GPS just keeps on giving… I seem to find out about more mathematics in GPS all the time. Einstein published his theory of special relativity in 1905, and a (more mathematically difficult) theory of general relativity in 1915. Special relativity predicts that clocks in orbit around the earth will tick slower than our clocks, by about 7 microseconds per day. General relativity predicts that clocks in orbit will tick faster than our clocks, by about 45 microseconds per day, if you do your curved space-time calculations correctly. Put together, the net effect is that clocks in GPS satellites would go about 38 microseconds faster per day than our clocks.
If this error were allowed, it would quickly lead to huge errors in GPS readings. Errors of only 20 nanoseconds are allowed (1 microsecond = 1,000 nanoseconds). So apparently GPS clocks are designed to compensate for the effects of Einstein’s theories of relativity.
Read more details here. I suppose this is another proof that general relativity is “correct.”
In other news, just today there is a post on BBC about an up and coming use of GPS. Your mobile phone transmits your GPS received location to your phone company all the time. When you are near a shop, you will receive a text message from your bank saying you can borrow money at a low low rate! So you can go ahead and buy that new coat. Targeted offers based on your location will be big in the future, and they are already here, in fact. The Turkish are good at these algorithms.