Trivia time: your GPS is an ongoing experiment that verifies the General and Special Theories of Relativity.
GPS satellites are constantly ticking, each tick being a time and position signal that has eight or nine decimal places of accuracy thanks to the atomic clocks they carry and the efforts of the US military in tracking all their satellites to within a few metres.
This allows anyone that hears a tick to know exactly how far away they are from the clock. If you don't know anything else except that distance, then all you know is that you're somewhere on a sphere which has that distance for its radius, and that satellite for its centre.
That's obviously not much help in determining where you are, since most of that sphere is in space and some of it will be under the Earth's crust. Even if your GPS ignores all the impossible points of the sphere*, it describes two honking great arcs across the surface. The exception to this is when the satellite is directly overhead, but that's like a stopped clock telling the right time twice a day.
So, you need more than one sphere, ie more than one satellite, to work out where you are. The US military has now got 32 of them up there now, meaning at least 4 are in direct line of sight no matter where you are on Earth at any time.
Your GPS device is a computer that works out the solution to the problem: where do I have to stand to be at the intersection of these spheres? That's always a unique solution, and due to the 8/9 decimal places of accuracy, it's an sphere 5-10 metres across.
The reason I've told you all this is because you've already heard in this thread and from other places that Relativistic effects are far too tiny to be noticed in normal daily life, and that's why we still teach people the incomplete Newtonian equations. Well, GPS is the one normal daily thing that works to such a high degree of accuracy that the difference shows up.
The velocity of the satellites means their time signals would rapidly come out of sync. That's Special Relativity - they're moving fast relative to us, so time moves more slowly for them.
The other effect is that of General Relativity. They're higher up Earth's gravity well and so time moves more quickly for them. The effect of General is larger than that of Special, so overall, we're running slow. Or they're running fast. It really is the same thing.
Oh, it's about ten kilometres/day's worth of inaccuracy.
*which it can't, unless it already knew the exact and entire topography of the Earth to a 5-10 metre accuracy, and if you had a device with that information stored in it, you'd no longer need GPS anyway.
posts
