New Atomic Clock Reaches the Boundaries of Timekeeping
SonicSpike sends an article from NPR about a high-tech clock being built at the University of Colorado Boulder. It's more precise than any clock before, able to keep perfect time for five billion years. "At the heart of this new clock is the element strontium. Inside a small chamber, the strontium atoms are suspended in a lattice of crisscrossing laser beams. Researchers then give them a little ping, like ringing a bell. The strontium vibrates at an incredibly fast frequency. It's a natural atomic metronome ticking out teeny, teeny fractions of a second." But this precision leads to a problem: the relativistic differences between keeping the clock on the floor versus hanging it on the wall now introduce more significant fluctuations than the clock itself. "Tiny shifts in the earth's crust can throw it off, even when it's sitting still. Even if two of them are synchronized, their different rates of ticking mean they will soon be out of synch. They will never agree. The world's current time is coordinated between atomic clocks all over the planet. But that can't happen with the new one."
Moving faster causes time to slow down (special relativity), but so does beeing in a deeper gravitational well (general relativity). As you move away from the Earth, both effects have opposite (but not equal) magnitude. I'm too lazy to do the math right now, but here's a walkthrough (for the case of GPS satellites, but the same equations hold; you just need to know the distance from Earth's center to Death Valley and to Mount Everest, and work out their linear velocity from that).
No, it is NOT wrong. Your assertion is a common misconception. I assure you: I looked into this technology in depth.
Then perhaps you can provide a reference?
Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation.
No: basic geometry dictates that, to find a position in three dimensions, you need three measurements of distance. The trouble is that the signal from one satellite gives you no information about your position: the signal (roughly speaking) tells you where the satellite is, and the time by that satellite's clock - but since you have nothing to compare it against, you have no idea how long that signal took to reach you, so you get no information about your position.
It's similar to if you asked me my height, and I said "I'm a foot taller than Fred". If you don't know how tall Fred is, you're no nearer to knowing how tall I am, even though you've been given one measurement. Sure, if you look at probability distributions of height you can have a good guess at how tall I might be, and this is similar to getting a 2D fix (where you assume that your elevation is "at or near the surface of the Earth"), but you can't know for certain that one of both of us don't have unusual heights.
Once you have a signal from two satellites, you can subtract the timestamps, which doesn't directly tell you position, but tells you which satellite is closer to your position, and by how much. This allows you to constrain your position in one dimension (i.e. you still have two degrees of freedom - a surface rather than a solid), and another satellite's signal will give you another constraint (pinning you down to a line); only with a fourth satellite can you determine your position precisely (well, actually the solution can give more than one point but generally only one is realistic).
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