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Global Positioning System (GPS) relies on Einstein's theories
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U.S. Library of Congress - Famous People
Here's a question for you! Jack and Jill are 1st cousins who were born in Chicago on January 1, 1930 at the exact same nanosecond. Shortly after her birth, Jill and her family move to Denver where she went to school, raised her family, attended church and grew old with her husband and high school sweetheart Bill. Bill is planning Jill's 80th birthday next January.
Shortly after his birth, Jack's mother moved to Hollywood to pursue her dream of becoming a famous film actress. Unfortunately for young Jack, things did not work out so well for him and his mother. Unlike his Denver cousin Jill, Jack spent all his life in Los Angeles. He hung around with the wrong crowd, dropped out of school, spent years in and out of local jails, got hooked on various drugs and could never maintain a stable relationship. Miraculously, Jack remains alive and kicking in LA and has just accepted Bill's invitation to travel to Denver to celebrate his 80th birthday along with his cousin Jill.
Question: When Jack and Jill meet on January 1, 2009 to celebrate their 80th birthday, which of the two cousins will be older?
Before answering that question, a few Technology insights which will provide us with some clues:
When Jack drives to Denver for the joint celebration on January 1, 2010, he plans to use his new GPS. When we refer to "Global Positioning System" (GPS) we usually mean a GPS receiver. The current GPS configuration consists of 27 earth orbiting satellites (24 operational and 3 back-up satellites in case of failure). Each of the 24 operational satellites in the GPS configuration orbits at an altitude of 12,000 miles from the ground and has an orbital speed of about 7,500 miles per hour. The orbits of each of these 3000 to 4000 pound orbs are synchronized to make two complete rotations a day and are arranged so that at anytime, anywhere on Earth, there are no fewer than four satellites visible in the sky. A GPS receiver's task is to find at least four of these satellites, calculate the distance to each and analyze that information to calculate its own location. This process is based upon a simple mathematical principle called trilateration.
The precision of current GPS technology is phenomenal: even a simple hand-held GPS receiver can determine your exact location on the surface of the Earth to within 5 to 10 meters in only a few seconds. A GPS receiver in Jack's car will give accurate readings of its position, speed, and heading in real-time as it travels from LA to Denver.
To achieve this level of precision, the clocks ticking from the GPS satellites must be known to an accuracy of 20-30 nanoseconds ( a nanosecond is equal to one billionth or .0000000001 of a second).
Because Jack's car detects the satellites in motion relative to it, Einstein's theory of Special Relativity predicts that we should see the clocks on the satellites ticking more slowly. In fact, the on-board atomic clocks on the satellites should fall behind the 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 (a microsecond is equal to one millionth or .00000001 of a second). To complicate things further, a prediction of Einstein's General Relativity is that clocks closer to a massive object such as the Earth's will seem to tick more slowly than those clocks located further away from. A calculation using General Relativity predicts that the clock in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
The combination of these special and general relativistic effects means that the clocks on board each satellite should tick faster than the clocks on the ground by 38 microseconds per day (45-7=38). If these time discrepancies were not properly taken into account, errors in global positions would continue to accumulate at a rate of about 6 miles each day so that instead of Jack reaching Jill's front door in Denver, Jack may wind up in Boulder Colorado.
So while his liver may not look like it, it takes an Einstein to figure out the Jack is actually younger than Jill. Jill has lived her 80 years in Denver's higher elevation which is in a slightly weaker gravitational field than Los Angeles. Since LA's clocks are closer to the center of the Earth, they run slower relative to Denver's clocks. Accordingly, Jack is actually few nanoseconds younger than Jill. Way to go Jack!
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