We demonstrate a time scale based on a phase stable optical carrier that accumulates an estimated time error of $48pm94$ ps over 34 days of operation. This all-optical time scale is formed with a cryogenic silicon cavity exhibiting improved long-term stability and an accurate $^{87}$Sr lattice clock. We show that this new time scale architecture outperforms existing microwave time scales, even when they are steered to optical frequency standards. Our analysis indicates that this time scale is capable of reaching a stability below $1times10^{-17}$ after a few months of averaging, making timekeeping at the $10^{-18}$ level a realistic prospect.
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