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 } } \over { \alpha } } < 3.5 \times 10 ^ { -15 } year ^ { -1 } , 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 } } \over { R } } < 10 ^ { -15 } year ^ { -1 } .
Including terrestrial and other astronomical measurements places limits ( 2 \sigma ) on slow oscillations of R from the present to the epoch of cosmic nucleo-synthesis , just seconds after the big bang , of { { \Delta R } \over { R } } < 10 ^ { -5 } .