Reposting bc I dun goofed before
this post was submitted on 15 Feb 2024
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It's arbitrary in the same way measuring the time between photon absorption/emission in a cesium atom is arbitrary or the rotation of our planet is arbitrary.
Picking the smallest is arbitrary just like picking a larger interval.
In the cesium clock case, you count 9192631770 because it's close to 1 second we already are familiar with and arbitrarily say 9192631770 transitions is defined as 1 second.
For example Planck time is defined as 5.391247(60)×10−44 seconds. But what is that second? It's the arbitrary 9192631770 cesium transitions we picked because it's close to the second that come from Earth's spin.
Planck time doesn't appear to be arbitrary, but a feature of our universe, hence the shortest measurable unit of time. It's length in seconds is arbitrary because seconds are arbitrary. And seconds are arbitrary because the only non-arbitrary unit of time we have found so far is too unwieldy to use for anything but scientific purposes, and it's very unwieldy for many of those.