In June 1977, a satellite called NTS-2 went into orbit carrying the first caesium atomic clock of the programme that would become the Global Positioning System — and carrying, too, a quiet institutional hedge. Not everyone on the project was fully convinced that Einstein's relativity would really show up in engineering hardware, so the clock was fitted with a switch: a frequency synthesizer that could apply the predicted relativistic correction, left off at launch. For about 20 days, ground stations watched the orbiting clock drift steadily away from clocks on Earth, at almost precisely the rate the equations demanded. Then the synthesizer was switched on, and the drift disappeared. Every satnav fix made since has been, in effect, a repeat of that experiment — a daily, planet-wide confirmation of the strangest idea in twentieth-century physics: that time does not run at the same rate everywhere.
GPS is, at heart, a constellation of flying clocks. At least 24 satellites circle about 20,200 km above the Earth, each completing two orbits a day and each carrying atomic clocks stable to around a billionth of a second. A receiver — a phone, a tractor, an airliner — fixes its position by comparing the precisely timestamped signals of at least four satellites, turning tiny differences in arrival time into distances. The margins are unforgiving: radio waves cover about 30 centimetres in a nanosecond, so a timing error of a mere millionth of a second becomes a position error of some 300 metres.
Two corrections, pulling opposite ways
Einstein interferes with those clocks twice, in opposite directions. Special relativity, his 1905 theory, says that a moving clock ticks slowly compared with one at rest; GPS satellites travel at about 14,000 km per hour, so their clocks fall behind Earth-bound ones by roughly 7 microseconds per day. General relativity, the 1915 theory of gravity, says that clocks deeper in a gravitational field run slower than clocks above it; at 20,200 km the Earth's pull is markedly weaker than at the surface, which lets the satellite clocks run fast by roughly 45 microseconds per day. Gravity wins the tug-of-war. The net result is that a GPS clock gains about 38 microseconds — 38,000 nanoseconds — on the ground every single day.
Thirty-eight millionths of a second sounds like pedantry until it is multiplied by the speed of light. Left uncorrected, the offset would corrupt positions by roughly 10 kilometres per day — and it would accumulate, morning after morning, until the world's most sophisticated navigation system could not reliably tell you which town you were in. The cure is disarmingly simple: the clocks are deliberately detuned before launch. Instead of ticking at their nominal 10.23 MHz, they are set fractionally slow, at 10.22999999543 MHz, so that once in orbit they appear from the ground to tick at exactly the right rate. Receivers then apply a further on-the-fly correction, because each satellite's slightly elliptical orbit keeps changing its speed and altitude — and therefore the rate of its time — as it swings around the Earth.
From Cold War to car dashboard
The system's ancestry runs straight back to Sputnik. In 1957, physicists at Johns Hopkins University's Applied Physics Laboratory tracked the Soviet satellite by the Doppler shift of its radio beeps and realised the trick worked in reverse: a satellite in a known orbit could locate a listener on the ground — the germ of the US Navy's Transit system for submarines. The first true GPS satellite flew in 1978, and the constellation was declared fully operational in 1995. Civilians owe their access partly to tragedy: after a Soviet fighter shot down Korean Air Lines Flight 007 in 1983, when the airliner strayed into forbidden airspace with 269 people aboard, President Reagan promised that GPS would be opened to civilian use. Even then, a deliberate blurring called Selective Availability capped civilian accuracy at about 100 metres; when it was switched off in May 2000, accuracy improved roughly tenfold overnight.
None of the underlying physics was truly in doubt. Hafele and Keating had already flown atomic clocks around the world on commercial airliners in 1971 and measured the gains and losses relativity predicted, and the rival systems that followed — Russia's GLONASS, Europe's Galileo, China's BeiDou — all bake in the same corrections. But there is something pleasing in the fact that the most abstract theory in modern physics has become a precondition for finding a petrol station. Einstein never learned to drive; every driver now navigates by his equations.
Quiz nuggets
- GPS satellite clocks run a net 38 microseconds a day fast: special relativity slows them by about 7 microseconds, while general relativity speeds them up by about 45.
- Without relativistic corrections, GPS position errors would grow by roughly 10 km every day.
- GPS atomic clocks are deliberately detuned before launch, from 10.23 MHz to 10.22999999543 MHz, to cancel the relativistic drift.
- The Soviet downing of Korean Air Lines Flight 007 in 1983 prompted Reagan to open GPS to civilians; the Selective Availability blur was switched off in May 2000.
- The 1971 Hafele–Keating experiment flew atomic clocks around the world on airliners and confirmed Einstein's time dilation.