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

Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle