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Assume the time standard clocks and any memories about the time standard are destroyed. Can we recover the time standard again exactly?

Recovering the time standard again means we can determine the date and time that are exactly the same as the destroyed time standard clocks will show (if they are not destroyed).

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The answers (3) show different meaning for that "time standard". Could You please specify what You mean with that? –  Georg Jan 18 '11 at 21:27
    
@Georg: I guess it was an implicit question inside the question : what is a time standard. I guess my answer was not clear enough but I wanted to address both frequency and phase, with a link to @Steve Allen's website on a similar effort made for historic period. Steve then provided an answer giving more precision on the accuracy of the phase reconstruction. Then @Tom came, misunderstood my answer and said it was impossible. But I'm pretty sure the 3 answers (Tom, Steve and myself) take the time standard to be the same thing (i.e. frequency + phase) and understood the question the same way –  Frédéric Grosshans Jan 20 '11 at 16:39
    
Hello Frederic, what I meant is that xports question makes not clear, whether he speaks of a rubidium clock (or what ever kind of atomic clock is used today as a time standard, "etalon" Zeitnormal) which allows to "produce" a second, or if he speaks of the "absolute time" which runs since some 30 (?) years now, saying that it is that much date and time, not a second later or sooner. This absolute time, I think, would be lost, new built atomic clocks would start from a new startpoint. Georg –  Georg Jan 20 '11 at 22:42
    
@Georg : Anyway, I inended to answer both questions. Do you think I should edit my answer to make this clearer ? –  Frédéric Grosshans Jan 21 '11 at 14:18
    
Anything we did once (like establishing a time standard) we can do twice. (Maybe better the second time.) –  Mike Dunlavey Dec 1 '11 at 14:00
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3 Answers

up vote 15 down vote accepted

It depends on your definition of "any memories". If you don't remember what a second is, there is no solution.

If you remember the "old" definition (a day has 24 h on 60 minutes, each of it is 60 s), and live on Earth not to far from now, you can rebuild an approximate time standard. If you remember the modern definition, i.e.

(the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.)

you can reconstruct it as good as we can now, even if you are in a spaceship far away from Earth.

That would give you a second duration, from which you can define a time-scale. The next-step is to synchronize your new time-scal with the old time-scale. This is basically what historian do when they translate Egyptian or Mayan date in our modern system of datation. To have something precise, you basically need some record of an astronomical event.

The best analogue I can see is the work discussed here and here, where the difference between the solar time and atomic time is extrapolated in the past, before the atomic clock era. There are 10 s error bars around 1700, and 3h error bar for the year 1000 BC.

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Very nice and informative explanation. Thank you. –  xport Nov 30 '10 at 5:15
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"Imagine for a moment what would happen if, just as a practical joke, someone found a way to stop all atomic clocks, just for a short time. This would cause such a tremendous disturbance in world affairs that the loss of TAI would be a totally insignificant matter! Furthermore, when it came to setting it up again, the phase of TAI could be retrieved to within a few tenths of a microsecond by observations of rapidly rotating pulsars..."

-- Claude Audoin & Bernard Guinot, p. 252, sec. 7.3.1 of "The Measurement of Time: Time, Frequency and the Atomic Clock", Cambridge University Press, 2001

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Uh, what's TAI? –  ptomato Nov 30 '10 at 7:44
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@ptomato: en.wikipedia.org/wiki/International_Atomic_Time –  KennyTM Nov 30 '10 at 8:03
    
The phase could not be recovered from pulsars. How would you know how many pulses passed? 1000? 1001? Even knowing the spin-down rates, pulsars have glitches, so unless they are being continuously monitored (which means you are simply watching a clock the whole time anyway), phase information is lost. –  Chris White Jun 16 '13 at 4:45
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Recover the time standard? No. Time is the phase of an oscillator, i.e. keeping track of time is counting oscillations. To recover the phase, you have to have another clock, because a clock is something that keeps track of the phase. No memory = no knowledge of the time.

Frédéric's reply concerns the frequency of the oscillation, which is reproducible. That will tell you the length of a second, but not which second (or fraction thereof) it is.

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You did not read my answer to the end : the frequency is the first part, and I address the second part after saying "The next-step is to synchronize your new time-scal with the old time-scale". It's mainly on external websites, but the 10s error par around 1700 is an arror bar on the phase. @Steve Allen also give deatils on how to recover the phase within a few tenths of a microsecond. –  Frédéric Grosshans Jan 20 '11 at 16:26
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