  Recent observations on the quasar absorption spectra supply evidence for the
variation of the fine structure constant $\alpha$. In this paper, we propose
another interpretation of the observational data on the quasar absorption
spectra: a scenario with spacetime inhomogeneity and anisotropy. Maybe the
spacetime is characterized by the Finsler geometry instead of the Riemann one.
The Finsler geometry admits fewer symmetries than the Riemann geometry does. We
investigate the Finslerian geodesic equations in the Randers spacetime (a
special Finsler spacetime). It is found that the cosmological redshift in this
spacetime deviates from the one in general relativity. The modification term to
the redshift could be generally revealed as a monopole plus dipole function of
spacetime locations and directions. We suggest that this modification
corresponds to the spatial monopole and dipole of $\alpha$ variation in the
quasar absorption spectra.
