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.
U. D. Jentschura, "Gravitational Effects in G -Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle," Physical Review A, vol. 98, no. 3, American Physical Society (APS), Sep 2018.
The definitive version is available at https://doi.org/10.1103/PhysRevA.98.032508
Keywords and Phrases
Gravitational effects; Quantum electronics; Relativity; Wave functions, Diatomic molecules; Dirac Hamiltonian; Einstein's equivalence principle; Equivalence principles; General Relativity; High-precision spectroscopy; Position dependence; Transition frequencies, Hamiltonians
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 2018