  Strong evidence has recently emerged for a variation in the fine structure
constant, $\alpha\equiv e^2/\hbar c$, over the history of the Universe. This
was concluded from a detailed study of the relative positions of redshifted
optical quasar absorption spectra. However, {\it radio} absorption lines at
high redshift offer a much higher sensitivity to a cosmological change in
$\alpha$ than optical lines. Furthermore, through the comparison of various
radio transitions, \HI, OH and millimetre molecular (e.g. CO) lines, any
variations in the proton g-factor, $g_p$, and the ratio of electron/proton
masses, $\mu\equiv m_e/m_p$, may also be constrained. Presently, however,
systems exhibiting redshifted radio lines are rare with the bias being towards
those associated with optically selected QSOs. With its unprecedented
sensitivity, large bandwidth and wide field of view, the SKA will prove
paramount in surveying the sky for absorbers unbiased by dust extinction. This
is expected to yield whole new samples of \HI ~and OH rich systems, the latter
of which will prove a useful diagnostic in finding redshifted millimetre
absorbers. As well as uncovering many new systems through these blind surveys,
the SKA will enable the detection of \HI ~absorption in many more of the
present optical sample -- down to column densities of $\sim10^{17}$ \scm, or
$\gapp2$ orders of magnitude the sensitivity of the current limits. Armed with
these large samples together with the high spectral resolutions, available from
the purely radio comparisons, the SKA will provide statistically sound
measurements of the values of these fundamental constants in the early
Universe, thus providing a physical test of Grand Unified Theories.
