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tokens: al. 2004 ; Rahmani et al. 2014 ; Albareti et al. 2015 ) out to redshifts z ∼ 1, where δλ denotes the separation between two spectral lines, and the subscript refers to the redshift. Our results are not in contradiction with this upper limit. The studies of the variation of the fine structure constant use multiplets of a given atomic element. The targeted spectral features, such as the [O iii ] doublet ( λλ 4960, 5008 Å), cover a relative narrow spectral window (Δ λ ≲ 100 Å). In comparison, our study covers a wavelength window at least 30 times larger. In this context, we wonder whether analyses of the variation of the fine structure constant based on absorption lines (e.g., Quast et al. 2004 ) may suffer from similar type of systematic effects. In addition, the use of nebular emission lines might present equivalent systematic complications in the determination of the centroid of the line, this time caused by the gas kinematics, but such musings are beyond the scope of this paper. Is the result shown in this paper an absolute limit to the accuracy one can achieve with galaxy spectra? Although the present data cannot provide an accuracy better than one part in 100,000 out to z ≲ 0.25, we speculate that high S/N spectra at significantly higher resolution— R ≳ 10,000—can be used to probe in detail the effective shapes of the absorption lines, potentially allowing us to break this barrier. The denser sampling at higher resolution will decrease the statistical weight in the methodology due to differences in the number of fitting points between the blue and the red sides of the spectral features, caused by the stretching of the spectra. APPENDIX POTENTIAL SYSTEMATICS A.1. Wavelength Calibration A.1.1. Testing the Wavelength Calibration of SDSS Spectra In addition to the signal found in the simulated data (Section 4 ) one could also consider the possibility of an inaccurate wavelength calibration of the SDSS spectra. The official SDSS pipeline quotes typical errors (Abazajian et al. 2009 ) of order 2 km s −1 , which translates into an uncertainty of δ Δ( z ; λ 0 ) ∼ 7 × 10 −6 for individual spectra. Although this effect should be significantly lower than our measurements, especially if we consider that the whole analysis rests on the determination of approximately 6.8 million individual spectral features, we nevertheless explore below a possible systematic from a wavelength calibration trend. If the observed signal is due to a calibration wavelength problem, then we should not expect the calibration bias to depend on the redshift bin considered. Consequently, we conduct the following test: for each redshift bin we select only those lines within the common observer-frame window, between 4500 and 6800 Å. We calculate in this region how much the observed wavelengths ( λ obs ) depart from the standard (1 + z ) law for each redshift bin. In this test, we hypothesize that such departures are caused by an inaccurate wavelength calibration, so that the