√

The passage around this formula

It is worth being honest about how far current best precision still has to travel to make a genuinely compact version of this measurement realistic. The most precise fractional frequency resolution reported to date, 7.6$\times$10^{-21} , comes from comparing atoms at different heights inside a single shared optical lattice, where systematic effects common to both heights cancel almost completely [ 13 ] . If that exact resolution were ever achieved between two independently operated, physically separated network clocks — which is not what was demonstrated, and which faces a substantially harder common-mode-rejection problem — the same scaling gives h $\propto$ $\sqrt{\sigma_y}$ and a required…

Read this part in the article →