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A null test of general relativity based on a long-term comparison of atomic transition frequencies


The local position invariance principle of general relativity stipulates that non-gravitational experiments should give outcomes that are independent of the position and orientation of the reference frames in which they have been performed. Here, we study the change in the rates of clocks on Earth with the spatial change of the solar potential, constraining the variation of a non-gravitational interaction—the hyperfine splitting in hydrogen and caesium atoms—to β = (2.2 ± 2.5) × 10−7, a factor of two improvement over previous estimates. Our result is based on the comparison between the long-term fractional frequency variation of four hydrogen masers that are part of an ensemble of clocks comprising the National Institute of Standards and Technology, Boulder, and the fractional frequencies of primary frequency standards operated by leading metrology laboratories in the United States, France, Germany, Italy and the United Kingdom over a period of more than 14 years. Using our results together with the previous best estimates of β, we impose strict limits on the variation of fundamental constants, resulting in a test of general relativity with an unprecedented level of precision.

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Fig. 1: Position of Earth and Jupiter on modified Julian day (MJD) 56263 (2 December 2012).
Fig. 2: Frequency shifts of H and Cs for maser S3 for MJD 51508 (11 November 1999) to MJD 56959 (29 October 2014).
Fig. 3: Addressing the drift in the H maser with fitting functions.


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We acknowledge funding from NASA grant NNH12AT81I. We also thank the atomic standards group at NIST for maintaining the H masers and sharing the data. We thank E. Donley, S. Jefferts and C. Oates for providing valuable suggestions that have helped improve this paper. We thank J. Sherman and J. Ye for discussing the planned clock comparisons between NIST and JILA. This work is a contribution of NIST and is not subject to US copyright.

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Authors and Affiliations



T.E.P. compiled data from BIPM and analysed maser versus primary frequency standard data. N.A. and B.R.P. carried out the data analysis and performed the calculations that were the basis of the main conclusions of this paper. B.R.P. wrote the manuscript with input from all of the authors, and all authors discussed the results and the conclusions.

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Correspondence to Bijunath R. Patla.

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Supplementary notes, Supplementary Tables 1,2, Supplementary Figure 1 and references

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Ashby, N., Parker, T.E. & Patla, B.R. A null test of general relativity based on a long-term comparison of atomic transition frequencies. Nature Phys 14, 822–826 (2018).

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