Try to Break It
Every theorem is an invitation. Every assumption is stated explicitly. Every derivation is public. If you find an error — in the mathematics, the assumptions, or the logic — we want to know.
“A heterodox programme must be more rigorous than the mainstream if it is to earn serious consideration.”
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- 1. Read the theorem — statement and assumptions are shown below. Click through to the full derivation.
- 2. Challenge it — find an error in the proof, a hidden assumption, or a logical gap.
- 3. Report it — click “I Found an Issue” to email the author with your finding, or discuss on the forum.
- 4. Get credit — valid corrections are acknowledged in the monograph and on the contributors page.
Theorem 1.1(Empirical Equivalence)
LET and SR yield identical predictions for all observable phenomena.
Assumptions
Both employ identical transformation equations (Lorentz) applied to identical dynamical laws.
Theorem 3.1(Unruh–Visser Acoustic Metric)
Sound in a moving barotropic fluid propagates on an effective curved spacetime.
Assumptions
Inviscid, irrotational, barotropic fluid. Linearised perturbations.
Theorem 3.2(Gravity–Ether Identity)
The PG metric is exactly the acoustic metric for ether flowing at free-fall velocity.
Assumptions
Constant ether density. Radial inflow at Newtonian free-fall velocity. Conformal factor is constant.
Theorem 3.3(Emergent Lorentz Invariance)
Lorentz symmetry is exact at λ ≫ ℓ_e, violated at O(ℓ_e/λ)².
Assumptions
Ether has discrete microstructure at scale ℓ_e. Low-energy effective field theory applies.
Theorem 3.4(Kerr–Ether Identity)
Kerr metric in Doran coordinates is the ether metric with spiralling inflow.
Assumptions
Constant density (leading order). Doran coordinate transformation exact. Unit-lapse foliation.
Theorem 3.5(Nonlinear Ether Field Equation)
The ether’s field equation is G_μν = (8πG/c⁴)T_μν — derived, not postulated.
Assumptions
Weinberg–Deser–Lovelock uniqueness: Lorentz invariance, Newtonian limit, energy conservation, second-order field equations.
Theorem 3.6(Post-Newtonian Parameters)
β = γ = 1; all ten PPN parameters match GR exactly.
Assumptions
Ether metric transformed to isotropic PPN gauge. Weak-field expansion to post-Newtonian order.
Theorem 3.7(Hawking Radiation)
Ether horizon emits thermal radiation at T_H = ℏc³/(8πk_BGM).
Assumptions
Mode analysis near the horizon. Bogoliubov coefficients from analytic continuation. Jacobson universality (UV insensitivity).
Theorem 3.8(GW Polarisations)
Exactly two tensor modes (+ and ×). Scalar breathing mode is non-radiative.
Assumptions
Linearised Einstein equation. Lorenz gauge. Decaying boundary conditions.
Theorem 3.9(Unruh Radiation)
T_U = ℏa/(2πk_Bc) for uniformly accelerating observer.
Assumptions
Uniform acceleration in flat ether. Rindler horizon mode analysis.
Theorem 3.10(Einstein Eq from Ether Thermodynamics)
G_μν + Λg_μν = (8πG/c⁴)T_μν derived from ZPF entanglement entropy + Clausius relation. G derived from mode counting.
Assumptions
Acoustic metric (Theorem 3.1). ZPF entanglement entropy S = k_B c³ A/(4ℏG). Unruh temperature at horizons (Theorem 3.9). Local thermodynamic equilibrium (Clausius relation δQ = TdS).
Theorem 4.1(Gravitational Dielectric)
Superfluid ether EOS yields MOND: ∇·[μ_e g] = −4πGρ_m.
Assumptions
Superfluid BEC with X^{3/2} EOS (Berezhiani–Khoury). Phonon-mediated gravitational coupling. Phase transition interpolating function.
Theorem 4.2(ZPF Lorentz Invariance)
ρ(ω) ∝ ω³ is uniquely Lorentz-invariant; gives w = −1.
Assumptions
Lorentz invariance of the ground state. Doppler transformation of mode frequencies.
Theorem 4.3(Cosmological Perturbation Reduction)
Ether perturbations reduce to ΛCDM for all CMB-relevant k; corrections < 10⁻⁶.
Assumptions
Linearised perturbation theory. Sound speed c_s ≪ c. Jeans wavenumber k_J ≫ k_CMB.
Theorem 5.1(EM Dielectric Equation)
Full Stix tensor derived from ether SED dynamics.
Assumptions
Linearised response. Cold plasma limit. Radiation reaction negligible (ωτ ~ 10⁻⁸).
Theorem 5.2(Alfvén–Ether Equivalence)
v_A = √(B₀²/μ₀ρ) with magnetic tension as shear rigidity.
Assumptions
MHD limit (ω ≪ |Ω_i|). Ideal MHD (zero resistivity). Quasi-neutrality.
Theorem 6.1(Boyer (1969))
SED oscillator reaches ⟨E⟩ = ℏω₀/2.
Assumptions
Classical charged harmonic oscillator. Lorentz-invariant ZPF. Radiation reaction. Equilibrium reached.
Theorem 6.3(Hydrogen Ground State)
SED equilibrium radius = Bohr radius a₀ = 0.529 Å.
Assumptions
Circular orbit approximation. ZPF absorption = Larmor radiation. Equilibrium stability.
Theorem 7.1(Nelson (1966))
Stochastic diffusion with D = ℏ/(2m) yields the Schrödinger equation.
Assumptions
Brownian motion with D = ℏ/(2m). Irrotational current velocity. Newton’s stochastic law.
Theorem 8.1(Bell–CHSH)
Local hidden variables: |S| ≤ 2.
Assumptions
Locality (factorisation of joint probabilities). Determinism. Freedom of choice.
Theorem 8.3(SED Entanglement)
Parametric coupling + ZPF → entangled Gaussian state.
Assumptions
Two parametrically coupled oscillators. Shared ZPF bath. Ornstein–Uhlenbeck stationary state.
Theorem 8.5(Bell Violation at T = 0)
|S| = 2√2 via Nelson osmotic velocity mechanism.
Assumptions
Nelson bridge (Theorem 7.1). Born rule detection probabilities. CHSH-optimal angles.
Theorem 8.8(Thermal Bell)
|S(T)| = 2√2/(1 + 2n_th)² — the falsifiable prediction.
Assumptions
Thermal + ZPF decomposition. Independent detector thermal noise. Bose–Einstein occupation.
No Errors Found?
If you’ve examined the theorems and found them sound, consider contributing to the open problems — extending the framework is as valuable as testing it.