The Analogy Between LV Fermion–Gravity and Fermion–Photon Couplings

Adopting a non-relativistic reduction method, we study the one-fermion matrix elements between the fermion–gravity and the fermion–photon interactions in the presence of minimal Lorentz-violating fermion coefficients. We prescribe the Lense–Thirring metric with the test-particle assumption, as this metric is essentially curved and may demonstrate some novel Lorentz-violating matter–gravity couplings beyond the conventional tests of the equivalence principle. With some bold but reasonable assumptions, we get a Lorentz-violating spin–gravity interaction Hamiltonian, from which we derive Lorentz-violating corrections to spin precession and gravitational acceleration. With some ad hoc assumptions, we get some very rough bounds on several Lorentz-violating coefficients, such as $|3\overrightarrow{\tilde{H}}-2\overrightarrow{b}|\le 1.46\times {10}^{-5}\text{eV}$, from spin–gravity measurements like those with Gravity Probe B.