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The First Nuclear Clock Will Test if Fundamental Constants Change
(www.quantamagazine.org)
This is a most excellent place for technology news and articles.
They will be called "variables" in the future, and scientists will try to figure out how they tick. And: They were seen as constants for a sufficientyl long time, so still treating them like constants won't hurt, as the value will probably only vary over long reaches of time or unlikely/uncommon circumstances like relativistic speeds.
We treat g = 9.81m/s², well knowing that this changes depending on height and location. But this value is totally sufficient for everyday purposes, and no bridge will ever collapse just because of local derivations from 9.81. The precise local value of g is only of relevance for a very small range of applications.