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We say that atomic clocks are the most accurate clocks ever made, they may lose or gain $x$ seconds in $y$ years. How do we find this uncertainty because we do not have an ideal clock to compare with the clock that we made?

RogUE
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    We measure multiple clocks against each other and compare the statistical errors. This assumes that the clocks do not have the same systematic errors, of course. In practice this is controlled by using different technologies with different systematic errors and by having multiple clocks of the same technology built and operated by different groups of people in different locations of the world. In addition we are also comparing against precision clocks provided by nature, like pulsars. While those are not quite as accurate as our atomic clocks, they are guaranteed to be independent of us. – CuriousOne Dec 18 '14 at 14:31
  • @CuriousOne we are also comparing against precision clocks provided by nature, like pulsars. How is this possible? They are far away from us, aren't they? – RogUE Dec 18 '14 at 14:38
  • The nearest known pulsars are hundreds of lightyears away. In cosmic terms that's the front yard. – CuriousOne Dec 18 '14 at 14:40
  • @CuriousOne If we have taken the speed of light into account and do the calculations to use pulsars to check accuracy, I think that we do not know the actual distance between earth and a pulsar, also the distance is changing constantly( red shift and in other means), so they are not very accurate, actually,we are not able to use them for time keeping(or testing) due to our limited technology. – RogUE Dec 18 '14 at 14:49
  • Absolute distance doesn't matter for the precision of a clock. The largest changes to the frequency of a pulsar are probably due to the motion of the Earth in the solar system and the rotation of the planet, both of which are known with very high precision. As I said, pulsars are not as good as clocks as our atomic clocks, but they give us an independent means to verify our local time keeping and they are valuable resources for that purpose. – CuriousOne Dec 18 '14 at 14:53
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    @CuriousOne All the clocks that we posses will not keep the correct time and we do not have an ideal clock, then what's the point in comparing these clocks with each other, if this is the way we use to estimate the accuracy of our clocks, then there must be error in the estimated error(or accuracy) of a clock. – RogUE Dec 18 '14 at 14:59
  • Of course there are errors. Nothing is perfect in life. If you are having issues with that, then I am afraid that physics can't help. – CuriousOne Dec 18 '14 at 15:03
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    @CuriousOne I am really sorry. Just because of curiosity, I asked this much. Thanks for your 'comments'. – RogUE Dec 18 '14 at 15:08
  • No problem. :-) Most everybody goes through that phase where any level of uncertainty feels threatening or disappointing, even (or especially) in science. People are looking for an anchor... until they notice that floating freely in infinity can actually be a lot of fun! Have fun and relax! The answers will come! – CuriousOne Dec 18 '14 at 15:11
  • The fundamental reason that atomic clocks are so accurate is that they are just counting devices. You count cycles. And when you count enough of them the bits that you may have missed at the beginning and the end get too small (fractionally) to care about. Then the problem becomes one of checking that you don't miss some as you go along and that is easier to do in comparison mode. – dmckee --- ex-moderator kitten Dec 19 '14 at 00:04
  • Related https://physics.stackexchange.com/q/574866/226902 https://physics.stackexchange.com/q/22091/226902 https://physics.stackexchange.com/q/98398/226902 https://physics.stackexchange.com/q/612447/226902 https://physics.stackexchange.com/q/591657/226902 – Quillo Sep 23 '23 at 15:51

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The nearest we have to a standard is International Atomic Time. This is:

TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide.

The errors in individual clocks can be assessed by comparing them to the weighted average.

Re the mention of pulsars in your comment, pulsars slow down over time and indeed atomic clocks are used to track their slowing. Also pulsars occasionally glitch. So atomic clocks are more accurate than pulsars are.

John Rennie
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