Abstract (Conditional Gauge Emergence from Scalar Gravity; Preprint)
We propose a mechanism by which the Standard Model gauge structure SU(3)×SU(2)×U(1) arises as the Berry connection on an internal mode bundle of a scalar optical medium (“DFD”), in which a refractive field ψ sets n=e^ψ and induces matter acceleration a=(c²/2)∇ψ. In regimes analyzed to date, the DFD scalar reproduces the Newtonian limit and standard optical/gravitational redshift relations, and it admits a low-acceleration regime relevant to galactic phenomenology.
Starting from a frame-stiffness penalty for twisting degenerate internal modes, we derive a Yang–Mills action with effective couplings g_r∼κ_r^(-1/2) and an electroweak mixing relation tan θ_W=√(κ₂/κ₁). We prove a minimality result: the first internal geometry that can support SU(3)×SU(2)×U(1) with anomaly-free chirality is ℂP²×S³; smaller choices fail by algebra (no su(3)) or topology (H⁴=0).
We outline parameter-independent pattern tests in precision spectroscopy (hadronic/EM drift ratio δln μ/δln α ≈ 22–24, species ordering, three-clock triangle closure) and a tabletop non-Abelian holonomy experiment in photonic ψ-textures. Absolute seasonal drifts of high-energy parameters are predicted to be extremely small (δsin²θ_W∼10^(-13), δg_r/g_r∼10^(-12)); accordingly, near-term discovery potential lies in the pattern tests and holonomy.
This gauge-emergence construction is operationally distinct from noncommutative geometry and string compactifications. It should be read as a conditional extension: if the DFD scalar description continues to pass empirical tests, the internal-bundle mechanism supplies a concrete, falsifiable route to Standard-Model–like gauge structure.
Density_Field_Dynamics_as_the_Minimal__Testable_Origin_of_the_Standard_Model_Gauge_Structure