This is a response to some
comments recently posted under the
"Scott Rebuttal. I. GPS & Relativity". The commenter's text is in
red.
what part of
"The whole point about this page is to show that in practice the drift of the satellite clock rates compared to a ground clock does not accumulate if the position is determined by the difference between satellite timings rather than a comparison to a ground clock"
you don't understand?
Do you have practical knowledge of the software implementation running the gps structure?
The "correction" made by general relativity amounts to 0.5 cm, so completely irrelevant for a discussion of the experimental validity of this theory.
Furthermore as is clearly stated in the Thomas Smid page and in countless pages with gps info (google it, don't be lazy) the position of a receiver is not calculated having as reference a ground clock, but satellite clocks, which have the same "important to the problem" special relativity factor (ex. time dilation).
I've studied the books and documents used as training resources for those who wish to develop products using GPS signals (such as the references listed below). I also know a few people responsible for maintaining the precision timing systems needed for space flight, including GPS. I also have to keep track of timing issues in my day job where I must often assemble simulations and satellite datasets synchronized to different types of clocks, requiring use of the IAU standards on reference system (see references below). The newest ephemerides I use (
Wikipedia: Jet Propulsion Laboratory Development Ephemeris) includes an ephemeris time which needs relativistic corrections to synchronize with Earth clocks.
According to the references and documentation for GPS signals, Dr. Smid uses the wrong equations for GPS triangulation. It is not clear what the GPS 'operating model' is for the equations used by Dr. Smid but it is inconsistent with the GPS documentation (see references below).
Actually the importance (%) of General Relativity in the accuracy of the gps system is close to zero.
Have you read "Relativity in the Global Positioning System" by Neil Ashby. Be aware that one of the relavistic corrections was wrongly implemented in the first gps satellites but it didn't make much of a difference for the practical accuracy of the system.
I've been to talks by Dr. Ashby and read the Ashby reference, as well as many others. Perhaps the commenter should read the reference as well:
In Part 5, Relativistic Effects on Satellite Clocks:
"There is an interesting story about this frequency offset. At the time of launch of the NTS-2 satellite (23 June 1977), which contained the first Cesium atomic clock to be placed in orbit, it was recognized that orbiting clocks would require a relativistic correction, but there was uncertainty as to its magnitude as well as its sign. Indeed, there were some who doubted that relativistic effects were truths that would need to be incorporated [5]! A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by general relativity, then the synthesizer could be turned on, bringing the clock to the coordinate rate necessary for operation. After the Cesium clock was turned on in NTS-2, it was operated for about 20 days to measure its clock rate before turning on the synthesizer [11]. The frequency measured during that interval was +442.5 parts in 10^12 compared to clocks on the ground, while general relativity predicted +446.5 parts in 10^12. The difference was well within the accuracy capabilities of the orbiting clock. This then gave about a 1% verification of the combined second-order Doppler and gravitational frequency shift effects for a clock at 4.2 earth radii."
 |
| Plot of GPS relativity correction vs. Earth orbit radius (red curve). Note that for the GPS orbit at 4.2 Earth radii (vertical green line) intersects the red curve at 38 microseconds. |
In case you need help with the math, 442.5 parts in 10^12 is (86400 seconds/day)*(442.5e-12) = 38.2 microseconds/day.
There are similar stories about erroneous ideas about relativistic corrections in papers by C. Alley (see
Introduction to some fundamental concepts of general relativity and to their required use in some modern timekeeping systems,
Plans to improve the experimental limit in the comparison of the east-west and west-east one-way light propagation times on the rotating earth) who was also involving in many projects involving synchronization of precision clocks over large distances.
Therefore, the relativistic correction IS necessary. Two different frequency synthesizers were installed in the first satellites because of the doubters. Considering the commenter included the author and the article title of a publicly available resource so easy to check, the question arises as to whether the commenter is just blindly repeating something from another (false) source, or intentionally lying. Funny that they accuse me of laziness when they apparently never read the article.
Without the relativistic correction in clock rate, the satellite time will move out-of-sync with a ground clocks by 38 microseconds per day in the timestamp transmitted by the satellite clock. In the GPS pseudo-range equation (
Wikipedia:pseudorange), the daily accumulation of an offset of 38 microseconds between a satellite clock and receiver clock increases the value of the pseudo-range between the satellite & receiver by 38e-6 s * 3e5 km/s = 11.4 km, accumulated each day. This means the three or more ranges used to triangulate (
Wikipedia:Trilateration) an Earth position from the orbiting satellites will get deviate from an optimal solution. This is just the difference in satellite clock relative to the ground clock, needed to define a consistent time in the geocentric intertial reference frame. There is an addition correction that must be done at the receiver, to account for among other things, the fact that the receiver is in a rotating frame on the surface of the Earth, the GPS satellite orbit is not perfectly circular, etc. That the relativistic effects must be included holds true even if you use the 4 (or more) -satellite solution that doesn't explicitly require the receiver time. This is because it doesn't matter if the satellites are all in the same frame,
the correction comes about because the satellites and the receivers are in different reference frames (for more details, see
Relativity Denial: The GPS 4-Satellite Solution).
What pisses me off is the propagandization of science in misleading and inaccurate ways. What you should say is that atomic clocks orbiting the earth suffer a 38 microsecond delay per day, and this is consistent (within experimental accuracy) with special relativity and general relativity. NOT that the practical accuracy of the GPS or GALILEO or GLONASS systems are dependent on relativity, because they aren't!!!
What I find funny is this commenter goes from claiming the relativistic effects are ignorable in the first two paragraphs, to now claiming that the match between the (NOT ignorable) 38 microsecond/day relativity prediction and the actual GPS offset is NOT support for relativity!
The fact that the numbers agree is evidence for the theory and therefore supports the theory. Those who use this complaint tactic usually have no theory that can actually produce the numbers. When pressed, they might try an
ad hoc solution, such as relabeling the computation as a 'correction' or 'fudge' factor of unknown origin. This can work only so long as you don't need to know what is happening in some different case such as the satellites being in an elliptical rather than circular orbit. How do you calculate it then?
The other problem with the argument is you could make a similar argument for Maxwell's Equations or quantum theory. The fact that the theory gives numbers for configurations which we can actually measure could be just a coincidence. The fact that these mathematical tools work isn't proof that the behavior of particles and fields isn't being controlled by magical pixies who just happen to let it work that way and may change it's operation at any time. This ploy is a common excuse, especially when opponents to the science under discussion can provide nothing
testable which can explain the effects. Of course, I've yet to see one of these individuals actually do real stuff with these types of claims. They can only manufacture an explanation after someone else has gone through the effort to make it work!
The beauty of relativity is that it defines things at the very fundamental measurements of position and time in a way that we can use to derive the corrections for a variety of experimental and engineering configurations. As represented above, many who want to deny relativity construct ad hoc 'corrections' and 'adjustments' which are needed to make the technology work. Such a solution might work for copying a technology, but it is totally unclear how you would apply it in a new technology in realms where it has not be applied before, without building the technology first and then running it for a time to determine the 'adjustment' needed.
I've read a report, which I have yet to get confirmed, that the European Union's GALILEO system will not be adjusting their satellite clocks to account for the relativistic corrections. Instead they will require that all the corrections be performed in the receiver (the GPS signal can actually transmit the satellite orbit ephemeris so the correction can be computed). One advantage of this is that you can decide to place your satellites in a different orbits at launch time, or perhaps even change orbits after launch, rather than building the satellites specifically for a given orbit. But could this also be a clever way to lock the relativity-denying cranks out of the business of building GPS receivers?
So to return to the commenter's opening paragraph, where do I get my information? I've answered that. I get my information from those who write the books and references written by those who designed, built, and maintain the system, and used by others who need access and interpret the raw GPS signals, such as those listed below.
Now it is certainly fair to ask: what are the commenter's credentials? The commenter seems to rely on random pages found online.
Which is the more credible source?
References
- Neil Ashby. Relativity in the global positioning system. Living Reviews in Relativity, 6(1), 2003.
- Elliott D. Kaplan, Christopher Hegarty (Eds). Understanding GPS: Principles and Applications, Second Edition (Hardcover). Artech House Publishers. 2006
- B. Hofmann-Wellenhof, H. Lichtenegger, J. Collins. Global Positioning System: Theory and Practice Springer. 2001.
- Guochang Xu. GPS: Theory, Algorithms and Applications. Springer, 2003.
- Marc Weiss and Neil Ashby. Gps receivers and relativity. In The 29th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pages 69–84, 1998.
- Al Gifford, Robert A. Nelson, Richard S. Orr, A.J. Oria, and Beryl L. Brodsky. Time dissemination alternatives for the nasa space exploration program. In The 38th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pages 319–328, 2006.
- Robert A. Nelson and Todd A. Ely. Relativistic transformations for time synchronization and dissemination in the solar system. In The 38th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pages 305–317, 2006.
- Interface Specification (IS-GPS-200E, 8 June 2010). The relativistic corrections are described in Sections 3.3.1.1 and 20.3.3.3.3.
- The IAU Resolutions on Astronomical ReferenceSystems, Time Scales, and Earth Rotation Models: Explanation andImplementation, George H. Kaplan. U.S. Naval Observatory. October 2005
