Is GPS consistent with relativity? (Split from is Relativity 100% proven)

[Le Repteux]

I was commenting this post of yours in response to a post about SR: http://www.scienceforums.net/topic/83940-is-gps-consistent-with-relativity-split-from-is-relativity-100-proven/?p=813695

 

But my questioning is about the apparent impossibility to apply SR to 12 satellites going in different directions and at different speeds from one another. It seems to me that only GR is applicable. Is that so?

[xyzt]

I was commenting this post of yours in response to a post about SR: http://www.scienceforums.net/topic/83940-is-gps-consistent-with-relativity-split-from-is-relativity-100-proven/?p=813695

 

But my questioning is about the apparent impossibility to apply SR to 12 satellites going in different directions and at different speeds from one another. It seems to me that only GR is applicable. Is that so?

The theoretical foundation of GPS is entirely GR.

With one exception: there is a Sagnac effect that needs to be accounted for in the communication between satellites. The Sagnac effect is a classical effect, not a relativistic one, so GR (nor SR) are necessary in explaining it.

[Le Repteux]

Thank's Syst,

 

Now, since only the synchronism of the clocks is useful for positioning, we could use some other time for the satellites than the one we get from GR to synchronize them, which means that we use GR time only because it is more practical. If that is true, it means that, if we did not know about GR before installing the GPS system, we would nevertheless have found a way to synchronize it, would we? But what a surprise to observe all the satellites clocks drifting away from ours.

[Strange]

The GPS receiver has to correct for GR effects in both timing and distance in order to correctly triangulate positions. Without this it would only be accurate to 10s of meters (or maybe worse, it is a long time since I worked on them).

 

(I don't know what you mean by "GR time")

[xyzt]

Thank's Syst,

 

Now, since only the synchronism of the clocks is useful for positioning, we could use some other time for the satellites than the one we get from GR to synchronize them, which means that we use GR time only because it is more practical. If that is true, it means that, if we did not know about GR before installing the GPS system, we would nevertheless have found a way to synchronize it, would we? But what a surprise to observe all the satellites clocks drifting away from ours.

If you don't "know about GR", you don't have a means of synchronizing the clocks.

 

[Le Repteux]

Strange,

Swantson wrote the following text on post 13: you don't agree with him?

 

"if the GPS satellites were not corrected the system would still nominally work. Since all of the satellites' clocks would be off, the differences would still be valid as long as the clocks were not drifting off from each other, and it's timing differences that give the position. But they would drift, so they need to be synched up, and the choice was to use a ground control station to do that, hence the decision to shift the clocks to reflect time on earth (specifically UTC(USNO))."

 

By GR time, I mean the time that runs at the satellite's orbit.

 

xyzt,

To me, Swantson's post means that there is a way of synchronizing the orbiting clocks without using GR formulas, which is to use the time from our own clocks at ground level. You don't agree with him?

[xyzt]

 

xyzt,

To me, Swantson's post means that there is a way of synchronizing the orbiting clocks without using GR formulas, which is to use the time from our own clocks at ground level. You don't agree with him?

He doesn't mean that, you misunderstand.

[Strange]

Strange,

Swantson wrote the following text on post 13: you don't agree with him?

 

It is correct, but incomplete. That is only about sending corrections to the satellites. There are also corrections made in the receiver which need to take into account the differences between the receiver and each satellite (based on its relative velocity, etc.)

 

 

To me, Swantson's post means that there is a way of synchronizing the orbiting clocks without using GR formulas, which is to use the time from our own clocks at ground level.

 

No, because that Earth time would need to be translated to the reference frame of each satellite, which requires GR.

[Le Repteux]

It is correct, but incomplete. That is only about sending corrections to the satellites. There are also corrections made in the receiver which need to take into account the differences between the receiver and each satellite (based on its relative velocity, etc.)

You mean corrections for doppler effect I suppose, but these are not GR corrections, and all we need to make them is synchronized clocks, not GR notions.

No, because that Earth time would need to be translated to the reference frame of each satellite, which requires GR.

This requires that we can measure the drift of the satellite's clocks, but it seems to me that we do not have to know about GR to do that. What I mean is that even if GPS is consistent with Relativity, we could manage it even if we did not know about GR. Am I wrong?

Edited September 2, 2014 by Le Repteux

[xyzt]

You mean corrections for doppler effect I suppose, but these are not GR corrections, and all we need to make them is synchronized clocks, not GR notions.

 

 

This is false, the corrections ARE mandated by GR and are much more complex than Doppler effects. I explained the corrections here.

 

 

 

This requires that we can measure the drift of the satellite's clocks, but it seems to me that we do not have to know about GR to do that. What I mean is that even if GPS is consistent with Relativity, we could manage it even if we did not know about GR. Am I wrong?

 

Yes, you are wrong. Very wrong.

Edited September 2, 2014 by xyzt

[Le Repteux]

Without GR as a guide, once we put a couple of clocks on orbit and discover that they all drift the same amount, we can measure it with precision and include it in our corrections, no?

[Strange]

You mean corrections for doppler effect I suppose, but these are not GR corrections, and all we need to make them is synchronized clocks, not GR notions.

 

The problem that Doppler causes is the need to scan a wide range of radio frequencies to find each satellite at start up. It doesn't have (as far as I remember) any effect on the triangulation process.

 

Without GR as a guide, once we put a couple of clocks on orbit and discover that they all drift the same amount, we can measure it with precision and include it in our corrections, no?

 

GR has to be used when doing the triangulation otherwise the times and distances used would be wrong. Remember this is the theory of relativity, i.e. the receiver needs to calculate the difference between its frame of reference and the satellite's. This is, potentially, different for every satellite.

Edited September 2, 2014 by Strange

[Le Repteux]

The problem that Doppler causes is the need to scan a wide range of radio frequencies to find each satellite at start up. It doesn't have (as far as I remember) any effect on the triangulation process.

OK

This is, potentially, different for every satellite.

You mean, because of the small differences in their orbital parameters, I suppose?

[Strange]

You mean, because of the small differences in their orbital parameters, I suppose?

 

Each satellite will be moving at a different speed relative to the receiver. The receiver itself may be moving. The receiver's altitude may vary. And so on...

[Le Repteux]

Each satellite will be moving at a different speed relative to the receiver.

Do you mean that SR calculations would be necessary? If so, this is not what I understood from xyzt and Swantson's explanations.

[Strange]

Do you mean that SR calculations would be necessary? If so, this is not what I understood from xyzt and Swantson's explanations.

 

If it was just the relative velocity, you could approximate it with SR. But it isn't.

[swansont]

 

xyzt,

To me, Swantson's post means that there is a way of synchronizing the orbiting clocks without using GR formulas, which is to use the time from our own clocks at ground level. You don't agree with him?

 

No, pretty much the opposite. We use the clocks at ground level, but that's only possible because we have applied a GR correction to the space-borne clocks. Without that correction they could not be synchronized with the ground clocks. In principle they could synchronize with each other, which is a technologically more complicated problem, and there would still be corrections (from GR) owing to their orbits not being circular.

 

 

BTW, it's swansont

[Le Repteux]

Call me Le Repteut for a few times and I will remember that your "t" goes at the end.

 

OK for GR, but what about Strange that seems to say that SR is part of the equations?

[swansont]

Call me Le Repteut for a few times and I will remember that your "t" goes at the end.

 

OK for GR, but what about Strange that seems to say that SR is part of the equations?

 

SR is a special case of GR. (It's in the name; a special case and a general case)

 

All of the calculations trivially rely on relativity, because the calculations rely on c being invariant.

[xyzt]

Without GR as a guide, once we put a couple of clocks on orbit and discover that they all drift the same amount, we can measure it with precision and include it in our corrections, no?

The problem with your reasoning is that the clocks do not "drift the same amount", the amount of drift accumulates over time. So, measuring the amount of drift is useless, you need to adjust the frequency (as it is being done, at launch). You do not know by how much to adjust the frequency UNLESS you apply the predictions of GR. You did not read my post I linked in, the one that explains all this, did you?

[Le Repteux]

Yes Swanson"t", I know that both relativities rely on the invariance of light, but I also know that their equations are different: one is about motion, the other is about gravitation. If it is easy for me to figure out how to adjust the satellite's clocks with GR, it is impossible to figure out how to adjust them with SR since, at the same time, each of them would have to run at a different rate from each of the others, which is in fact physically impossible.

 

Yes xyzt, I read your link, but it did not help me a lot. I still think that, if we can synchronize the clocks for their mechanical drift once they are in orbit, then we can do so for their GR drift too. No?

[xyzt]

 

 

Yes xyzt, I read your link, but it did not help me a lot. I still think that, if we can synchronize the clocks for their mechanical drift once they are in orbit, then we can do so for their GR drift too. No?

No. I explained why.

 

 

 

I also know that their equations are different: one is about motion, the other is about gravitation.

 

False, GR handles BOTH the effects of gravitational potential and of motion. You claimed that you read my linked post, it is explained there. Can you follow the math?

Edited September 2, 2014 by xyzt

[Strange]

Yes Swanson"t", I know that both relativities rely on the invariance of light, but I also know that their equations are different: one is about motion, the other is about gravitation. If it is easy for me to figure out how to adjust the satellite's clocks with GR, it is impossible to figure out how to adjust them with SR since, at the same time, each of them would have to run at a different rate from each of the others, which is in fact physically impossible.

 

You don't need to do both GR and SR. They are not two different theories. You do the GR calculations. That includes any effects that would be covered by SR.

 

If you don't need to worry about gravity, then you can get away with the simpler SR calculations.

[Le Repteux]

False, GR handles BOTH the effects of gravitational potential and of motion. You claimed that you read my linked post, it is explained there. Can you follow the math?

Yes, I can follow the maths. So what you say is that we have to change the clocks to account for gravitational effect prior to their launch because it would be impossible to do so once in orbit, and my question is, can we change them for the radial motion effect too or do we have to program the receivers to account for that? Also, what about the transverse effect, does it affect the system?

[swansont]

Yes, I can follow the maths. So what you say is that we have to change the clocks to account for gravitational effect prior to their launch because it would be impossible to do so once in orbit, and my question is, can we change them for the radial motion effect too or do we have to program the receivers to account for that? Also, what about the transverse effect, does it affect the system?

 

The clocks are adjusted for both gravitational and kinematic effects, i.e. for the effects of GR.