  The passage of time is tracked by counting oscillations of a frequency
reference, such as Earth's revolutions or swings of a pendulum. By referencing
atomic transitions, frequency (and thus time) can be measured more precisely
than any other physical quantity, with the current generation of optical atomic
clocks reporting fractional performance below the $10^{-17}$ level. However,
the theory of relativity prescribes that the passage of time is not absolute,
but impacted by an observer's reference frame. Consequently, clock measurements
exhibit sensitivity to relative velocity, acceleration and gravity potential.
Here we demonstrate optical clock measurements surpassing the present-day
ability to account for the gravitational distortion of space-time across the
surface of Earth. In two independent ytterbium optical lattice clocks, we
demonstrate unprecedented levels in three fundamental benchmarks of clock
performance. In units of the clock frequency, we report systematic uncertainty
of $1.4 \times 10^{-18}$, measurement instability of $3.2 \times 10^{-19}$ and
reproducibility characterised by ten blinded frequency comparisons, yielding a
frequency difference of $[-7 \pm (5)_{stat} \pm (8)_{sys}] \times 10^{-19}$.
While differential sensitivity to gravity could degrade the performance of
these optical clocks as terrestrial standards of time, this same sensitivity
can be used as an exquisite probe of geopotential. Near the surface of Earth,
clock comparisons at the $1 \times 10^{-18}$ level provide 1 cm resolution
along gravity, outperforming state-of-the-art geodetic techniques. These
optical clocks can further be used to explore geophysical phenomena, detect
gravitational waves, test general relativity and search for dark matter.
