Once Before Time - Martin Bojowald [16]
2. Objects move along trajectories in space-time, but space-time itself is changing. (Orbita [Orbit]), 2007. Sculpture and photograph: Gianni Caravaggio.)
The global positioning system (GPS) is an example of an applied technology with crucial general relativistic effects. This is a system of twenty-four satellites, all carrying atomic clocks. They are distributed around the earth so that every place is almost always in reach of at least four satellites above the horizon. Each satellite sends out regular signals encoding its position and the time its clock measures. Comparing the signals of several satellites at a given point on the earth’s surface allows one to compute one’s position very precisely, usually with an accuracy of five to ten centimeters!8
If one were to ignore relativity while computing the travel time of GPS signals, the resulting position measurements would be useless. After just two minutes of uncorrected clock time in orbit, clear deviations would be seen in the measured positions on Earth; waiting a single day would make measurements deviate from the correct values by up to ten kilometers. The role of general relativity in this system is of enormous importance, but it is very complicated and for a long time remained incompletely understood. The first GPS satellites were launched in 1978, but in 1979, 1985, and finally 1995—the year of the system’s official inauguration—entire conferences were still being organized with the aim of understanding the role of general relativity in the GPS. Even so, an erroneous technical report was apparently published in 1996. Examples of difficulties are the role of synchronization and of the comparison of clocks on different satellites, and even the possible influence of the sun’s gravity, whose strength would differ slightly on the day and night sides of Earth with their different distances from the sun. The latter turned out not to be important, given the current precision of clocks. (Which, to be sure, are very precise: They are rubidium clocks, whose measured times after ten days would differ by just half a nanosecond, that is, by half a billionth of a second.) But the changing gravitational field around Earth, and in particular its deviations from a perfect spherical shape caused by the oblong nature of the rotating planet, are of great importance to the clocks’ precision. One can also ask whether special relativistic or general relativistic effects are dominant. At the altitude of GPS, about 27,500 kilometers, the clear winner is general relativity.
GPS applications are becoming more and more numerous, for instance with a cell phone feature especially popular in predominantly Islamic countries that always shows the precise direction to Mecca. The military applications for which the system was initially developed are by now clearly a minority, and those of geological exploration dominate, such as releasing light GPS devices in tropical storms to measure their temperature and pressure with position resolution. Also, the motion of the earth’s crust as a consequence of tectonics can be followed precisely, and these data can perhaps one day be used to predict earthquakes. Even the motion and deformation of buildings or bridges under weight can be registered with the enormous precision of GPS. In agriculture, GPS is sometimes used to distribute fertilizer and pesticides very precisely, and archaeologists use it to find and map ancient historical sites. GPS, a child of relativity, now provides feedback on the exploration of general relativity itself: It serves to define a worldwide clock standard, which can then be used, for instance, to precisely measure the orbits in Hulse and Taylor’s double pulsar.
All this shows the technological relevance of relativity theory, whose implications may be tiny in quantitative terms but are important given the current sensitivity of applications. When considering cosmic scales, on the other hand, the consequences of relativity become immense. Time is no longer rigid, as it was for Newton, but is influenced by matter in the universe.