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

TL;DR

This paper investigates how gravitational effects influence high-precision atomic and g factor measurements, exploring the limits of Einstein's equivalence principle and identifying potential quantum and noncommutative effects that could impact experimental results.

Contribution

It derives a generalized Dirac Hamiltonian incorporating gravitational and electromagnetic couplings and analyzes the subtle compatibility of g factor measurements with the equivalence principle.

Findings

Atomic transition frequencies are compatible with the equivalence principle.

g factor measurements require deeper analysis to confirm compatibility.

Large higher-order gravitational effects are predicted for diatomic molecule transitions.

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, 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.