Varying Alpha, Thresholds and Extra Dimensions

We consider variation of coupling strengths and mass ratios in and beyond the Standard Model, in the light of various mechanisms of mass generation. In four-dimensional unified models, variations in charged particle thresholds, light quark masses and the electron mass can completely alter the (testable) relation between Δlnα and Δlnμ, where μ≡m_p/m_e. In extra-dimensional models where a compactification scale below the fundamental scale is varying, definite predictions may result even without unification; we examine some models with Scherk-Schwarz supersymmetry-breaking.