1. Department of Physics, 366 Le Conte Hall MS 7300, University of California, Berkeley, California 94720, USA
2. Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA
3. Institut für Physik, Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, 10117 Berlin, Germany
4. US Department of Energy, 1000 Independence Avenue SW, Washington, District of Columbia 20585, USA

Correspondence to: Holger Müller^1,2 Correspondence and requests for materials should be addressed to H.M. (Email: hm@berkeley.edu).

Abstract

One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c², where c is the velocity of light, as compared to a similar clock outside the potential¹. This effect, known as gravitational redshift, is important to the operation of the global positioning system², timekeeping^{3, 4} and future experiments with ultra-precise, space-based clocks⁵ (such as searches for variations in fundamental constants). The gravitational redshift has been measured using clocks on a tower⁶, an aircraft⁷ and a rocket⁸, currently reaching an accuracy of 7 × 10^-5. Here we show that laboratory experiments based on quantum interference of atoms^{9, 10} enable a much more precise measurement, yielding an accuracy of 7 × 10^-9. Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity¹¹. Improving the redshift measurement is particularly important because this test has been the least accurate among the experiments that are required to support curved space-time theories¹.

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