AMO
In the literature: open
Is $\alpha$ drifting today at the $1e-19$ per year level?
In plain words
Two clocks whose ticking depends differently on $\alpha$ would slowly drift apart if $\alpha$ changed. So far no drift has been seen at about one part in $10^{18}$ per year.
Precise statement
Present laboratory bounds from optical clock ratios (for example the Yb+ E3/E2 comparison) give |d ln(alpha)/dt| of order 1e-18 per year. Determine whether d ln(alpha)/dt is nonzero at the 1e-19 per year level using multi-year ratios of clocks with large differential sensitivity, including the Th-229 nuclear transition.
What would settle it
A multi-year ratio of a Th-229 nuclear clock (or highly charged ion clock) to an optical atomic clock with fractional uncertainty below 1e-18, analyzed for a linear drift.