New experimental limit on the validity of local position invariance

Abstract

Local position invariance (LPI) is part of the more general Einstein equivalence principle (EEP) which in turn is a foundation of Einstein's theory of general relativity. The EEP predicts a dependence of clock rates on the local gravitational potential U. LPI predicts that the gravitational shift is independent of the atomic species involved as a reference in the clock. It can thus be tested by comparing two different kinds of atomic frequency standard in the same time-varying gravitational potential $U(t).$ In our experiment we made use of the time dependence of $U(t)$ due to Earth's annual elliptical orbital motion. ${U(t)/c}^{2}$ varies between $\ifmmode\pm\else\textpm\fi{}3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ $(c$ is the speed of light). Comparing a cesium atomic fountain frequency standard with a hydrogen maser for about one year allowed us to set an upper limit on a possible frequency variation of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ of this amount. Compared to previous similar experiments the limit of the notional violation of LPI was reduced by a factor of more than 30.