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.



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)

2469-9926; 2469-9934

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2018 American Physical Society (APS), All rights reserved.

Publication Date

01 Sep 2018

Included in

Physics Commons