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A time scale is a procedure for accurately and continuously marking the passage of time. It is exemplified by Coordinated Universal Time (UTC), and provides the backbone for critical navigation tools such as the Global Positioning System (GPS). Present time scales employ microwave atomic clocks, whose attributes can be combined and averaged in a manner such that the composite is more stable, accurate, and reliable than the output of any individual clock. Over the past decade, clocks operating at optical frequencies have been introduced which are orders of magnitude more stable than any microwave clock. However, in spite of their great potential, these optical clocks cannot be operated continuously, which makes their use in a time scale problematic. In this paper, we report the development of a hybrid microwave-optical time scale, which only requires the optical clock to run intermittently while relying upon the ensemble of microwave clocks to serve as the flywheel oscillator. The benefit of using clock ensemble as the flywheel oscillator, instead of a single clock, can be understood by the Dick-effect limit. This time scale demonstrates for the first time sub-nanosecond accuracy for a few months, attaining a fractional frequency uncertainty of 1.45*10-16 at 30 days and reaching the 10-17 decade at 50 days, with respect to UTC. This time scale significantly improves the accuracy in timekeeping and could change the existing time-scale architectures.

The pursuit of ever more precise measures of time and frequency is likely to lead to the eventual redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on a microwave transition between hyperfine levels in ground-state $^{133}$Cs, it is necessary to measure the absolute frequency of candidate standards, which is done by comparing against a primary cesium reference. A key verification of this process can be achieved by performing a loop closure$-$comparing frequency ratios derived from absolute frequency measurements against ratios determined from direct optical comparisons. We measure the $^1$S$_0\!\rightarrow^3$P$_0$ transition of $^{171}$Yb by comparing the clock frequency to an international frequency standard with the aid of a maser ensemble serving as a flywheel oscillator. Our measurements consist of 79 separate runs spanning eight months, and we determine the absolute frequency to be 518 295 836 590 863.71(11) Hz, the uncertainty of which is equivalent to a fractional frequency of $2.1\times10^{-16}$. This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty of $<$3$\times10^{-16}$, limited by the current realization of the SI second. We use these measurements to tighten the constraints on variation of the electron-to-proton mass ratio, $\mu=m_e/m_p$. Incorporating our measurements with the entire record of Yb and Sr absolute frequency measurements, we infer a coupling coefficient to gravitational potential of $k_\mathrm{\mu}=(-1.9\pm 9.4)\times10^{-7}$ and a drift with respect to time of $\frac{\dot\mu}{\mu}=(5.3 \pm 6.5)\times10^{-17}/$yr.