Inertial and gravitational effects on a geonium atom

Abstract

We reveal all linear order inertial and gravitational effects on a non-relativistic Dirac particle (mass $m$) on the Earth up to the order of $1/m$ in the Foldy-Wouthuysen-like expansion. Applying the result to Penning trap experiments where a Dirac particle experiences the cyclotron motion and the spin precession in a cavity, i.e., a geonium atom, we study modifications to the $g$-factor of such as the electron. It is shown that each correction from gravity has different dependence on the cyclotron frequency and the mass $m$. Therefore, their magnitude change depending on situations. In a particular case of an electron $g$-factor measurement, the dominant correction to the observed $g$-factor comes from effects of the Earth's rotation, which is $\delta g/2\simeq 5.2\times 10^{-17}$. It may be detectable in the near future.

arXiv comment23 pages, 2 figures, 1 table, typos corrected, minor changes

References in corpus (17)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
• The Muon Anomalous Magnetic Moment: A Harbinger For "New Physics"
• Cavity Control of a Single-Electron Quantum Cyclotron:\\Measuring the Electron Magnetic Moment
• Testing new physics with the electron g-2
• Direct Measurement of the Proton Magnetic Moment
• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• A formalism for magnon gravitational wave detectors
• Quantification of GR effects in muon g-2, EDM and other spin precession experiments
• Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle
• The general relativistic effects to the magnetic moment in the Earth's gravity
• Post-Newtonian effects of Dirac particle in curved spacetime - II : the electron g-2 in the Earth's gravity
• Post-Newtonian effects of Dirac particle in curved spacetime - III : the muon g-2 in the Earth's gravity
• Gravitational effects on geonium and free electron ${\mathrm{g}}_s$-factor measurements in a Penning trap
• On systematic and GR effects on muon $g-2$ experiments

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