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Clock readings have a confidence interval

You may be able to read a machine’s time-of-day clock with microsecond or even nanosecond resolution. But even if you can get such a fine-grained measurement, that doesn’t mean the value is actually accurate to such precision. In fact, it most likely is not—as mentioned previously, the drift in an imprecise quartz clock can easily be several milliseconds, even if you synchronize with an NTP server on the local network every minute. With an NTP server on the public internet, the best possible accuracy is probably to the tens of milliseconds, and the error may easily spike to over 100 ms when there is network congestion [57].

Thus, it doesn’t make sense to think of a clock reading as a point in time—it is more like a range of times, within a confidence interval: for example, a system may be 95% confident that the time now is between 10.3 and 10.5 seconds past the minute, but it doesn’t know any more precisely than that [58]. If we only know the time +/- 100 ms, the microsecond digits in the timestamp are essentially meaningless.

The uncertainty bound can be calculated based on your time source. If you have a GPS receiver or atomic (caesium) clock directly attached to your computer, the expected error range is reported by the manufacturer. If you’re getting the time from a server, the uncertainty is based on the expected quartz drift since your last sync with the server, plus the NTP server’s uncertainty, plus the network round-trip time to the server (to a first approximation, and assuming you trust the server).

Unfortunately, most systems don’t expose this uncertainty: for example, when you call clock_gettime(), the return value doesn’t tell you the expected error of the timestamp, so you don’t know if its confidence interval is five milliseconds or five years.

An interesting exception is Google’s TrueTime API in Spanner [41], which explicitly reports the confidence interval on the local clock. When you ask it for the current time, you get back two values: [earliest, latest], which are the earliest possible and the latest possible timestamp. Based on its uncertainty calculations, the clock knows that the actual current time is somewhere within that interval. The width of the interval depends, among other things, on how long it has been since the local quartz clock was last synchronized with a more accurate clock source.

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