List of Theorems and Key Results

Theorem 1.1 (Empirical Equivalence). LET and SR yield identical predictions. Section 1.2, (1.6).

Theorem 3.1 (Unruh–Visser). Sound in a moving fluid propagates on an effective curved spacetime. Section 3.3, (3.16).

Theorem 3.2 (Gravity–Ether Identity). The PG metric is exactly the acoustic metric for ether flowing at free-fall velocity. Section 3.5, (3.21).

Theorem 3.3 (Emergent Lorentz Invariance). Lorentz symmetry is exact at λ≫ℓe\lambda \gg \ell_e, violated at O(ℓe/λ)2O(\ell_e/\lambda)^2. Section 3.8.

Theorem 4.1 (Gravitational Dielectric). Superfluid ether EOS yields MOND: ∇ ⁣⋅ ⁣[μe g]=−4πGρm\nabla\!\cdot\![\mu_e\,\mathbf{g}] = -4\pi G\rho_m. Section 4.2, (4.17).

Theorem 4.2 (ZPF Lorentz Invariance). ρ(ω)∝ω3\rho(\omega) \propto \omega^3 is uniquely Lorentz-invariant; gives w=−1w = -1. Section 4.3, (4.143).

Definition 5.1 (Plasma as Perturbed Ether). Three criteria: quasi-neutrality, collective response, statistical validity. Section 5.2.

Theorem 5.1 (EM Dielectric). Stix tensor derived from ether SED dynamics. Section 5.4, (5.46)–(5.47).

Theorem 5.2 (Alfvén–Ether Equivalence). vA=Geff/ρeffv_A = \sqrt{G_{\text{eff}}/\rho_{\text{eff}}} with Geff=B02/μ0G_{\text{eff}} = B_0^2/\mu_0. Section 5.5, (5.79).

Theorem 6.1 (Boyer). SED oscillator reaches ⟨E⟩=ℏω0/2\langle E\rangle = \hbar\omega_0/2. Section 6.2, (6.21).

Corollary 6.1.

Ether Lorentz invariance → ZPF spectrum → quantum ground state. Section 6.2.

Theorem 6.2.

SED position distribution =∣ψ0(x)∣2= |\psi_0(x)|^2. Section 6.3.

Theorem 6.3 (Hydrogen Ground State). SED equilibrium radius =a0=0.529= a_0 = 0.529 Å. Section 6.4.

Theorem 7.1 (Nelson). Stochastic diffusion with D=ℏ/(2m)D = \hbar/(2m) yields Schrödinger equation. Section 7.4, (7.26).

Theorem 8.1 (Bell–CHSH). Local hidden variables: ∣S∣≤2|S| \leq 2. Section 8.1.

Theorem 8.3 (SED Entanglement). Parametric coupling + ZPF → entangled Gaussian state. Section 8.3.

Theorem 8.5 (Bell Violation, T=0T = 0). ∣S∣=22|S| = 2\sqrt{2} via Nelson osmotic velocity. Section 8.5.

Proposition 8.3 (No-Signalling). Alice's marginals independent of Bob's setting. Section 8.5.

Proposition 3.1 (Sourced Ether Wave Equation). □Φ=−4πGρm\Box\Phi = -4\pi G\rho_m gives GW generation; Peters formula follows. Section 3.7.2, (3.42a).

Proposition 6.1 (Transverse Microstructure Constraint). Single-parameter model ℓe=ℏ/(mec)\ell_e = \hbar/(m_ec) fails; ether must be multi-component. Section 6.6.4, (6.50).

Corollary 6.2.

Transverse sector requires ℓe≲3\ell_e \lesssim 3 nm, energy scales ≫mec2\gg m_ec^2. Section 6.6.4.

Proposition 7.2 (Spin Emergence Pathway). Multi-component ether with nodal spectrum → spin-½ via Volovik's theorem. Section 7.6.

Theorem 8.8 (Thermal Bell). ∣S(T)∣=22/(1+2nth)2|S(T)| = 2\sqrt{2}/(1 + 2n_{\text{th}})^2 — falsifiable prediction. Section 8.7, (8.81).

PART I: FOUNDATIONS