Before 2019, the ampere was essentially defined by fixing the vacuum permeability $\mu_0$ to be $4\pi\times10^{-7} \frac{H}{m}$. From 2019 onwards, the ampere was essentially defined by fixing the elementary charge $e$ to be $1.602176634\times10^{-19} C$. Was there any motivation for this change? Both the vacuum permeability and the elementary charge are fundamental constants of the universe, so why did the International Bureau of Weights and Measures decide to switch the fundamental constant upon which the ampere was defined?
1 Answers
The vacuum permeability is still well-defined, albeit not exactly:
$$\mu_0=\frac{2\alpha h}{e^2c}.$$
The fine-structure constant is not known to perfect accuracy, but the accuracy is still very high.
In reality, it doesn't make any sense why permeability would be $4\pi\times10^{-7}$. The $4\pi$ part is fine, it shows up elsewhere too, but for it to be multiplied by exactly $10^{-7}$ is suspect since there's no reason why 0.00000001 should show up anywhere in nature.
Along with those changes, we also defined $c$, $h$, and a couple other constant to be exact. $c=299792458$ exactly, $h=6.62607015\times10^{-34}$ exactly, etc. This has actually been very convenient now that we don't need to add as many plus-or-minuses to calculations to account for inaccuracies. Keep in mind that we didn't change the constants, we changed the units we use to measure them so that they're exact. We didn't change what we consider to be the speed of light, we changed the meter to be exactly the distance that light covers in $1/299792458$ of a second (the second being defined as the time it takes for an isotope of cesium to oscillate a certain number of times).
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