Gravitational Effect on Fundamental Physical Observables

Abstract

This report studies possible gravitational effects on measurements of fundamental physical observables such as the fine structure constant and the lepton magnetic moment. Although a static gravitational potential does not contribute to physical observables owing to Einstein's equivalent principle, a dynamic degree with finite momentum transfer can contribute to them. In other words, a laboratory frame fixed on the Earth is not an inertial system; thus, Earth's gravity can contribute to local observables. We investigate experimental results measuring the fine structure constant and electron and muon magnetic moments using the quantum field theoretic method under the Schwarzschild background field. We prepare classical vierbein and spin-connection fields owing to the Schwarzschild metric in the momentum space of the local Lorentz space and estimate possible gravitational effects at the surface of the Earth as ${\mathcal O}(10^{-9})$, which is consistent with the current discrepancy between measured and calculated values of the muon anomalous magnetic moment. On the other hand, the gravitational effect does not contribute to the fine structure constant measurements. We propose a possible test of gravitational effects in particle physics using precise measurement of muon properties in the J-PARK.