Testing the equivalence principle by Lamb shift energies

The Einstein equivalence principle has as one of its implications that the nongravitational laws of physics are those of special relativity in any local freely falling frame. We consider possible tests of this hypothesis for systems whose energies are due to radiative corrections, i.e., which arise purely as a consequence of quantum field theoretic loop effects. Specifically, we evaluate the Lamb shift transition (as given by the energy splitting between the $2S_{\frac{1}{2}}$ and $2P_{\frac{1}{2}}$ atomic states) within the context of violations of local position invariance and local Lorentz invariance, as described by the $\mathrm{TH}\epsilon \mu$ formalism. We compute the associated redshift and time dilation parameters, and discuss how (high-precision) measurements of these quantities could provide new information on the validity of the equivalence principle.