Einstein equivalence principle and the polarization of radio galaxies

The theoretical foundations of metric theories of gravitation rest largely on the Einstein equivalence principle (EEP). Schiff has conjectured that no consistent Lorentz-invariant theory can obey the weak equivalence principle and not obey the EEP. However, a counterexample has been proposed by Ni in a theoretical framework for studying electromagnetism coupled to gravity. Under the assumption that gravitational fields vary smoothly over a Hubble time, we show that Ni's counterexample would lead to a rotation in the plane of polarization of radiation from distant radio sources. As such rotation is not observed, we may put stringent limits on the magnitude of the parameter which violates the EEP, of less than about 10^-40 GeV.