28 November 2011
The next line of that Chicago song is “Does anybody really care”. The answer is yes somebody does, and the “somebody’s” are those who keep your GPS working.
If you have not seen any of the Minute Physics videos on YouTube, they are a real treat and very informative. Check out this one on GPS and relativity:
You probably know that the atomic clocks have to be adjusted because of relativity, but you likely do not know the whole story. Hopefully, you learned in high school physics that clocks traveling at orbital velocities (of ~8 km/second) will run SLOWER than clocks on the ground, and they do indeed. However, there are other relativistic effects you might not know about.
Relativity ALSO says that clocks will run FASTER in a weaker gravity field, compared to those in a stronger field. A clock, slowly sinking into the immense gravity field surrounding a black hole, will run slower and slower. It will actually appear to come to a stop as it approaches the event horizon (compared to a clock far outside). With GPS this effect is very small, but the clocks in orbit are further away from the surface of the Earth, and are in a weaker gravity field, so this must be accounted for!
So to summarize, if you think that the clocks are made to run faster in orbit due to relativity, you will be wrong. The gravity field correction is 45,900 nanoseconds per day. In other words the clocks run faster by this amount. However, They run SLOWER by 7,200 nanoseconds per day due to their velocity. Subtracting gives a correction of plus 35,700 nanoseconds per day!
So the next time someone tells you that the clocks on the GPS run slower due to relativity, you can tell them, that actually they run slower and faster, but on the whole, faster! There are other relativistic effects, but these are the main two.
The cool things I learn watching physics lectures…