Note: The Weekly Edition will be on a summer break for the next three weeks, during which time we will present features previously published elsewhere. We will return with original material on September 4.

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A new article by historian and physicist David Kaiser in Historical Studies in the Natural Sciences explores how corrections for the effects of general relativity were integrated into the satellite-enabled Global Positioning System between the 1960s and 1980s.

While developing his general theory of relativity in the 1910s, Albert Einstein concluded that time would move at different rates on account not only of different observers’ relative speeds, as his special theory found, but also their different positions within a gravitational field. Kaiser notes that this phenomenon’s implications for GPS has become a common reference point in discussions of the relevance of fundamental science for practical technology as well as a problem frequently assigned to undergraduates studying relativity.

Kaiser’s article is part of a set of historical inquiries that various scholars are making into the renaissance of general relativity in the middle of the twentieth century. While Einstein’s initial formulation of general relativity inspired a flurry of elaborations on it, research in the area declined in the years leading up to World War II. A revival in the second half of the century informed important work on, notably, cosmology and black holes. However, general relativity was also spurred on by Cold War R&D. A prior article that Kaiser wrote with Benjamin Wilson explored the subject’s connection to the development of ballistic missile guidance and planetary radar, and the GPS history is, of course, closely related.

The origins of GPS

The idea of using satellites to assist navigation dates to the beginning of the Space Age in 1957. At the Johns Hopkins Applied Physics Laboratory, a contracting organization administered by the university, William Guier and George Weiffenbach developed a method for tracking the Soviet Sputnik satellite based on the Doppler shift of the signals it transmitted. It turned out to be about as accurate as radar tracking. Months later, their supervisor, Frank McClure, asked if they could reverse the method to use signals from satellites of known position to pinpoint one’s own position on Earth.

Funded by the new Advanced Research Projects Agency, work on the method proceeded quickly, and the first satellite of what became the US Navy’s “Transit” system launched in April 1960, and the system entered full operation in 1964. The Navy was initially interested in Transit to allow its Polaris submarines to precisely locate themselves, allowing them to launch nuclear missiles at targets more accurately. A version of Transit was made available for civilian use in 1967, and the system remained in operation until 1996, when its functions were handed over to GPS.

Whereas Transit offered accuracy to within about 200 meters—Kaiser’s article states 400 meters, but different sources offer different numbers—GPS promised to improve that by about two orders of magnitude by correlating time signals rather than Doppler shift measurements. Roger Easton at the Naval Research Laboratory came up with the idea around the same time that Transit began operating. To obtain the needed precision in time measurement, the system would employ atomic clocks, which were developed after World War II and were just then entering commercial production. This system was called “Timation,” a portmanteau of “time” and “navigation.”

Meanwhile, a collaboration between the Air Force Office of Scientific Research and the Aerospace Corporation, a government contractor, initiated a parallel effort called Project 621B. Whereas Timation focused on navigation, Project 621B was intended to improve weapons targeting. In the shadow of Transit, neither the Navy nor the Air Force project moved ahead quickly, and in April 1973 the Defense Department combined them into a single project called the NAVSTAR Global Positioning System. Its first satellite, NTS-2, finally launched in June 1977. (NTS-1 was a Timation test satellite; NTS stood for Navigation Technology Satellite.)

To turn to the point of Kaiser’s article, it was understood as early as the mid-1960s that general relativity would affect the accuracy of timekeeping satellites, when John Cocke, a Cornell-trained physicist at the Aerospace Corporation, published a generalized analysis of the subject in Physical Review Letters. University of Maryland physicist Carroll Alley, who had trained at Princeton and consulted for the Air Force, applied Cocke’s calculation to GPS. He found that orbiting clocks would advance at a rate 445 trillionths faster than clocks on the ground, resulting in a compounding error that would exhaust the system’s error budget within just a few seconds.

At the time, Alley encountered skepticism as to whether such effects would be real, and so NTS-2 was equipped with a switch that could turn the correction for relativity on and off. It turned out that the correction was indeed needed and that the measured discrepancy in clock rates closely matched the calculated prediction.

Did the military get relativity wrong?

GPS was a secret defense program, and only hints of its progress found their way into the public record. Kaiser’s article devotes considerable attention to four physicists, all trained in general relativity, who soon leveled a scathing outsider critique at it: Jeffrey Cohen, Harry Moses, Arnold Rosenblum, and Angelo Skalafuris.

Their critique hinged on the fact that there are three kinds of relativistic effects on time: time dilation, resulting from a large difference in objects’ relative speeds; gravitational redshift, resulting from differing positions in a gravitational field; and an effect deriving from rotational motion often referred to as the Sagnac effect. In 1977, motivated by academic interest, Cohen and Moses published an article in Physical Review Letters that highlighted the startlingly large effect that rotational motion would have in distorting time between orbiting satellites. As they learned about GPS, they became convinced the military was neglecting this same effect and recruited Rosenblum and Skalafuris to their effort to get to the bottom of it.

Their concern was fueled by an article published in the engineering journal Radio Science in 1979 by Neil Ashby, a physicist at the University of Colorado Boulder, and David Allan, chief of the Time and Frequency Coordination Group at the National Bureau of Standards’s Boulder laboratory. The article was one of the few public articulations of GPS’s approach to relativity, and, given where it was published, Cohen and Moses only discovered it several years after it appeared. When they did, they concluded it badly mishandled the general relativity problem, a view shared by Rosenblum and Skalafuris as well as two other experts they sent the paper to: Hans-Jürgen Seifert in Hamburg, Germany, and Christopher Clarke at the University of York in Britain.

The four American critics pressed their case in public and private, urging the Defense Department to look into this potentially fatal flaw in GPS. Kaiser does not mention the context, but the campaign in some ways echoed the outsider criticisms of the government’s anti-ballistic missile system proposals circa 1970 as well as of the Strategic Defense Initiative, which had just been announced in March 1983. It was an era when some physicists would feel emboldened to call out military folly.

Twin panels vindicate GPS

Of course, the critics did recognize they had little direct knowledge of the secret GPS program, and, while they requested funding to study the matter themselves, their campaign’s ultimate result was the creation of a pair of independent expert panels to investigate. One, set up by the Air Force Studies Board, was chaired by Washington University, St. Louis physicist Clifford Will and worked only with unclassified material. The other, carried out by the elite JASON study group, was given access to classified materials and chaired by University of California, Santa Barbara physicist Douglas Eardley, who also sat on Will’s panel.

Both panels concluded that the critics had misapprehended Ashby and Allen’s paper, with the Will panel’s report sympathetically noting that “some of [the paper’s] underlying assumptions and connections to fundamental theory are not spelled out as clearly as some theoretical physicists might hope.” Both reports explained that, unlike compounding errors produced by different clock rates, the error introduced by rotation was merely a time offset. Procedures for handling that error were not typically derived directly from relativity, but rather were hammered out through standards organizations under the rubric of the problem of “time transfer.” And in fact Ashby and Allen had participated in international efforts that demonstrated conventions for handling time offsets were sufficient even for the exacting requirements of GPS.

Soundly refuted, the critics did not further press their points. The JASON report suggested that, given that time transfer was a subject entrenched in the practical concerns of gray-literature reports, it would be good to produce a “pedagogical article” that would explain things to curious scientists “in the careful language of theoretical relativity.”

In any event, the episode did not slow the progress of the GPS satellite network, which was growing steadily by the time the two panel reports appeared in the mid-1980s. Its capabilities would be potently demonstrated during the 1991 Persian Gulf War. Commercial users were initially given access to a downgraded version of GPS, and the system’s full capabilities were made broadly available in 2000, paving the way for its ubiquitous use in the current century.

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William Thomas
American Institute of Physics
wthomas@aip.org

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