Real-World Relativity: The GPS Navigation System
People often ask me "What good is Relativity?" It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.
Consider for a moment that when you are riding in a commercial airliner, the pilot and crew are navigating to your destination with the aid of the Global Positioning System (GPS). Further, many luxury cars now come with built-in navigation systems that include GPS receivers with digital maps, and you can purchase hand-held GPS navigation units that will give you your position on the Earth (latitude, longitude, and ...view middle of the document...
The precision is phenomenal: even a simple hand-held GPS receiver can determine yourabsoluteÂ position on the surface of the Earth to within 5 to 10 meters in only a few seconds (with differential techiques that compare two nearby receivers, precisions of order centimeters or millimeters in relative position are often obtained in under an hour or so). A GPS receiver in a car can give accurate readings of position, speed, and heading in real-time!
To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.
Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see theÂ Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.
Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction ofÂ General RelativityÂ is that clocks closer to a massive object will seem to tick more slowly than those located further away (see theÂ Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be tickingÂ fasterÂ than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
The combination of these two relativitic effects means that...