How the Constants Move Together: Linkage Ratios Between Variations of Alpha and Mu and What They Let Each Probe Say

Constants rarely vary alone. In unification scenarios the fractional changes in the proton-to-electron mass ratio and the fine-structure constant are locked by a ratio set by two response parameters, and that ratio ranges from -0.3 in a minimal electromagnetic-response scenario to -19.5 in a grand-unified-like one and -4 in a large-response one. The consequence is concrete: if alpha had shifted by the full amount the quasar dipole claim allows, the grand-unified linkage would predict a mu shift of -2.34e-04, more than a thousand times the room the methanol measurement leaves. Joint statements, not single-constant ones, are therefore the correct currency of this field, and this paper tabulates the exchange rates. Computed from published relations, not measured.