Science at the frontier often seems far removed from our everyday life. This is true to some extent, but not always. Applications unimagined at the time may crop up later, sometimes in unexpected and game-changing ways. This is the case for Albert Einstein’s two magnificent theories of relativity: the theory of special relativity (1905) and the theory of general relativity (1915).
When Einstein wrote his papers a hundred years ago, he was writing for specialists. Little would he know that his arcane theories would be used by the world today as a navigation tool known as Global Positioning System or GPS.
The GPS in a Nutshell
The GPS is a satellite-based navigation system that is now part of our daily lives. The GPS configuration consists of 24 satellites that orbit the earth twice a day, each carrying a precise atomic clock. With a modestly priced GPS device, a user can pick up radio signals from any of these satellites to determine latitude, longitude and altitude for navigation purposes. But there are snags to overcome to receive accurate transmissions. It is here that Einstein’s relativity theories have a surprising role in making this happen.
The reason for this has to do with the behavior of the satellite clocks. First, these clocks move at a speed of 14,000 km per hour, much faster than clocks on the Earth’s surface. Einstein’s theory of special relativity says that rapidly moving clocks tick more slowly – by about 7 microseconds per day (each microsecond is equal to a millionth of a second). Second, the clocks are positioned 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein’s theory of general relativity says that gravity curves space and time, which causes the orbiting clocks to tick by about 45 microseconds faster per day. The net effect of these distortions is that time on a GPS satellite clock advances faster than a surface clock by about 38 microseconds per day, which, if left uncorrected, would cause errors in global positions to accumulate at a rate of about 10 km a day!
GPS software solves this problem by using Einstein’s predictions to mathematically correct the difference in the ticking rate of the orbiting clocks and the atomic clocks at the GPS ground stations. The precision achieved is so remarkable that even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in a few seconds, which is the reason why the GPS receiver in your car gives accurate readings of position, speed, and course in real-time. So, the next time you access a GPS device on a highway adventure or for emergency road side assistance, remember that you are literally holding relativity in the palm of your hands. Ain’t that cool?
Here is a short video given by Professor Brian Cox (University of Manchester) explaining the usefulness of Einstein’s theories of relativity for GPS: https://www.instagram.com/tv/CNpoGNODHvH/?igshid=r44d76jstac0
A well-written and relatively simple explanation of GPS corrections is given by Richard W. Poggle, “Real-World Relativity: The GPS Navigation System”, available at http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html