Comment by ludicrousdispla
Comment by ludicrousdispla a day ago
... a man with one clock knows what time it is, but a man with two can never be sure.
Comment by ludicrousdispla a day ago
... a man with one clock knows what time it is, but a man with two can never be sure.
The most important reason is that the frequencies of optical clocks can be very different, from ultraviolet to infrared.
When the frequency of one clock is 10 times greater than the frequency of another, it is hard to find a significance for any other kind of mean, except the geometric.
More clearly, if the input frequencies have the same relative uncertainty, the geometric mean will preserve that relative uncertainty. If the input frequencies have different relative uncertainties, the geometric mean will have a relative uncertainty that is intermediate between them.
Other kinds of means do not offer guarantees about the relative uncertainty when the ratio of the inputs is high. If one frequency is much bigger than the others, the arithmetic mean will depend only on that frequency, the others will not matter.
Unless he uses the ticks coming from the two clocks to generate a tick signal whose frequency is the geometric mean of the 2 tick frequencies (possibly by using a weighted mean, when one clock is known to be better than the other), and then displays the time by counting the ticks from the synthetic tick signal.
This is how the redefinition of the second will work, by using many different kinds of optical clocks, instead of the single cesium-based microwave clock that is used now.
In fact, today the big laboratories have many atomic clocks, whose clock frequencies are averaged to compute the time, even when the clocks are of the same kind. The international atomic time, TAI, is computed by averaging the clocks of all important laboratories.