  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.
