In this case the clocks isn’t displaying a time. It’s counting “tics”. Using math, they can determine how often these tics occur and how many should occur in one second. They can also measure the extremely tiny variations in how often these tics occur. They aren’t EXACTLY on time, but the variations are extremely small. So small that the total number of tics it would count in 15 billion years is only going to be off by the number they calculated occur in one second.
The smaller the variation in these “tics”, the more accurate the clock is. The counted number will closer to the expected number over time. They can also start counting at a specific time and use the number they have counted to calculate what the current time is based on the number of tics that have occurred.
In this case the tics aren’t a series of mechanical gears turning a second hand, but a measurement of the vibrations of cesium atoms.
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