Each of the 31 active GPS satellites carries an atomic clock. These clocks are accurate to within 30 nanoseconds per day. They have to be — because GPS works by measuring the precise time it takes a radio signal to travel from a satellite to your phone, and tiny timing errors compound into massive position errors.

Here's the problem: those satellites move at about 14,000 kilometers per hour. According to Einstein's special relativity, fast-moving clocks tick more slowly than stationary ones. Each GPS clock loses 7 microseconds per day to its velocity.

But there's a second effect. GPS satellites orbit at 20,200 kilometers altitude — far above Earth's gravitational well. According to general relativity, clocks higher in a gravity field tick faster than clocks deeper in it. Each GPS clock gains 45 microseconds per day from being so far from Earth.

The two effects don't cancel. They leave a net gain of 38 microseconds per day. Tiny — except light travels 30 centimeters in a nanosecond. Thirty-eight microseconds of clock drift translates to 11 kilometers of position error per day.

If the satellites were not pre-corrected for relativity, GPS would be useless within hours of launch. So engineers do what physicists tell them: every GPS clock is deliberately slowed down before launch. They tick at 10.22999999543 MHz instead of exactly 10.23 MHz on Earth. After they reach orbit, relativity speeds them up to exactly 10.23 MHz.

Einstein published the equations in 1915. The first GPS satellite launched in 1978. There is now a multi-billion-dollar global navigation system whose entire architecture depends on a thought experiment from 110 years ago.