Decompression Kinetics of the Primordial Neutron: Motion Without Time, Toroidal Snap-Through Barrier, Resolution of the Beam-Bottle Puzzle, and Weak Sector Acoustics (Paper 4)

AbstractThis paper presents a deterministic theory of nucleonic weak sector processes formulated within the continuum mechanics of an underlying elastic substrate (Field Dynamics, Document #0). Abstract gauge postulates of quantum field theory—such as the hypothetical intermediate vector boson W- (80.4 GeV), fundamental point neutrinos with artificial mass hierarchies, and the geometric time coordinate t—are completely eliminated. We demonstrate that: (1) Ontology of Time and Motion as Retarded Rotation: A continuous four-dimensional time coordinate t does not exist in nature. Physical time is an emergent discrete cycle counter tracking internal soliton rotations with baseline cavity frequency ν_0 = v_p / (2π R_p) ≈ 6.72 × 10²² s⁻¹. Translational motion through the absolute Field Ocean at velocity v redistributes the medium's capacity into translation, lowering the intrinsic cycle frequency: ν(v) = ν_0 √1 - v^2/c^2. The twin paradox is resolved without relativistic kinematic symmetry. (2) One Soliton in Two Pressure Phases and μ_n/μ_p = -2/3 Invariant: The proton and neutron represent two pressure-dependent phase states of the same three-blade cavitation soliton: the low-pressure proton [uud] (2 inflows → 1 outflow) and the high-pressure neutron [udd] (1 inflow → 2 outflows). Direct substitution into circulation invariants strictly reproduces the ratio μ_n/μ_p = -2/3 (μ_n ≈ -1.8633 μ_N, 2.6% agreement with CODATA) without SU(6) symmetry, while ambient decompression explains the primordial 75% H to 25% He-4 ratio. (3) Origin of the 879 s Timescale and Snap-Through Barrier: The free neutron is stabilized against instantaneous decay by an elastic toroidal snap-through buckling barrier S_E⁽⁰⁾ = 6Λ_0 - 3α_p ≈ 59.3106, setting the primordial baseline τcosmos ≈ 855.1 s matching Big Bang Nucleosynthesis (BBN) requirements (850–860 s). (4) Resolution of the Beam-Bottle Puzzle: The 4σ discrepancy is resolved across a three-step regime ladder with rigorous classification of proven theorems versus motivated estimates: Cosmos baseline (855.1 s) → Terrestrial bottle rest with reactive medium impedance τbottle ≈ 878.8 s (0.05% from UCN experiments) → NIST beam drift in a 4.6 T solenoid field τbeam ≈ 888.1 s (0.04% from NIST data). (5) Geometric Axial Form Factor g_A = 4/π: Derived as g_A = 4/π ≈ 1.27324 (0.17% from experiment) from circumscribed shear cell packing and spherical twist averaging. (6) Acoustic Nature of Neutrinos and Parametric L → T+T Decay: Neutrinos are identified as solitary longitudinal acoustic decompression pulses (L-modes). In dense stellar cores, they propagate at c_L ≈ 1.355 c (accounting for the 3-hour head start in SN1987A), converting via stimulated Brillouin scattering into bound transverse shear waves (v = c) upon entering vacuum, complying with IceCube limits (|v-c|/c < 2.5 × 10⁻¹²).