How long is a second? According to the latest definition of the SI units in 2019, a second is defined as "$9,192,631,770$ periods of the transition between the two hyperfine levels of the caesium-133 atom $\Delta\nu_{{\rm Cs}}$," and $c$ is fixed as $299792458$ metres per second.
However I am puzzled by the fact that all uncertainties have disappeared since I graduated. Following wikipedia, the "realization" of the meter has a relative uncertainty of about $2×10^{-11}$, but I could not find information about the second and its uncertainty. From what I recall before the redefinition, $\Delta\nu_{{\rm Cs}}$ had a relative uncertainty of O($10^{-15}$), so is that how well do we know the duration of the 'realization' a second?
 A: The second itself does have an uncertainty. When we're using it without uncertainty, we're basically using the following trick:

*

*The time span of $n$ seconds is defined as $2\times n\times 9\,192\,631\,770$ transitions between the two Cs hyperfine levels.

*Making $n$ big, we can still count exactly how many transitions have occured, so the error on the total time span is constant. A single second can then be computed as $\tfrac1n$ of that time, and the uncertainty becomes as small as we like. In other words, there is no uncertainty in the definition of the second, only in a concrete experiment we might perform to implement it.

A: There's a shift from the old way of having standard examples of the units that everyone can compare against, to defining the units in terms of fundamental physics.
There was an uncertainty in measuring the speed of light.  Then, the units were defined in terms of the speed of light, thus fixing the value exactly.  Now there is still uncertainty in making the measurement when calibrating your clock or ruler, but the big advantage is that as such measurement technology improves you can immediately make use of it in a definitive way.
The big advantage of doing it this way is that you don't have to curate an artifact and have people go reference that specific object.  This was a royal pain for the standard kilogram, which gained or lost weight for unexplained reasons.
When such a shift is made, it is done by fixing the value of the physical constant by definition, to the best-known value determined in the previous system.
A: A second is a second long by definition, but if you measure any time in seconds, the number of seconds you infer will be subject to an error of at least $\mathcal O(10^{-15})$ because of the uncertainty of Caesium clocks as you correctly point out. This is true even if you make a higher precision measurement using new clocks like Quantum Clocks with uncertainties of $\mathcal O(10^{-18})$.
Edit: For completeness, I include this quote from here:

The second is defined by taking the fixed numerical value of the caesium frequency $\Delta$Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9,192,631,770 when expressed in the unit Hz, which is equal to s$^{–1}$.

and I note that one day this standard may change.
A: Cited: "The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1."
"The second, so defined, is the unit of proper time in the sense of the general theory of relativity."
Source: https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507
resp. https://en.wikipedia.org/wiki/SI_base_unit
