  In the expanding Universe, the dimensional quantities like the wavelength and
the temperature of photons are cosmologically redshifted by the relative
difference between the observed and emitted ones. Therefore, it can be
physically meaningful to talk about the constancy or variability of any
dimensional constant (not only of dimensionless one) when the Universe is
expanding. It has been known that one can measure the temporal variation of the
fine structure constant $\alpha$ in the emission and absorption lines of quasar
spectra when the speed of light varies for cosmic time, even though this
statement is model dependent. Current observations based on the alkali doublet
method and on the many-multiplet one show superficially contradictory results.
The former finds no statistically significant evidence for a time dependence of
$\alpha$, while the latter does. The so-called meVSL model can reconcile these
results naturally without any contradiction.
