully, or didn't understand it.

Uh, yes, that was exactly my point. Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock. Similarly, if you calculate the instantaneous rate of ticking for orbiting vs. ground clocks in different frames you can find a reciprocal relationship, but all frames will agree on which clock elapses more time over the course of an entire orbit. In both cases, "reciprocal time dilation" only applies to instantaneous ticking rates, not to elapsed times. Therefore, the fact that the GPS clock objectively elapses less time over an entire orbit does not imply a failure of "reciprocal time dilation". Again, do you disagree with any of these statements? If so, quote the first one you specifically disagree with.

I suggest you read the twins thread that exists. I posted there.

If you want to operate in this place, that post is not yet challenged.

Let's go there now. and we can come back here OK?

 

[JesseM]

I suggest you read the twins thread that exists. I posted there.

If you want to operate in this place, that post is not yet challenged.

Let's go there now. and we can come back here OK?

OK, I answered your question there. Now please answer mine:

Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock. Similarly, if you calculate the instantaneous rate of ticking for orbiting vs. ground clocks in different frames you can find a reciprocal relationship, but all frames will agree on which clock elapses more time over the course of an entire orbit. In both cases, "reciprocal time dilation" only applies to instantaneous ticking rates, not to elapsed times. Therefore, the fact that the GPS clock objectively elapses less time over an entire orbit does not imply a failure of "reciprocal time dilation". Again, do you disagree with any of these statements? If so, quote the first one you specifically disagree with.

 

[cfrogue]

Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock. Similarly, if you calculate the instantaneous rate of ticking for orbiting vs. ground clocks in different frames you can find a reciprocal relationship, but all frames will agree on which clock elapses more time over the course of an entire orbit. In both cases, "reciprocal time dilation" only applies to instantaneous ticking rates, not to elapsed times. Therefore, the fact that the GPS clock objectively elapses less time over an entire orbit does not imply a failure of "reciprocal time dilation". Again, do you disagree with any of these statements? If so, quote the first one you specifically disagree with.

OK,
1) Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock.
False

2) Similarly, if you calculate the instantaneous rate of ticking for orbiting vs. ground clocks in different frames you can find a reciprocal relationship, but all frames will agree on which clock elapses more time over the course of an entire orbit.

I have been looking for you and your friends to prove this with the path integral for both directions.

3) In both cases, "reciprocal time dilation" only applies to instantaneous ticking rates, not to elapsed times. Therefore, the fact that the GPS clock objectively elapses less time over an entire orbit does not imply a failure of "reciprocal time dilation". Again, do you disagree with any of these statements? If so, quote the first one you specifically disagree with

I have no idea what system of logic you are using to conclude this.

 

[JesseM]

OK,
1) Since "reciprocal time dilation" in SR only works when you're talking about instantaneous rates of ticking in different frames, it does not imply a reciprocal relationship between the total elapsed time on each twin's clock.
False

What part do you think is false? Do you think reciprocal time dilation does imply a reciprocal relationship between the total elapsed time on each twin's clock, meaning that each twin should make the reciprocal prediction that the other twin's clock will have elapsed less time when they reunite?

And if your answer is "no", if you agree with me that there is a single objective truth about whose clock has elapsed more time when they reunite, then how is this "reciprocal"?

 

[Jorrie]

IMO, using three purely inertial clocks, one can demonstrate coordinate independent relativistic time dilation without invoking acceleration as part of the test. I do not wish to dilute this thread by debating it here, but unless already beaten to death in this forum, maybe we can devote another thread to it.

Can you do this please?

I do not think another thread is necessary.

JesseM and me just cleared some possible confusion, but such an "Acceleration vs. Frame Swap" analysis does not belong in the GPS thread. Maybe rather in the other current Twins thread.

 

[yuiop]

With reference to Jesse's towers and satellites experiment:

If you try to synchronise all the satellite clocks with each other you will find it is impossible to do. Each satellite clock can be synchronised with its immediate neighbour but when you get to the final two satellites they are completely out of sync. That is a strong indication that the satellite observers are not in an inertial reference frame and that is one reason that their reciprocal perception of the tower clocks running slower than the satellites on a local scale does not hold on a larger scale.

 

[cfrogue]

With reference to Jesse's towers and satellites experiment:

If you try to synchronise all the satellite clocks with each other you will find it is impossible to do. Each satellite clock can be synchronised with its immediate neighbour but when you get to the final two satellites they are completely out of sync. That is a strong indication that the satellite observers are not in an inertial reference frame and that is one reason that their reciprocal perception of the tower clocks running slower than the satellites on a local scale does not hold on a larger scale.

Is this when they are apparently moving together they cannot sync?

Also, do you have any mainstream papers that show the synchronization methods between satellites?

 

[yuiop]

Is this when they are apparently moving together they cannot sync?

Yes. It is the same for clocks placed on the rim of rotating turntable. Observers on the turntable can not get all the clocks to sync from their point of view.

Also, do you have any mainstream papers that show the synchronization methods between satellites?

I am talking about straight forward Einstein synchronisation method using light signals, i.e. placing a signalling device exactly half way between two clocks and starting the clocks when they receive the signal.

 

[cfrogue]

Yes. It is the same for clocks placed on the rim of rotating turntable. Observers on the turntable can not get all the clocks to sync from their point of view.



I am talking about straight forward Einstein synchronisation method using light signals, i.e. placing a signalling device exactly half way between two clocks and starting the clocks when they receive the signal.

OK, this is the sagnac effect.

Is this correct?

 

[yuiop]

OK, this is the sagnac effect.

Is this correct?

It's related.

 

[yogi]

A way to look at the SR time dilation in GPS is to treat it as a round trip Twin paradox - but there are no accelerations because the satellite is in orbit and therefore it remains in an inertial system during the entire experiment - First, stop the earth. Then measure the data for completion of one orbit as follows: the satellite passes over head and a clock T1 in the satellite is started and a clock T2 on the ground station is started - the satellite makes one orbit and both clocks are read - there are 4 factors -the change in time dT2 of the clock on the ground (the non rotating Earth reference), the distance traveled by the satellite in the Earth frame (the circumference of the orbit = D), the time lapsed as measured by the orbiting clock dT1, and the distance traveled by the ground clock T2 which is zero. To find the SR time dilation -simply apply the principle of the "invariance of the spacetime interval" in each frame"