Foundations of Field Dynamics: Deterministic Reduction of Mass, Charge, and Standard Model Invariants from Elastic Continuum Kinematics

AbstractThis synthesis establishes the fundamental mechanical ontology and mathematical core ofField Dynamics (the Unified Elastic Field framework). Standard physics separates physical real-ity into independent phenomenological entities—inertial mass, electric charge, gauge fields,spacetime curvature, and unobservable quantum vacuum fluctuations—stitched togetherby over thirty adjustable empirical parameters. Here, we demonstrate that all fundamentalphenomena reduce deterministically to the classical elastodynamics and cavitation kinematicsof a single three-dimensional Euclidean (R3) quasi-incompressible continuous monolith (theField Ocean), characterized by two fundamental mechanical invariants: reference densityρ0 ≈ 4.30 × 1018 kg/m3 and shear modulus μ0 = ρ0c2 ≈ 3.865 × 1035 Pa.We demonstrate that: (1) The speed of light c = √μ0/ρ0 is the classical acoustic transverseshear wave velocity of the monolith, rather than an abstract cosmic barrier. (2) Rest mass isnot an innate substance or Higgs coupling, but the confined kinetic energy of high-speedsubstrate circulation: m ≡ 1c2∫ ρ0v2dV . (3) Mass, electric charge, and electromagnetismrepresent three projections of a single state: rotation energy, topological boundary circulation(∮ v · dl = const), and dynamic shear stresses (Tij = μ0γij ) transmitted through the locallyentrained medium, eliminating action-at-a-distance. (4) Light momentum p = ¯hk = E/c andradiation pressure P = I/c are proven as exact acoustic theorems of the Cauchy stress tensorvia Stokes wave drift. (5) A single dimensionless cavitation equation 12 αx2 + 12 x = 1 seamlesslybridges the micro- and macro-domains: yielding the superluminal proton pump (vp ≈ 1.185 c,Rp = 0.8414 fm, structural break at 278 MeV) at packing αp ≈ 0.3023, and the universal blackhole horizon wall velocity limit vmax = √2 c ≈ 1.414 c at the vanishing curvature limit α → 0.(6) Rest energy work upon absorption into a black hole strictly satisfies continuum volumeconservation: ∆V = mp/ρ0 = Vp/αp ≈ 3.31 Vp. (7) Fundamental Standard Model constantsemerge directly from Y -junction topology: mp/me = 6π5 (0.002%), fine-structure constantα−1 = 27π56(Λ+4/(3Λ2)) ≈ 137.033 (0.002%), capillary string tension σ = μ0πR2p6 ≈ 0.894 GeV/fm(0.5%), and proton Landé factor gp = 163 (1 + αp/2π) ≈ 5.5899 (0.075%).