GPS, Relativity, and Tinkering

One of the great examples of practical application of both special and general relativity is in the Global Positioning System (GPS). There’s a nice description of how relativity simply has to be accounted for if GPS is going to work well or for long; read it here. The short version is that relativistic considerations cause a difference in the rate at which the atomic clocks aboard the GPS satellites tick, such that measurements based on them would be off by about ten kilometers in a day, and the errors would accumulate. The whole system is engineered with the consideration of relativity built in, as evidenced by textbooks and even the GPS specification.

Some people, though, don’t like the very notion of a theory of relativity. While looking up other material on GPS systems, I ran across a rant that appeared in the Usenet sci.physics newsgroup early this year. A fellow by the name of Tom Potter posted his “The GPS – General Relativity Myth” message there on February 1st. After a general round of name-calling, Potter gets to his argument:

I, for one,
would like to see any General Relativity Cultists
start with the basic General Relativity equation,
and work their way, step by step,
to the artifact they claim is proof that
General relativity is essential to the GPS System,

and then show why this cannot be handled in a system
by simply setting constants and multipliers to values
that provide the desired results.

For example, note that constants are used to
set calendars to agree with Moses, Jesus, Mohammed, etc.
and multipliers/dividers are used to adjust the clocks
on the Earth to agree with days or years, etc.

The Mayans, Chinese, Babylonians, etc.
managed to sync their days and moons
up to the rotation of the Earth about the Sun,
and to my knowledge they never used General Relativity.

I found this an intriguing way to argue. After all, this concedes that the “General Relativity Cultists” actually do derive the adjustments needed to make the GPS system work based on the theory. All Potter is trying to assert, then, is that the theory was not necessary to the implementation of a working GPS system: all the needed adjustments could be derived ad hoc as we go along. I have two responses. Perhaps a working GPS could come about without knowledge of relativity, but it seems unlikely to happen in one go. Without a theory of relativity, the satellites would quite likely not have any capacity built in to adjust the basic clock rate. Why would they? In classical physics, an atomic clock under any conditions of acceleration or position relative to a large mass would keep the same time. It would only be after the first set of satellites went up that the engineers would discover that the calculations were off, and getting further off with time. So maybe the second set of satellites goes up, and these have an adjustment facility built in. (Oh, and somebody has to turn off or destroy the first set of satellites, the ones that were wildly erroneous.) Now comes a period of adjustment as the engineers try to solve a problem in a large number of variables. It probably could be done. It almost certainly would be no fun, and it would leave the issue of how to validate the system. Remember, GPS was originally a military project, where part of its work was to assure the proper placement of ordnance. Once you’ve dropped your bomb, it is a bit late to be worrying over whether the engineers managed to empirically adjust the actual situation your GPS is dealing with at the moment.

That leads to the second point. Machine learning is a fascinating field. I’ve spent a good chunk of my career with it in one form or another. But one generally doesn’t use machine learning techniques to address a problem with a closed-form solution. Why would you? And the theory of relativity provides some excellent analytical solutions to problems like those posed in implementing a GPS system. It at once provides you with an understanding of the mechanics of what is happening and the means to engineer general solutions, with all the confidence that goes with the decades of testing the theory has undergone. It doesn’t leave one wondering if one has suitably managed to train a learning system to generalize appropriately from a sample of training cases. It is easy to explain how your system works under any particular set of parameters. So, Tom Potter, let’s use machine learning for things where we have no efficient solutions worked out in closed form, and let’s apply our best knowledge when it is appropriate to do so. That latter clause includes applying relativity to GPS systems.

Wesley R. Elsberry

Falconer. Interdisciplinary researcher: biology and computer science. Photographer. Husband. Christian. Activist.

9 thoughts on “GPS, Relativity, and Tinkering

  • 2009/11/20 at 6:56 pm

    Wow… I hadn’t known antievolutionist Tom Bethell disliked relativity. Thanks for the link.

    Update: That’s fantastic. The thread has Prof. Barr pointing out that Bethell is an ignoramus when it comes to relativity. Then Bethell himself makes an appearance in the comments to assert that he does, too, know what he’s talking about. His proof? Take this, Prof. Barr!

    Let me remind his readers of Petr Beckmann’s “crackpot idea” on which this reward was based. It is very simple. Einstein postulated in his special theory that the speed of a light is a constant (with respect to the source and the observer). Beckmann said that is wrong — the experiments say no. There is a difference between the speed of light to the east and the west, measured on the Earth’s surface.
    The reward goes to Mr. Barr if he can point to an experiment which does indeed show that the speed of light is the same, to the west and the east, to within 50 meters per second.
    It may not be easy for Mr. Barr to collect, however, because experiments have already been published showing this east-west light- speed difference. The best known was by Hafele and Keating, published in Science magazine in 1972. I am sure Mr. Barr knows how to look it up. There are other experiments but I won’t bore the readers.

    Bethell doesn’t get enough of a rise out of people with that, so he goes after it again:

    Does anyone on this blog have a response to the finding that there is an east-west light-speed differential? Someone should look up Hafele and Keating in Science magazine and see for themselves.

    Clifford Will was already familiar with the experiment and said so:

    I write to correct one statement made by Tom Bethell in his November 8 post. He stated that the Hafele-Keating experiment published in Science in 1972 supported Beckmann’s theory of an east-west difference in the speed of light. This is incorrect. The experiment had nothing to do with the speed of light. What was measured was a difference in the time accumulated on an atomic clock, which first traveled around the world eastward, and then made a similar trip westward. On returning home, after each trip, the traveling clock was compared with an identical clock that stayed in the laboratory (the clocks were Caesium-based standards, the best available at the time). All the trips were flown on commercial flights (these were the pre-TSA days!), each totaling around 45 hours in flight. Because the clock flew at high altitudes where gravity is a bit weaker than on the surface, Einstein’s general relativity predicts that its rate should differ compared to the stay-at-home clock. And because it traveled at different speeds (an eastward moving clock moves slightly faster relative to inertial space than a westward moving clock) special relativity predicts additional differences in its rate. Accurate logs of all altitudes and airspeeds were recorded. When the clock returned to base and was compared with the home clock, there was a difference in accumulated time between eastward and westward trips, and between each trip and the home clock. But the differences were in total agreement, within the measurement errors, with what was predicted by general and special relativity, given the itineraries. No light signals were ever used, so the experiment said nothing about the speed of light. The results agree completely with relativity.

    And I see that you got yourself a piece of that action, too… good job!

    It isn’t all that common that the subject of criticism shows up to demonstrate just how richly deserved the criticism was.

  • 2009/11/22 at 8:36 am

    Exactly! Not sure whether Bethell is going to return, or whom he’ll bring with him, but I’ll keep my eye on the thread.

  • 2009/11/22 at 7:59 pm

    The fellow with the fishy name is famed for crankery on as well, having brought a creationist engineer there in 1995.

  • 2010/02/24 at 1:38 am

    Hello, I’m new here–hope you don’t mind my intrusion… I’ve quite a few questions I’ve been pondering, though, and am looking for answers…

    I would like to address what looks to be one of the final comments on this forum where Austringer quotes Clifford Will…

    First of all, Will seems to suggest that the effect of gravity is significantly weaker at cruising altitude. It’s been a while since I was a practicing physics major, but it seems, to me, that the gravitational differential between a 1971 commercial jet at the surface of the earth (at some 6400km from its center of gravity) and at common cruising altitude (some 6412km from the earth’s center) is negligible in the gravitational equation (The resultant force differential would be approximately 1/200,000)… I don’t think this is what Einstein would call a significant difference (Newton would hardly call it significant).

    Second, (and here’s my real problem–question–with the whole of the results of the experiment itself) where in Einstein’s G.T.R. does he ever suggest that DIRECTION is significant to the warp?!? My understanding was that the sum total of his entire theory was to demonstrate that direction was SPECIFICALLY INSIGNIFICANT and that velocity/acceleration was the significant factor. I’ll grant that the earth is spinning easterly under the jets at some 1500ish kph so the west-east plane had less velocity relative to earth and the east-west plane had more, but neither clock should have sped up faster than the stationary clock on the ground should it have? The whole point is that, if you get in a plane and approach the speed of light (REGARDLESS OF WHICH DIRECTION YOU HEAD) your measuring yard and timeline shrink… No? It seems that the results of the Cesium clocks suggest that if you hop in your approaching-the-speed-of-light-plane and head the wrong way–relative to the earth’s magnetic field?–you will get older instead of younger!?!

    Third, couldn’t an observer on earth correctly be relatively described as traveling at an equal-and-opposite rate to you in the plane? As such, wouldn’t they also be growing younger when compared with you? Wouldn’t their clocks be slowing down compared to yours? Wouldn’t their metal rods be shrinking too? Or what if you put a cesium clock in a fast jet going N-S (thereby neglecting the earth’s rotation) and another in a equally fast jet going S-N… What do you reckon Einstein (or any of his faithful followers) would (should) sauggest as the result? Both clocks would have seemingly significant velocity relative to each other (at least according to what the Hafele-Keating experiment would suggest) so each should slow down relative to the other? So, upon landing, both clocks would be discovered to be a bit slower than their counterpart? Both captains younger than each other?

    Seriously, I’m not trying to start a war–I’m seriously asking. I’ve been studying Physics/Einstein since I was 16. I’m only recently coming to these questions–but I’m having trouble finding anyone with answers approaching validity. If any of you have good insights, please feel free to email me… I’ve got more questions for you.


  • 2010/02/24 at 1:46 am

    I meant “suggest”

  • 2010/02/24 at 4:26 am


    I am not a physicist, but…

    The Wikipedia article on the experiment lists the various equations for components of the time difference.

    I don’t think Will was saying that the gravitational difference for a cruising airplane was large, just that it would be measurable. Given the numbers reported in the Wikipedia page, it is apparent that the effect of gravity must be taken into consideration in order to predict the outcome sufficiently accurately.

    I think that you are overlooking that velocity and acceleration are always defined in terms of the inertial frame. The point of the experiment is that given an inertial frame, a timekeeper at rest with respect to that frame (the US Naval Observatory atomic clock), a timekeeper moving faster with respect to that inertial frame (the atomic clock on the airplane flying eastward), and a timekeeper moving slower with respect to that inertial frame (the atomic clock on the airplane flying westward), the prediction of general and special relativity is that the faster-moving clock will show less elapsed time and the slower-moving clock will show more elapsed time. And the experimental results show this to actually be the case.

    For the North-South and vice versa cases, one would expect that the effect would be effectively zero for the kinematic component: you haven’t moved the clocks relative to the inertial frame. On the other hand, the gravitational component would remain, and would be much larger than the empirical kinematic component (not likely to have an exact N-S or S-N flight), which would lead to an expectation that for the N-S, S-N cases that traveling traveling clocks would each show more elapsed time than the clock on the ground. I’m not considering the Sagnac effect here… it’s way too early in the morning.

    The use of the east-west directions maximizes the effect of differences relative to the inertial frame, an important consideration for the experimental design, given that the precision of the initial experiment was criticized as being barely sufficient to yield definitive results.

    Another nice article about relativity and GPS I’ve run across is by Neil Ashby.

  • 2010/02/24 at 9:58 am

    Nature Vol. 463, Issue 7283, p.847 has a news brief about a letter on pages 926-929. There, it is reported that the “gravitational redshift” has been measured to an accuracy of 7e-9, improving on previous efforts to measure this with precision by a factor of about 10,000.

    “Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity.”

Comments are closed.