  We study the interplay of general relativity, the equivalence principle, and
high-precision experiments involving atomic transitions and g factor
measurements. In particular, we derive a generalized Dirac Hamiltonian, which
describes both the gravitational coupling for weak fields, as well as the
electromagnetic coupling, e.g., to a central Coulomb field. An approximate form
of this Hamiltonian is used to derive the leading gravitational corrections to
transition frequencies and g factors. The position-dependence of atomic
transitions is shown to be compatible with the equivalence principle, up to a
very good approximation. The compatibility of g factor measurements requires a
deeper, subtle analysis, in order to eventually restore the compliance of g
factor measurements with the equivalence principle. Finally, we analyze small,
but important limitations of Einstein's equivalence principle due to quantum
effects, within high-precision experiments. We also study the relation of these
effects to a conceivable gravitationally induced collapse of a quantum
mechanical wave function (Penrose conjecture), and space-time noncommutativity,
and find that the competing effects should not preclude the measurability of
the higher-order gravitational corrections. Surprisingly large higher-order
gravitational effects are obtained for transitions in diatomic molecules.
