Spacetime nonmetricity can be studied experimentally through its couplings to fermions and photons. We use recent high-precision searches for Lorentz violation to deduce first constraints involving the 40 independent nonmetricity components down to levels of order $10^{-43}$ GeV.
The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler $b$ space parametrized by a prescribed background covector field. This work identifies systems in classical phys
ics that are governed by the three-dimensional version of Finsler $b$ space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler $b$ spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.
