Gravitational Effect on Fundamental Physical Observables

TL;DR

This paper investigates how Earth's gravity might influence fundamental physical measurements like the muon magnetic moment, finding potential effects at the order of 10^{-9} that could explain current experimental discrepancies.

Contribution

It introduces a quantum field theoretic approach to estimate gravitational effects on particle observables in a Schwarzschild background, highlighting potential impacts on muon measurements.

Findings

Gravitational effects at Earth's surface estimated at ~10^{-9}

No significant gravitational influence on fine structure constant measurements

Proposes experimental test using muon properties at J-PARK

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.