Comment by cnvogel | Hacker News Reader

Comment by cnvogel | Hacker News Reader

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    > atomic clocks in general is that they have very good
    > short term stability, but not-so-great long-term
    > stability

Well... The normal number to look at is the "Allan Variance". Over a timescale of days (100'000 seconds) a good rubidium will achieve about 10^-12, which is 10ns. A hydrogen maser will have 10^-13 or 10^-14 over even longer timescales. This is pretty great long-term stability in my book. A good, but undisciplined, quartz oscillator will have 10^-12 over timescales of hours.

http://ivs.nict.go.jp/mirror/publications/gm2002/takahei/img... http://www.ke5fx.com/rb.htm http://www.thinksrs.com/assets/instr/PRS10/PRS10diag2LG.gif

By definition, anything steered by GPS will have infinite precision for infinitely long time-scales, as GPS time and UTC time ultimately are steered such that they are within a certain tolerance of each other.

http://www.leapsecond.com/pages/tbolt-tc/

And UTC time is the pretty elaborate average of ensembles of atomic clocks, hence atomic clocks produce the international reference time there is.

You can, of course, improve the long-term stability of any clock by locking it to a GPS (or other means of time-signal distribution). And for a good Caseium that might only require you to look at the phase, and slightly nudge a potentiometer (magnetic correction field adjustment) on the front by a tiny amount every week. But atomic clocks in general are pretty darn impressive.

UPDATE: This presentaiton has all the interesting plots combined, it seems: http://www.hipster.net/ShadNygren_Atomic_Clocks_for_Amateur_... (pages 45 and following).

Nice presentation! Thanks for the link!

The particular nit you pick here is a fair one, if you take my comment literally, rather than as the (over?)simplification of a complex concept I was trying to summarize.

Yes, in absolute terms, an atomic clock will have excellent stability over the long term in its own frame of reference. As long as you don't need your atomic clock to match any other clock in the universe, the long-term stability is excellent.

The particular topic being discussed here, though, is equipment that is designed to synchronize events across a large area. Even atomic clocks that are literally 100% accurate will diverge if installed in different locations. So if you want your atomic clock to actually be able to tell you what time it is (in a way that matches up closely with anyone else), you have to constantly be adjusting it to match a common standard (e.g. UTC)

These adjustments are a form of instability, since to correct for changes, you have to make your seconds either faster or slower than they actually are locally, on a constantly-changing basis, or you have to step your time and have less (or more) than (Y - X) time actually elapse between timestamps X and Y.

As soon as you move beyond a single frame of reference, you can't have both short and long term stability.

I suppose I could have used a different word than 'stability', but that seemed to get across the underlying effect best. I suppose another way of saying it (that is more correct) is that atomic clocks are great for telling you how much time has passed (in your local reference frame), but not so great for telling you what time it is. GPS is great for telling you what time it is, but not so great for telling you how much time has passed (in your local reference frame).

(The best clocks for timekeeping, of course, are atomic clocks disciplined by a common reference like GPS, which gives you the option of deciding your own long term vs. short term tradeoff however you'd like. But the original question was "why do we need GPS at all, and not just atomic clocks?".)

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