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

Fine structure constant variation or spacetime anisotropy?