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?
$\begingroup$ 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. $\endgroup$– CuriousOneDec 18, 2014 at 14:31
$\begingroup$ @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? $\endgroup$– RogUEDec 18, 2014 at 14:38
$\begingroup$ The nearest known pulsars are hundreds of lightyears away. In cosmic terms that's the front yard. $\endgroup$– CuriousOneDec 18, 2014 at 14:40
$\begingroup$ @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. $\endgroup$– RogUEDec 18, 2014 at 14:49
$\begingroup$ 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. $\endgroup$– CuriousOneDec 18, 2014 at 14:53
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.