  We present measurements of absorption by the 21cm hyperfine transition of
neutral hydrogen toward radio sources at substantial look-back times. These
data are used in combination with observations of rotational transitions of
common interstellar molecules, to set limits on the evolution of the fine
structure constant: (dot alpha)/alpha < 3.5e-15/yr to a look-back time of 4.8
Gyr. The neutral hydrogen observations employed Very Long Baseline
Interferometry in order to mitigate the substantial uncertainty arising from
the fact that observations at very different wavelengths may probe different
lines-of-site due to frequency dependent structure of the background source. We
discuss the implication of these results on theories unifying natural forces
based on compact quantum dimensions. In the context of string theory, the limit
on the secular evolution of the scale factor of these compact dimensions, R, is
(dot R)/R < 1e-15/yr. Including terrestrial and other astronomical measurements
places limits (2sigma) on slow oscillations of R from the present to the epoch
of cosmic nucleosynthesis, just seconds after the big bang, of (Delta R)/R <
1e-5.
