Gravitational effects in g -factor measurements and high-precision spectroscopy: Limits of Einstein's equivalence principle

Abstract

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 and 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 (the Penrose conjecture), and space-time noncommutativity, and find that the competing effects should not preclude the measurability of the higher-order gravitational corrections. In the course of the discussion, a renormalized form of the Penrose conjecture is proposed and confronted with experiment. Surprisingly large higher-order gravitational effects are obtained for transitions in diatomic molecules.