It's been a hundred years since Einstein first formulated his theory of relativity, as NOVA intends to celebrate on Einstein's Big Idea. However, I encountered another interesting fact which boggled my mind.
The GPS system for computing a person's location on the surface of the Earth works simply by placing a bunch of clocks in orbit which transmit their current time. If you know the current time on the Earth and you know the current time on a satellite in Earth's orbit as transmitted to you, you can measure your distance from you to that satellite: light moves at approximately one foot per nanosecond, so if you know the time to within a nanosecond of when the signal was sent and when you received it, you can get the distance quite easily.
Of course if you have a handheld GPS device, it cannot have a nanosecondaccurate clock. So what happens is you get the current time from four or five satellites, and knowing their exact position in space and the time when they sent their signal, and you can solve for the only point on Earth by solving the simultaneous equations for distance and current time. The side effect of those calculation is not only do you know where you are, but to the nanosecond what time it currently is.
But there's a rub.
According to Einstein's General Theory of Relativity states, amongst other things, that a clock in a gravitational field will run slower than a clock that is not as deep in a gravitational field. What this means is that, for example, a clock on a satellite in Earth's orbit moves slightly faster than a clock on the surface of the Earth: the General Theory of Relativity predicts that the difference, while small, is measurable.
And it turns out that the difference is around 442.5 parts in 10^{12} faster than clocks on the ground. This results in an error of around 38 microseconds per day.
While that sounds like a small amount, realize that light travels around 1,000 feet per microsecond, so an error of 38 microseconds corresponds to an error of around 7 miles per day.
So how do we compensate for this relativistic error?
Well, the clocks on GPS satellites are adjusted to run slightly slow to compensate. What they did was to compute the relativistic shift in the spacetime frame for satellites in orbit approximately 4.2 Earth radiiassuming a perfectly spherical Earth in an otherwise empty universeand adjusted the clocks accordingly.
Now this works pretty well. But to get better accuracy, you need accuracy to within a nanosecondpreferably to 100's of picoseconds. And to get that level of accuracy you need to take into account the gravitational wells of the other major bodies in our solar systemincluding the Sun, the Moon, Jupiter and Saturn. Their combined errors contribute to the +/ 20 nanosecond shift in the GPS system, which is why your GPS is only accurate to around 20 feet or so.
It's the fact that the error of 20 feet in my GPS gadget is caused by the relativistic space time distortion caused by the Moon, Jupiter and Saturn which causes me to think how fucking amazing modern technology is!



