Most of us rely upon our GPS receivers without awareness of our debt to the imagination of Albert Einstein. He published his Special Theory of Relatvity in 1905 and his General Theory of Relatvity in 1915, but for decades afterward, nothing much was done with them; good old Newtonian physics worked just fine for earthbound and even space-bound adventures. The Global Positioning System (GPS, designed in 1973) was the first man-made system that requires relativistic factors to work, because it requires that clocks in different gravitational fields and traveling at different velocities tick in precise synchronism across great distances.
Here’s a good paper by Richard Pogge at astronomy.ohio-state.edu that explains this in easy-to-understand language. Briefly, GPS relies upon precise timing within nanoseconds (billionths of a second) to measure the radio signal transit time from each GPS satellite to our GPS receiver.
- Special Relativity predicts that the clocks onboard the satellites will, from our perspective, seem to tick slower because of their velocity relative to us.
- General Relativity predicts that a clock near a large mass (Earth) will tick slightly slower than a clock that’s in an orbiting satellite, away from the spacetime distortion caused by the Earth.
1 nanosecond = approx 1 foot at the speed of light
Let’s see . . . the radio signal travels at about 186,000 miles per second, and each satellite is in an orbit of about 11,000 miles, so when a satellite is directly overhead the signal transit time is about 11,000/186,000 or 0.059 seconds. An error of one second will result in an error of 186,000 miles. An error of one tenth of a second will result in an error of 18,600 miles. An error of one microsecond will result in an error of 0.186 miles, and an error of one nanosecond will result in an error of 0.00019 miles, or about one foot.
Because nanoseconds are significant, if General and Special Relativity were ignored, the Global Positioning System simply wouldn’t work. Each day, an error of about 10 kilometers would accumulate to previous errors.
We’re so grateful, Uncle Albert.
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