GPS won't work without relativity - true or false?

[MikeS]

@Dr.Strangelove

Maybe. I don’t think we know how to describe gravity outside the framework of general relativity. It might be that there’s no way to get gravity out of a universe where general relativity isn’t true.

It’s not too hard to concoct a theory of gravity that doesn’t involve curved spacetime, so long as you’re only concerned with apples (that are not moving near the speed of light.) What’s hard is to get light-bending to work without actually curving spacetime.

[Zerc]

I emailed Phil Plait with the question as I put it in the OP and I got the reply -

Hi-

Its not that they wouldn’t work without relativity, as you point, but that if we don’t account for it the satellites wouldn’t work.

-Phil

Unfortunately, he didn’t say his statement is wrong but he did confirm that my basic assumption is correct.

[Francis_Vaughan]

@Keeve

Is this really true?
I once heard that the original GPS systems – that is, when the whole system was being set up and tested and such – were NOT designed with relativity in mind.
If that is true, then although today’s GPS systems are are designed with relativity in mind, the original ones were not.

As per the thread that Andy L linked to. The answer is no, that is not the story. The story does get mixed up in the retelling. There was no question about the need for GR to be taken into account, although there was some argument about the exact mathematics involved. GR isn’t simple, and you are talking some hairy issues. The first constellation of Navsats (pre GPS) were flown in the mid 70’s, not much after the first flown atomic clock experiments were done (that did validate GR.) The early sats were explicity designed so that they could be reprogrammed from the ground in case some of the issues in the nuances of GR corrections turned out to be incorrect. As it was, there was no need for this capability - the original programming and understanding of GR was correct. There was also an experiment run with some early satellites specifically to measure some of these GR effects, and to confirm they that had got it right - which they had.

Adding these capabilities and experiments was good engineering and project management at time when there may have been a chance that there were some not fully understood subtle issues in GR. As it was, no such issues ever arose, and the success of the Navsat and later GPS systems have been a shining confirmation of GR.

Finding some slight issue in GR with the system would probably have resulted in a free trip to Stockholm for the guys that found it.

[brossa]

To expand a bit on Francis Vaughan’s post: there are a number of relativistic effects that make GPS satellite clocks run at different rates than ground-based clocks. For one, the orbital clocks are moving quickly relative to a ground observer, which slows them down; on the other hand, they are much higher in the Earth’s gravitational well than the ground clock so they tend to run faster. It’s not too hard to predict which term will predominate ahead of time, but how certain are you going to be that you haven’t missed some other confounding term, like the eccentricity of the orbit which results in both altitude and velocity changing over time? Better to make a prediction and then verify it experimentally while allowing for the possibility of error.
However, here’s a more subtle question: could GPS work in a universe in which the speed of light was not the same for all observers regardless of their motion relative to the light source? I would imagine that if light travelled faster when the satellite was moving toward us and then slower as it receded, it would preclude the kind of travel-time difference checking that GPS as we know it is based on.

[Napier]

@Senegoid

Can somebody tell me how right or wrong I am in thinking this? Or, to ask it another way: How much does GPS accuracy rely on on-going empirical measurements, Relativity adjustments notwithstanding?

I am aware that GPS readings are also greatly affected by atmospheric conditions. To get from that 50-100 meters accuracy down to centimeter accuracy, they do it like this, basically: Take readings from a site of unknown (or mobile) location. Also take readings from a nearby stationary site. (Location not necessarily known precisely. The important thing being that it’s stationary.) The stationary site appears to be wandering around, to do shifting atmospheric conditions. The amount of movement can be applied to adjust the readings of the other (unknown or mobile location) to obtain its exact location precisely.

GPS timekeeping is compared to and adjusted by other GPS clocks and ground-based clock ensembles. But the size of the accomodation for relativistic effects is much bigger than the adjustments. It is fairly easy to keep time to much better than the accuracy corresponding to these relativistic effects, even without comparisons to other standards. Check out Project GREAT: General Relativity Einstein/Essen Anniversary Test for an account by an amateur timekeeper who demonstrated the relativistic effect of altitude on a camping trip with his kids, using his own personal atomic clocks. Note that rubidium atomic clocks can be bought for under $1000 these days.

About the means of correcting GPS position measurements, it is much more accurate to say that the distance between the ground position and each individual satellite gets corrected according to the measured distance between a nearby known ground position (a CORS or constant observation reference station for example) and that satellite. In other words, you can’t get much better accuracy by referencing measured GPS coordinates to nearby receivers, you have to do it based on the individual distances or “pseudoranges”.

[standingwave]

@Senegoid

Now here’s a question I have on the subject: Just how precisely accurate are those GPS atomic clocks (and our measurements of them), even with Relativistic accounting? My “intuitive” guess is that they must be much more accurate than without that accounting (obviously), but probably still have some residual inaccuracy. I should imagine that they still need to recalibrate regularly by empirically measuring drift from benchmark sites of known location. Is this so?

All clocks drift. It’s just that atomic clocks drift less than others. As long as you know what the rate is, it really doesn’t matter what the “absolute time” on the satellite is. You just need to compensate.

The atomic clocks aboard the satellites maintain their time to a very high degree of accuracy. However, there will always be a slight variation in clock rates from satellite to satellite. Close monitoring of the clock of each satellite from the ground permits the control station to insert a message in the signal of each satellite which precisely describes the drift rate of that satellite’s clock. The insertion of the drift rate effectively synchronizes all of the GPS satellite clocks.

Introduction to GPS

[Aji_de_Gallina]

I think it is clear now that the phrase “GPS wouldn’t work without relativity” is either non-informative (because everything is bound by it) or misleading (by implying that there is something unique about relativity without which there could be no GPS).