  The Einstein Equivalence Principle has as one of its implications that the
non-gravitational 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
$2S_{1/2}$ and $2P_{1/2}$ atomic states) within the context of violations of
local position invariance and local Lorentz invariance, as described by the $T
H \epsilon\mu$ formalism. We compute the associated red shift and time dilation
parameters, and discuss how (high-precision) measurements of these quantities
could provide new information on the validity of the equivalence principle.
