Implications of Gauge Unification for Time Variation of the Fine Structure Constant

Unification of the gauge couplings would imply that time variations of the fine structure constant are accompanied by calculable and very significant time variations in the QCD scale parameter $\Lambda_{QCD}$. Since $\Lambda_{QCD}$ is the dominant factor in setting the hadron masses, estimates made by simple variations of the fine structure constant may not provide meaningful limits. There may also be related variations in Yukawa couplings and the electroweak scale. Implications for the 21 cm hyperfine transition, big bang nucleosynthesis, and the triple alpha process are discussed. We find that the first of these already provides strong constraints on the underlying theory. It is emphasized more generally that time (and space) variations of fundamental couplings and their correlations may be a significant probe of ultra-high-energy physics.