We consider possible tests of the Einstein Equivalence Principle for
quantum-mechanical vacuum energies by evaluating the Lamb shift transition in a
class of non-metric theories of gravity described by the \tmu formalism. We
compute to lowest order 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.Comment: 4 pages, latex, epsf, 1 figur