Astronomical Constraints on the Cosmic Evolution of the Fine Structure Constant and Possible Quantum Dimensions

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.