List of Theorems & Key Results

The Lorentz Ether Theory and Special Relativity yield identical predictions for all observable phenomena. The choice between them is non-empirical.

Establishes the logical foundation: the ether was set aside by philosophical judgement, not by experiment.

Sound propagation in a moving barotropic fluid obeys a curved-spacetime wave equation with an effective metric determined by the flow velocity and local sound speed.

The bridge between fluid mechanics and general relativity. Sound in a fluid "sees" curved spacetime.

The Painlevé–Gullstrand metric is exactly the acoustic metric for an ether of constant density flowing radially inward at the Newtonian free-fall velocity. Every prediction of Schwarzschild gravity follows.

The keystone result. Gravity is not a force — it is the flow of the ether. This is not an approximation; it is a mathematical identity.

Lorentz symmetry is exact at wavelengths much larger than the ether microstructure scale, with violations suppressed as the square of their ratio.

Explains why no Lorentz violation has been detected — the ether is smooth at all accessible scales.

The superfluid ether equation of state yields the MOND field equation with the Radial Acceleration Relation, without invoking dark matter particles or modified gravity.

Galaxy rotation curves explained from the ether's constitutive properties. The acceleration scale a₀ emerges from cosmological parameters.

The spectral energy density ρ(ω) ∝ ω³ is the unique Lorentz-invariant zero-point spectrum, yielding a cosmological constant with equation of state w = −1.

Dark energy is the zero-point phonon energy of the ether. The energy scale is set by the healing length, not the Planck length — reducing the vacuum catastrophe from 10¹²² to a single condensate parameter.

The complete Stix dielectric tensor is derived from the ether's SED dynamics, reproducing all standard magnetised plasma wave modes.

The ether's electromagnetic response is not postulated — it is derived from the same medium that produces gravity.

Alfvén wave propagation in the ether realises the elastic-ether structure that Young postulated in 1801, with magnetic tension providing the shear rigidity.

The transverse rigidity problem — the historical objection that killed the luminiferous ether — is resolved by magnetohydrodynamics.

A charged harmonic oscillator immersed in the electromagnetic zero-point field reaches thermal equilibrium with ground-state energy ½ℏω₀ — the quantum ground state emerges from classical stochastic dynamics.

The cornerstone of Stochastic Electrodynamics: quantum ground states are maintained by the ether's electromagnetic fluctuations, not by axiom.

The SED equilibrium position distribution equals |ψ₀(x)|² — the Born rule for the ground state emerges from classical statistics.

The probability interpretation of quantum mechanics is not an axiom — it is a consequence of stochastic dynamics in the ether.

The SED equilibrium radius for hydrogen equals the Bohr radius a₀ = 0.529 Å — the hydrogen atom is stabilised by the zero-point field.

The stability of matter, unexplained classically since Rutherford, follows from the ether's electromagnetic fluctuations.

Brownian motion through the ether with diffusion coefficient D = ℏ/(2m) yields the Schrödinger equation — quantum dynamics emerges from stochastic mechanics.

The Schrödinger equation is not a postulate — it is the Fokker-Planck equation for a particle diffusing through the ether.

Any local hidden-variable theory satisfies |S| ≤ 2. Quantum mechanics predicts |S| = 2√2.

The theorem that the ether must overcome: how can a local medium produce non-local correlations?

A two-mode Gaussian state with covariance matrix σ is separable only if the partial transpose of σ has all symplectic eigenvalues ≥ 1/2. For symmetric states, inseparability is equivalent to Δ²(Xₛ − Xᵢ) + Δ²(Pₛ + Pᵢ) < 2.

Provides the criterion used to verify that the SED state is genuinely entangled — not merely classically correlated.

Parametric coupling between two oscillators via the shared zero-point field produces a genuinely entangled Gaussian state.

Entanglement is not a primitive — it emerges from two systems sharing the same ether fluctuations.

For two random variables (X, Y) drawn from a bivariate Gaussian with correlation r(θ) = r₀cos(2θ), the CHSH parameter of the sign-binned outcomes satisfies |S_SED| ≤ 2, with equality iff r₀ = 1.

Proves that naive Gaussian measurement cannot violate Bell's inequality — the detection model must go beyond sign-binning.

At zero temperature, the Nelson osmotic velocity mechanism produces |S| = 2√2 — the Tsirelson bound is saturated.

The ether reproduces the maximum quantum violation of Bell's inequality. Non-locality emerges from long-range order in the zero-point field.

The stationary covariance matrix at temperature T is related to the zero-temperature covariance matrix by σ(T) = (1 + 2n_th(ω, T)) σ(0).

Quantifies how thermal noise scales the entangled state — the starting point for the thermal Bell prediction.

At temperature T, the two-point field correlation decomposes into a temperature-independent ZPF component with power-law decay |G^(ZPF)| ~ r⁻² and a thermal component with exponential decay on the scale ξ_th = ℏc/(k_BT).

Explains why ZPF correlations survive at macroscopic distances while thermal noise is spatially confined — the physical basis for temperature-dependent Bell violation.

|S(T)| = 2√2 / (1 + 2nₜₕ)² — Bell violations degrade algebraically with temperature, not exponentially as standard QM predicts.

The single most important prediction in the monograph. Parameter-free, testable with current superconducting circuit technology. If confirmed, it rewrites quantum foundations. If falsified, the ether's quantum sector falls.