We discuss how laboratory experiments can be used to place constraints on possible variations of the fine structure constant alpha in the observationally relevant redshift interval z ~= 0 - 5, within a rather general theoretical framework. We find a worst case upper limit for Delta alpha / alpha of 8 x 10^-6 for z <= 5 and Delta alpha / alpha of 0.9 x 10^-6 for z <= 1.6. The derived limits are at variance with the recent findings by Webb et al. (1998), who claim an observed variation of Delta alpha/alpha = -2.6 +- 0.4 x 10^-5 at 1<z<1.6.
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