### 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.

Original language | English |
---|---|

Article number | 032508 |

Journal | Physical Review A |

Volume | 98 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 25 2018 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Gravitational effects in g -factor measurements and high-precision spectroscopy : Limits of Einstein's equivalence principle.** / Jentschura, U.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Gravitational effects in g -factor measurements and high-precision spectroscopy

T2 - Limits of Einstein's equivalence principle

AU - Jentschura, U.

PY - 2018/9/25

Y1 - 2018/9/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85054031046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054031046&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.032508

DO - 10.1103/PhysRevA.98.032508

M3 - Article

AN - SCOPUS:85054031046

VL - 98

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 032508

ER -