# Test of general relativity by a pair of transportable optical lattice clocks

Abstract

A clock at a higher altitude ticks faster than one at a lower altitude, in accordance with Einstein’s theory of general relativity. The outstanding stability and accuracy of optical clocks, at 10−18 levels1–5, allows height differences6 of a centimetre to be measured. However, such state-of-the-art clocks have been demonstrated only in well-conditioned laboratories. Here, we demonstrate an 18-digit-precision frequency comparison in a broadcasting tower, Tokyo Skytree, by developing transportable optical lattice clocks. The tower provides the clocks with adverse conditions to test the robustness and a 450 m height difference to test the gravitational redshift at (1.4 ± 9.1) × 10−5. The result improves ground-based clock comparisons7–9 by an order of magnitude and is comparable with space experiments10,11. Our demonstration shows that optical clocks resolving centimetres are technically ready for field applications, such as monitoring spatiotemporal changes of geopotentials caused by active volcanoes or crustal deformation12 and for defining the geoid13,14, which will have an immense impact on future society. A pair of transportable optical lattice clocks with 10−18 uncertainty is developed. The relativistic redshift predicted by the theory of general relativity has been tested at the 10–5 level by the two optical clocks with a height difference of 450 m on the ground.