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We present measurements of absorption by the 21 cm 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: { \. {}}<3. 510^-15yr^-1, to a look-back time of 4. 8 Gyr. In the context of string theory, the limit on the secular evolution of the scale factor of the compact dimensions, R, is { \. {}R}R<10^-15yr^-1. Including terrestrial and other astronomical measurements places 2 limits on slow oscillations of R from the present to the epoch of cosmic nucleosynthesis, just seconds after the big bang, of R<10^-5.
Carilli et al. (Mon,) studied this question.