Let me first deal with Scott's response under his caption of “THE (NON)USEFUL PRODUCTS OF ASTROPHYSICS “ [7, pg 1-2] to my mention that the accuracy of the Global Positioning System depends on the inclusion of relativistic effects[6, pg 4]. Dr. Scott dug up a reference from 1995, Henry F. Fliegel and Raymond S. DeEsposti. Gps and relativity: An engineering overview [2]. Here's the part Dr. Scott quotes:

Except for the leading γ [gamma] factor [in their final equation], it is the same formula derived in classical physics for the signal travel time from the GPS satellite to the ground station. As we have shown, introducing the γ factor makes a change of only 2 or 3 millimeters to the classical result. In short there are no “missing relativity terms.” They cancel out.Now this might look like an impressive response from Dr. Scott. Here was what appeared to be a legitimate official source claiming that relativistic corrections in the GPS system were negligible. The paper itself is available at the archive site for the 28th Annual Precise Time and Time Interval (PTTI) meetings. An examination of the paper reveals that the authors treated some relativistic contributions as separate additive components when in fact they were really the same effect measured from the two observers. This causes a number of their contributions to cancel.

But Dr. Scott apparently failed to follow-up on this source. The systematic approach is to discover who else has referenced this paper. Those papers will tell you if this paper was erroneous or legitimate.

Ashby responded to Fliegel and DeEsposti shortly thereafter[8]. Fliegel and DeEsposti are also referenced in Ashby's 2003 article I referenced on the GPS system[1]. In Section 6 of Ashby[1], “TOPEX/POSEIDON Relativity Experiment”, Ashby references Fliegel and DeEsposti and the confusion it caused being from an apparent official source. The controversy was sufficient that an additional experiment, using the TOPEX/POSEIDON satellite, was developed to test the situation. And relativity won again.

But there is another source we can investigate, one that should be OBVIOUS.

The GPS is an implemented system, publicly available to a wide variety of users who may wish to develop new products utilizing the position and timing accuracy provided by the system. NASA and commercial satellite operators use the system for synchronizing the clocks of other satellites[3, pg 13-14, 657]. Work is already under way to standardize clock synchronization for interplanetary missions and the inclusion of relativistic effects between planets is explicitly mentioned for the standard [9,10].

The developers of GPS need to get the correct information to satellite and product developers on how to read the GPS signals and properly convert them to positions and times. There are TEXTBOOKS on how interpret and utilize the GPS signals. Here's just three that I was able to find (links are to amazon.com):

- 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.

If it that isn't enough for you, I suggest you RTFM. It's available at the Navigation Center under the U.S. Coast Guard. Under GPS Related Technical documents, see Interface Specification, IS-GPS-200D. The relativistic corrections are described in Sections 3.3.1.1 and 20.3.3.3.3.

This invites a number of questions for Dr. Scott (and other GPS/relativity deniers):

- If, as Dr. Scott claims, these relativistic corrections are unnecessary, why are they documented in what are basically the TEXTBOOKS and the SPEC for developing products that read the GPS signals? Are the authors of the textbooks lying?
- If the textbooks are teaching it wrong, why does the system work at all?
- If the textbooks are teaching it wrong, how do other users develop working GPS products? Is there some hidden (occult?) knowledge related to the GPS system that the textbooks are hiding?
- What happens to engineers who don't read the spec?

References

- Neil Ashby. Relativity in the global positioning system. Living Reviews in Relativity, 6(1), 2003.
- Henry F. Fliegel and Raymond S. DeEsposti. Gps and relativity: An engineering overview. Technical Report. ATR-97(3389)-1, The Aerospace Corporation, El Segundo, U.S.A., 1996.
- 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.
- W.T. Bridgman, “The Electric Sky: Short-Circuited” Draft 2008-Mar-22.
- D.E. Scott. “D.E. Scott Rebuts T. Bridgman”. April 2009. PDF
- 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.

Sam Wormley's GPS-related Books & Publications

Wikipedia: Global Positioning System

Edwin Taylor GPS exercise: Project A. Illustrates the proper way to do the relative time calculation between the orbiting satellite and an observer on the Earth.

## 5 comments:

On the thunderbolts site, there is this thread

GPS satelite Clock Error ExplanationI took a look at the work which they reference at

Global Positioning System (GPS) and Relativity.

It's not clear where Dr. Smid gets Equation 4 which appears to be made up as a way to include the 38 microsecond per day number. I can find no equivalent expression in any of the GPS documentation available for use by vendors developing products to read the GPS signals. It certainly has no relevance to the physics of the problem.

It is important to note that there are TWO relativistic corrections to the GPS system. These are documented in a number of the references listed above.

1) One correction is the ~38 microseconds per day which is the difference in the clock rates of an atomic clock on the GPS satellites compared to clocks on the ground. This correction includes effects of the orbital motion and the gravitational field. This is needed to keep the entire system synchronized by a method sometimes called Einstein Synchronization (though periodic corrections are sent from the ground operators because of error accumulation in the clocks).

2) The second correction to GPS is the time-of-flight of the signal from the satellites to the GPS receiver. The time that the signal leaves the satellite is encoded in the transmitted signal and compared with the clock on the receiver. This difference is used to compute the pseudo-range which is subject to a number of corrections to compute the true range. Note that since this true range represents an actual distance between satellite and receiver, an error of 1 nanosecond (1e-9 seconds) corresponds to a error in distance of 3e10 cm/s * 1e9 = 30 cm ~ 1 foot! If one separates some of the contributions, there is an Earth rotation (Sagnac) correction which can reach up to 30 meters, and a general relativistic path range correction which can be up to 2 cm (for high-precision measurements) [Xu, pp 60-62].

Hi Tom,

I just came accidentally across your blog post referencing my page Global Positioning System (GPS) and Relativity.

Just for clarification: that page discusses the principle of the GPS location determination by means of a one dimensional model (i.e. assuming only two satellite transmitters). And Eq.(4) on that page is the location error due to an error in the satellite clock rates as compared to the time standard used to calculate the position from the satellite timings. If you insert a relative error epsilon=4.4*10^-10 (corresponding to 38 microseconds/day), then you get an error of about 1 cm for this.

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. So the frequently made argument (for instance by Neil Ashby) that a neglection of relativistic effects would lead to a location drift of 11 km/day and thus render GPS useless is misleading and incorrect.

Thomas

P.S.: By the way, I am not affiliated with Plasma Cosmology or any of the other references you gave in your opening post.

To Thomas Smid,

But isn't this solution just a hack? What will this 'correction' be if your satellites are in different orbits? Or in different parts of the solar system? How you you adjust your clock then, considering it would be best to set this prior to launch?

Your 'fix' 'just happens' to match the correction predicted by relativity.

One could also make the case that Newton's laws are 'hacked' to make force, mass, and acceleration work properly in units.

Mr. Bridgman

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).

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.

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!!!To Anonymous,

My reponse is linked here: Relativity Denial: A response to more comments about GPS

Post a Comment