Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 Â 10 À 16 , have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 Â 10 À 16 . Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 Â 10 À 16 .

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.