http://leapsecond.com/great2005/

In what amount of time? Not instantly, right?

How hard or expensive would it be for a reasonably equipped lab to build their own optical clock though? I see there are optical clocks the size of few rack units on the market for a rather hefty price, are the materials needed that expensive or is it just the expertise?

How can anything … you know what? Never mind. No matter what answer anyone provides, I won’t understand.

https://github.com/jauderho/nts-servers/tree/main

it's a human construct so whatever is agreed upon is correct.

https://en.wikipedia.org/wiki/Second#Atomic_definition

For example, every electron is exactly the same as every other electron, they do not vary in the slightest. You utilize properties like that to make exact references to time.

For example even very small magnetic fields will change the clock speed, thermal changes will as well (so will lots of other things). So you try to shield from that, and keep the temperature stable (and of course you need to figure out every other things that could add noise).

Then you measure all those influences that you just are unable to control, and calculate what affect they have on the clock, and that's your accuracy number.

One way to directly measure that, instead of calculate it, is to have two identical clocks, synchronize them, and let them run. Then compare them, and see if they differ. (Watch out for relativity messing with time.)

You can build two and see how much they shift relative to each other. That gives you precision.

So what's the point of a clock if you just define it to be correct? Again, having two clocks is what makes it interesting. Some people have commented that according to general relatively there will be measuralbe time dilation, but there are other fun experiments, e.g.

- Measure shift of fundamental "constants": If you have two clocks that use different elements, the frequency ratio can be related to some things we thought were constants in the universe. If they shift, they aren't constant.

- Look for preferred directions in space: does one clock give a different reading if you turn it on its side?

- Some theories predict that dark matter might induce a frequency shift in these clocks. Put the clocks far apart and look for spacial modulations in the dark matter density.

- Measure anything else that had to be tweaked to make the clock stable. This includes the magnetic field, for example, so the clock is also a really sensitive magnetometer.

Being able to count trillions of ticks is entirely possible in clocks or rotary encoders, just nobody bothers to do so on rotary encoders very often.

They are used together with a laser (which is a component included in a so-called frequency comb, which acts as a frequency divider between the hundreds of THz of the optical signal and some hundreds of MHz or a few GHz of a clock signal that can be counted with a digital counter; that digital counter could be used as a date and time clock, except that you would need more such optical clocks, to guard against downtime; the present optical clocks do not succeed to operate for very long times before needing a reset because the trapped ion has been lost from the trap or the neutral atoms have been lost from the optical lattice; therefore you need many of them to implement a continuous time scale).

The laser is the one that provides a continuous signal. In this case the laser produces infrared light in the same band as the lasers used for optical fiber communications, and it is based on glass doped with erbium and ytterbium. The frequency of the laser is adjusted to match some resonance frequency of the trapped ion (in this case a submultiple of the frequency, because the frequency of the transition used in the aluminum ion is very high, in ultraviolet). For very short time intervals, when it cannot follow the reference frequency, because that must be filtered of noise, the stability of the laser frequency is determined by a resonant cavity made of silicon (which is transparent for the infrared light of the laser), which is cooled at a very low temperature, in order to improve its quality factor.

So this is similar to the behavior of the clock of a computer, which for long time intervals has the stability of the clocks used by the NTP servers used by it for synchronization, but for short time intervals it has the stability of its internal quartz oscillator.

This new optical atomic clock has the lowest ever uncertainty for the value of its reference frequency, but being a trapped single ion clock it has a higher noise than the clocks based on lattices of neutral atoms (because those can use thousands of atoms instead of one ion), so its output signal must be averaged over long times (e.g. many days) in order to reach the advertised accuracy.

For short averaging times, e.g. of one second, its accuracy is about a thousand times worse than the best attainable (however, its best accuracy is so high that even when averaged for a few seconds it is about as good as the best microwave clocks based on cesium or hydrogen).

A single measurement cannot be precise. Precision is a measure of how close multiple measurements are to one another. Accuracy is how close a single measurement is to its true value.

A clock that can measure a point in time to 19 decimal places with respect to its true value is accurate.