Why isn't the second defined by fixing $G$?

Since 2019, the meter, kilogram, ampere, and kelvin, are defined by setting exact numerical values for the speed of light $$c$$, the Planck constant $$h$$, the elementary charge $$e$$, and the Boltzmann constant $$k_B$$.

The second still remains as being defined to be the duration of 9,192,631,770 periods of the caesium-133 atom, while the gravitational constant $$G$$ remains an imprecise number.

Why didn't the SI also fix $$G$$ to an exact value like $$6.674 \text{m}^3 \text{kg}^{-1}\text{s}^{-2}$$, such that all physical constants have an exact value, rather than the period of some random atom having an exact value?

• Because $G$ is really hard to measure experimentally so that makes it not much use as a standard. The frequency of light emitted by a random atom is very easy to measure to high precision. Jul 14, 2020 at 11:09
• Aside from the practical problem of measuring it, since we know that we don't yet have a model that can reconcile quantum mechanics and general relativity, do we even know what "G" is supposed to represent physically? It might turn out to be only a non-relativistic approximation to something else, for example. Jul 14, 2020 at 11:18
• Caesium-133 isn't just "some random atom". Caesium is the heaviest stable alkali metal, and it has only 1 stable isotope, Cs-133. Natural caesium is almost entirely composed of Cs-133, with a tiny trace of the long-lived weakly radioactive isotope Cs-135. These properties make it a good choice for the basis of an atomic clock; OTOH, we do now have better clocks based on other atoms. Jul 14, 2020 at 13:04
• @alephzero To be fair, all constants could be only a non-relativistic approximation to something else. Jul 14, 2020 at 14:59
• @alephzero would that necessarily be a problem? $e$ is also the low energy limit of the electromagnetic coupling, but you can use it to define the Ampere
– fqq
Jul 14, 2020 at 15:00

By contract Newton's gravitational constant is very hard to measure accurately. It is only known to an accuracy of about $$0.002\%$$, and that is from experiments far too complicated for me to routinely reproduce in my lab. Choosing $$G$$ as a primary standard would be of no use to me as an experimenter.