Gravitational Redshift in a Local Freely Falling Frame: A Proposed New Null Test of the Equivalence Principle

We consider the gravitational redshift effect measured by an observer in a local freely failing frame (LFFF) in the gravitational field of a massive body. For purely metric theories of gravity, the metric in a LFFF is expected to differ from that of flat spacetime by only "tidal" terms of order (GM/c(exp 2)R)(r'/R )(exp 2), where R is the distance of the observer from the massive body, and r' is the coordinate separation relative to the origin of the LFFF. A simple derivation shows that a violation of the equivalence principle for certain types of "clocks" could lead to a larger apparent redshift effect of order (1 - alpha)(G M/c(exp 2)R)(r'/R), where alpha parametrizes the violation (alpha = 1 for purely metric theories, such as general relativity). Therefore, redshift experiments in a LFFF with separated clocks can provide a new null test of the equivalence principle. With presently available technology, it is possible to reach an accuracy of 0.01% in the gravitational field of the Sun using an atomic clock orbiting the Earth. A 1% test in the gravitational field of the galaxy would be possible if an atomic frequency standard were flown on a space mission to the outer solar system.