Well over 10 years ago, I heard of an idea that the fine-structure constant might not be "constant":  It might be slowly varying over a period of billions of years, or by location.    I believe I recall reading a study that this had been determined by telescope analysis of light emitted  from galaxies maybe 10 billion years ago.

And, I just found this by google ' "fine structure constant" "varying" '

There was a proposal that using new kinds of clocks, the kind that seem to be becoming available (lattice clocks, ion clocks, etc) with accuracies of around 1 part in 10*18, it should be possible to compare the frequencies of two such clocks that use different atoms or ions.   If the ratios of clock frequencies can be monitored over periods of months or years, it should be possible to see a variation in a reasonably short period.

              Jim Bell