Testing Local Position Invariance with Four Cesium-Fountain Primary Frequency Standards and Four NIST Hydrogen Masers

We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks—one at NIST and three in Europe—as the Sun’s gravitational potential at Earth’s surface varies due to Earth’s orbital eccentricity.

Figure 1

Fountain comparisons with maser S5 for 7 yr, showing fractional frequency deviation of the maser from the NIST-F1, PTB-CSF1, SYRTE-FO2, and IT-CSF1 fountains. The horizontal axis is given in modified Julian days (MJD). The error bars represent the evaluated uncertainties of the measurements, including time-transfer errors.

Figure 2

The frequency of the hydrogen masers as measured by cesium-fountain standards over the course of this study. The four masers are represented by four different symbols, while the dashed lines are the cubic fits for a particular maser. The variation in the solar potential, divided by $5000\times c^2$, is illustrated by the sinelike curve.

Figure 3

Frequencies of the four masers after removal of the cubic polynomial. The large amplitude sinelike curve is the previous maximum solar-potential induced frequency modulation on the hydrogen-cesium system, while the 23 times smaller curve is the limit arrived at in this study. Most of the outliers are associated with maser S3.