Time from Vacuum Entanglement: The Higgs Mass, Gauge Group, and Vacuum Stability from the Fisher–Bures Geometry of Sp(56,R)/U(28)

We derive the fundamental equation Δt = tP ΔS/˜η from the Page–Wootters mechanism by identifyingthe quantum vacuum as the universal entangled clock, with clock energy ε = EP ˜η. The parameter˜η is an adimensional vacuum processing rate derived from quantum field theory in curvedspacetime via the quantum geometric tensor (QGT) of the squeezed vacuum. The QGT on thevacuum state manifold M = Sp(56,R)/U(28) has a real part (Fisher information) that generatesgravity and an imaginary part (Berry curvature) that generates gauge fields. We demonstratefour results without free parameters: (i) the Berry connection of the vacuum, pulled back fromM to spacetime, undergoes dynamic holonomy reduction from U(28) to SU(3) × SU(2) × U(1) viathe Coleman–Weinberg mechanism, deriving the Standard Model gauge group; (ii) the Higgs massratio m2h/m2vW = 2.370 follows from the SO(5)/SO(4) sub-system triple plus one-loop correctionsweighted by gauge couplings, yielding mh = 123.8 ± 1.9 GeV; (iii) the Higgs vacuum expectationvalue v∗ = 248.1 GeV is predicted by marginal vacuum stability λeff (MPl) = 0 at three-loop order;and (iv) the electroweak vacuum is absolutely stable. All predictions are within 2.4% of measuredvalues.