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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."
It can't keep 'perfect time' for any length of time at all. Perfect means zero error. This might be an astoundingly accurate clock but that does not make it perfect.
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).
Thanks to GPS, the accuracy has improved, but now you need four clocks to get a 3-dimensional fix, and more to improve accuracy. Fortunately, on the open sea there isn't much blocking your view of the sky.
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wouldn't that make the concept of time fundamentally flawed?
In any given reference frame, time is a well-defined quantity. The fundamentally flawed concept here is the idea of some kind of universal time that passes at the same rate everywhere in the universe, because relativity tells us that the observed passage of time is affected by things like velocity, acceleration, and gravitation, and therefore varies between different reference frames -- and we have no objective reason to say that any particular reference frame in the universe is inherently superior.
So while the atomic clock might measure the local passage of time with near perfect accuracy in the reference frame where we place it, the results will just be approximate in any other reference frame.
We had this discussion a while ago, and I looked it up.
3 satellites for a basic fix. The 4th element is a ground station that corrects for most error. Further satellites can add a bit to accuracy but only with diminishing returns.
Best practice in the real world is four reference clocks or only one. With just three configured you run into the problem of ending up in the "just two clocks situation" more often then not. At which point, NTP is likely to oscillate between the two remaining good candidates (without the "prefer" keyword).
How you choose to configure NTP is a tricky art depending on how resilient you want to be and whether you have a local time source or need less then 5ms accuracy. For most situations (99% of servers), being within 500ms of the "internet time" is enough. Your goal is mostly to avoid the issue where the clock is off by tens of seconds or worse.
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No, that's wrong. Four satellites are needed to get a unique position solution. The ground stations only broadcast correction data that can move your position solution by a few meters at most.
No, it is NOT wrong. Your assertion is a common misconception. I assure you: I looked into this technology in depth.
Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation. (There are actually 2 solutions to the equation, but one of them makes no sense because it's at some point out in space.)
The 4th element is what is known as a "ground segment", which is used to increase the accuracy of the 3-satellite triangulation. Any further satellite signals are used only to further increase accuracy.
The 4th element is gradually being moved into orbit, which WILL make it a 4-satellite lock for accuracy boost. But the fact remains that your basic geolocation including elevation is still fundamentally based on 3 satellites. The 4th signal is only to improve accuracy for civilians, as they do not have access to the military-accurate signals.
Actually basic geometry does not say that at all. The receiver does not get given an accurate distance to each satellite, instead it is an inacurrate relative difference in distance. The intersection between the three spheres is a 3d region rather than a point. The extra fix is required to constrain the equations to a single point. There is more info here.
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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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This is incorrect. (I assure you: I *use* this technology in depth. :) )
The confusion arises from thinking about just the spatial component of the problem you are trying to solve, and not also the temporal. A GPS receiver has a generally *inaccurate* internal clock (which means it can be cheap, one of the brilliant parts of the design, IMO). Think of the "pseudorange" from a single satellite as providing a single equation with *four* unknowns: the three dimensions of position, and the *error* in your internal clock. To solve for all four unknowns, four equations (and thus four measurements) are needed.
Every GPS signal is the time...that's how it works.
Obviously yes. But the signal you hear from each satellite is offset by an unknown amount (assuming unknown time/position). So, you need to solve for 4 variables (time, x, y, z), so you require 4 satellites, as you said later on. If you know 1 of the variables (for instance, because you have an accurate local clock, or you guesstimate the altitude), you can survive on 3 satellites, but it will be less accurate.
Note that you need to know local time to nanosecond accuracy, so a regular quartz oscillator is only useful for a short time after synchronisation, and will drift away fairly quickly.