On October 25, 1977, a team of physicists launched a pair of atomic clocks aboard a Navy aircraft to test one of the strangest predictions in physics: that time itself runs at different speeds depending on where you are and how fast you're moving. The clocks gained 47 nanoseconds during the flight—exactly as Einstein's equations predicted. Within two decades, engineers would need to account for this same effect to prevent a multibillion-dollar satellite navigation system from failing spectacularly.
When Nanoseconds Cost Kilometers
GPS satellites orbit Earth at 20,000 kilometers altitude, circling the planet twice a day at 14,000 kilometers per hour. Each satellite carries atomic clocks accurate to one nanosecond—one billionth of a second. This precision sounds excessive until you realize that light travels 30 centimeters in a nanosecond. A timing error of just 10 nanoseconds translates to three meters of position error on the ground. To deliver the meter-level accuracy that guides your phone's maps, those clocks must maintain nanosecond precision.
The problem is that Einstein's relativity predicts those clocks won't keep the same time as identical clocks on Earth's surface. Not approximately the same time. Measurably, catastrophically different time.
Two Opposing Forces
Special relativity—Einstein's 1905 theory—states that moving clocks tick slower than stationary ones. From our perspective on the ground, GPS satellite clocks are racing overhead at four kilometers per second. This velocity causes them to lose about seven microseconds per day compared to ground clocks.
General relativity, published in 1915, adds a twist: clocks in weaker gravitational fields tick faster than those in stronger fields. At orbital altitude, satellites experience roughly one-fourth the gravitational field strength we feel on Earth's surface. This weaker gravity causes satellite clocks to gain about 45 microseconds per day.
The two effects work in opposite directions. Subtract the seven-microsecond loss from the 45-microsecond gain, and you get a net gain of 38 microseconds per day. That might sound negligible. It isn't.
The Cost of Ignoring Einstein
Thirty-eight microseconds equals 38,000 nanoseconds. Light travels 11.4 kilometers in that time. Without correcting for relativity, GPS position errors would accumulate at roughly 10 kilometers per day. The system would become useless for navigation within two minutes of operation.
This isn't a theoretical concern that engineers could have dismissed as a rounding error. The relativistic effects are nearly 4,000 times larger than the acceptable error budget for the system. GPS was designed to provide position accuracy within meters, not kilometers. Ignoring Einstein would have meant ignoring the dominant source of error in the entire system.
Engineering Around Spacetime
GPS engineers solved this problem with elegant simplicity. Before launch, they program each satellite's atomic clock to tick at 10.22999999543 MHz instead of the standard 10.23 MHz. This pre-correction accounts for the net relativistic effect. Once the satellite reaches orbit, its "slow" clock speeds up to exactly the right rate.
Additional corrections happen in real time. The microprocessor in your phone receives orbital data from the satellites and calculates residual relativistic effects based on each satellite's precise position and velocity. These adjustments happen continuously, invisibly, every time you check your location.
The system works so seamlessly that most people never realize their phones are performing relativistic calculations dozens of times per second.
The Paradox at Sea Level
Einstein's theories create an odd coincidence at Earth's surface. A clock at the equator moves faster than one at the poles because of Earth's rotation—about 460 meters per second faster. Special relativity says this motion should make the equatorial clock tick slower. But Earth's rotation causes the planet to bulge at the equator, placing that clock slightly farther from Earth's center. General relativity says this weaker gravity should make the clock tick faster.
The two effects cancel almost exactly. A clock at sea level ticks at the same rate whether it's at the equator or the poles, despite the 460-meter-per-second velocity difference. This isn't a coincidence—Earth's spin rate determines its shape, which is why the cancellation works. But it only works at sea level. Move up to GPS orbital altitude, and the balance breaks.
Why Your Phone Needs a Theory From 1915
GPS represents the first technology that ordinary people use daily which simply cannot function without accounting for relativity. The system's designers didn't have a choice about whether to include Einstein's corrections. The relativistic effects aren't subtle perturbations that improve accuracy by a few percentage points. They're the dominant source of error, larger than every other factor combined.
This makes GPS unusual among technologies. Most engineering can ignore relativity because the effects are too small to matter at human scales and speeds. GPS operates at just the right combination of altitude and velocity for relativistic effects to become impossible to ignore. The satellites move fast enough and orbit high enough that both special and general relativity contribute significantly, but not so extreme that the engineering becomes impossible.
Every time your phone shows your location on a map, it's proving Einstein right. The blue dot that follows you down the street exists only because engineers accounted for the warping of spacetime. Your phone needs Einstein not as an abstraction, but as a practical matter of making the numbers work. Without those equations from 1915, the satellites overhead might as well be randomly guessing your position. The fact that they're not—that GPS works with meter-level accuracy billions of times a day—is perhaps the most widespread experimental confirmation of relativity ever devised.