Every time you open a map on your phone, something extraordinary happens. Your device receives signals from at least four satellites orbiting 20,200 km (12,550 mi) above the Earth, compares their timing to nanosecond precision, and calculates your position to within a few metres.
For that to work, Einstein has to be right. Twice.
The first problem is special relativity. GPS satellites move at about 3.9 km/s (8,700 mph). Einstein's 1905 theory says a moving clock ticks slightly slow. GPS clocks lose about 7 microseconds per day from their speed.
The second problem is general relativity. GPS satellites orbit in weaker gravity than clocks on Earth's surface. Einstein's 1915 theory says a clock in weaker gravity ticks faster. GPS clocks gain about 45 microseconds per day from their altitude.
Speed slows the clocks. Altitude speeds them up. Net result: GPS clocks run 38 microseconds per day faster than clocks on the ground.
Thirty-eight microseconds sounds like nothing. But light travels about 300 metres (984 ft) in a single microsecond. GPS works by multiplying signal travel time by the speed of light. A timing error of 38 microseconds becomes a position error of more than 11 kilometres (7 mi). Every day.
For comparison, here is how the error accumulates:
- After 2 minutes: position fix is already wrong (Pogge, Ohio State)
- After 1 hour: ~400 metres (1,300 ft) off
- After 1 day: ~10 km (6 mi) off
- After 1 week: ~70 km (43 mi) off
The engineers who built GPS knew this. Their solution is one of the neatest pieces of applied physics in history: every GPS satellite clock is deliberately set to run slow before launch. The atomic clocks are tuned to 10.22999999543 MHz instead of the nominal 10.23 MHz — precisely slow enough that once relativity speeds them up in orbit, they tick at exactly the right rate as seen from the ground.
A theory published in 1905 by a patent clerk in Switzerland is silently running inside every phone, every car sat-nav, every aircraft instrument, every delivery route, every dating app's distance calculation — billions of times a day across the planet.
The next time your phone tells you to turn left in 200 metres, remember: that instruction is only correct because Einstein was right about the nature of time itself.