This four-part series proposes a mechanism-level, computable program for cross-scale unification based on an Elementary Energy-Quantum Sea (EP-sea): a collision-driven statistical background whose recursive phase transitions generate stable phase-membrane defects and their effective dynamics. Rather than treating geometry or symmetry groups as primitive, the series emphasizes a free-energy/response ledger and event-statistical closure that connect gravity, electromagnetism, nuclear interior phenomenology, and quantum measurement within a single effective-theory dictionary. Falsifiability pack (minimal must-hit constraints):(1) Double-slit visibility scaling under phase diffusion: η(t) ≈ exp[−γ_dec t] with leading-order γ_dec ∼ α_env Θ / ħ_eff.(2) Born statistics as hazard-rate counting: λ(x,t) = Γ(x)|ψ(x,t)|^2 and consistency with absorbing-potential norm loss.(3) Aharonov–Bohm phase calibration: Δφ_AB = (q/ħ_eff)∮A·dl, with q/ħ_eff fixed per tested species in laboratory regimes.(4) Spin-1/2 + Pauli coupling with tree-level g = 2 from SU(2) rotor (tethered-defect) + minimal coupling.(5) (Optional interface) Barrier crossover: activation exp(−ΔW/Θ) vs tunneling exp(−S_E/ħ_eff) with τ_* ~ ω_b^−1 at a quadratic barrier top. Key mechanisms / claims (overview):1) Gravity as a bulk–boundary free-energy response: mass is associated with a defect free-energy gap ΔF, inducing an effective potential Φ_eff through background stress/response gradients.2) Casimir and gravity as two limits of the same free-energy ledger: boundary-constrained fluctuations vs bulk gradients.3) Light speed vs sound speed: two mode identities. Sound is longitudinal (stiffness/inertia), while light is a transverse Maxwell-sector response with c^2 = (ε0 μ0)^−1 in vacuum-like regimes (c ≠ c_s), avoiding a macroscopic preferred frame.4) Operational charge and potentials: charge as boundary flux asymmetry; Aμ as effective response variables; AB phase as a topological consequence of minimal coupling.5) Quantum probability and measurement: |ψ|^2 is interpreted as event-density; measurement is modeled by thresholded absorption/nucleation with hazard Γ(x)|ψ|^2; Born statistics emerges as a frequency limit of Poisson/SDE event dynamics.6) “Collapse” is replaced by (i) absorbing norm loss and (ii) dynamical decoherence via phase diffusion.7) Spin-1/2 from tethered-defect topology (belt-trick): 2π rotation induces a sign change while 4π restores the full configuration (SU(2) double cover as a geometric constraint).8) Tree-level g = 2: once SU(2) rotor structure is in place, minimal coupling forces the Pauli term; deviations (g−2) are assigned to higher-order backreaction/noise-spectrum effects.9) Nuclear interior as a phase-transition landscape: a core–shell (χ1, χ2) closure yields two-scale kernels (e.g., double-Yukawa structure), saturation, and R ∝ A^(1/3), with decays treated as rare events.10) Unifying tunneling and activation: WKB and Kramers/Freidlin limits are related at the exponent level via intrinsic barrier timescales.11) Polarization and Malus’s law: polarization is a geometric projection of two transverse degrees of freedom; Malus’s law follows from deterministic projection plus intensity ∝ amplitude^2. Series structure:Paper I: Gravity and bulk–boundary free-energy closure (including Casimir interface).Paper II: Electromagnetism as transverse response; constitutive closure; why c differs from c_s.Paper III: Nuclear interior (tier-2) closure; two-scale kernels; saturation and rare-event decays.Paper IV: Quantum interface: ψ/|ψ|^2 closure, hazard-rate measurement, AB phase, spin/Pauli sector, decoherence scaling. Status and scope:This release is intended as a coherent, test-driven framework (effective-theory level) with explicit interfaces for numerical templates and data confrontation. Precision QED/GR-level matching is treated as follow-up work guided by the falsifiability pack above.
This paper shows that particle-like excitations can emerge naturally within classical wave physics as topological defects of an effective wavefield. Focusing on a two-dimensional elastic medium whose envelope dynamics reduces to an effective Schrödinger equation, we demonstrate that phase singularities—points where the wave amplitude vanishes—behave as robust, localized objects carrying conserved topological charge. These defects follow deterministic trajectories governed by a guidance equation formally identical to that of de Broglie–Bohm pilot-wave theory, yet derived entirely from classical continuum mechanics without invoking quantum postulates. The central result is that defect cores move with velocityv=(ℏeff/meff)∇S,\mathbf{v} = (\hbar_{\mathrm{eff}}/m_{\mathrm{eff}})\nabla S,v=(ℏeff/meff)∇S,where
S is the phase of the emergent wavefunction. This wave-guided dynamics arises as a kinematic constraint: the defect must remain a zero of the evolving field. The paper presents an asymptotic analysis of defect structure and motion, and discusses both the parallels with quantum particle dynamics and the fundamental limitations of the analogy, including the absence of superposed trajectories, entanglement, and quantum statistics. Overall, the work provides a concrete example of how topology and dispersion in classical systems can give rise to quantum-like behavior without quantization, illustrating a physically transparent route to emergent particle dynamics. Keywords: emergent dynamics; topological defects; phase singularities; pilot-wave theory; classical analogs of quantum mechanics; Schrödinger equation; guidance equation; elastic waves
We present a three-level organization of a bilocal relational theory inwhich structures usually associated with quantum mechanics arise atlogically distinct stages. The first level is purely geometric. Starting from the bilocalconfiguration space
M×M and its canonical cotangent bundle,the relative sector admits a radial--angular decomposition. For
N=3,the angular phase space is
T∗S2. Its non-singular sector isnaturally organized as
R+×SO(3) and therefore possesses the canonical doublecover
R+×SU(2)≃C2∖{0}. A classical two-component
SU(2)-spinorial carrier thus appearsbefore any Lorentzian dynamics or quantum postulate; its identificationwith a Lorentz-covariant Weyl spinor is not assumed at this stage.Reduction at fixed internalCasimir yields the Hopf fibration with
∣c1∣=1. For
N=3, defining
pμ=(pt,P) and
μint=κ1+iκ2rewrites the full constraint as
pμpμ+∣μint∣2=0.Its Clifford factorization then admits an exact chiral first-order formwith a two-dimensional complex kernel. At this stage the constructionremains classical: the momenta are phase-space variables and the kernelspinor is not yet a quantum wave function.The third level promotes this geometric and dynamical structure toquantum spinor dynamics. Geometry supplies an integer topological classbut not a universal scale of action; the identification
I=nℏ/2 therefore requires the quantum scale
ℏ.Together with the operator rule
pμ↦−iℏDμ, the classical chiral factorization becomesa quantum Dirac-type equation. If the internal complex contributionadmits a sector or limit in which it reduces to a real constant
m, the standard massive Dirac equation
(iℏγμDμ−m)ΨD=0is recovered. The construction therefore separates three ingredients that arenormally introduced together: spinorial and topological statestructure, Lorentzian dynamics, and quantum operator dynamics. We donot derive quantum mechanics from classical geometry. Rather, we showthat the spinorial carrier and the algebraic architecture of the Diracequation can arise before quantization, while the quantum scale andoperator realization remain independent inputs. This identifiesprecisely which elements of quantum spinor dynamics are geometric,which depend on the Lorentzian dynamical postulate, and which remaingenuinely quantum assumptions.