Important Open Problems (I1–I6)
These problems would significantly strengthen the programme.
I1. The EM Cutoff Problem.
Proposition 6.1 establishes that the naive single-parameter model (\ell_e = \hbar/(m_e c) \approx 197 nm) fails: the resulting EM cutoff frequency is 27 times below the Lyman-\alpha frequency. The ether must have multi-component structure (Corollary 6.2) with a transverse microstructure scale \ell_e \lesssim 3 nm. The precise mechanism determining \ell_e is not yet identified but the space of viable models is now sharply constrained.
Reference: Sections 5, 9. Difficulty: 6–12 person-months.
I2. The $\omega_p$–$\ell_e$ Relationship.
The plasma frequency \omega_p and the transverse microstructure scale \ell_e are both electromagnetic-sector quantities whose connection requires a theory of the ether’s transverse dynamics. A complete theory would determine both from the same condensate microphysics.
Reference: Section 5.7.2. Difficulty: 3–6 person-months.
I3. Constructive Nelson Detection Dynamics.
The osmotic velocity mechanism for Bell violation (Theorem 8.5) is identified, and the Nelson bridge theorem guarantees the result. A fully constructive derivation — explicitly solving the Nelson SDE for the joint photon-detector system — would provide independent confirmation without invoking the bridge.
Reference: Section 8.8.2. Difficulty: 6–12 person-months.
I4. The Bullet Cluster.
The superfluid ether model for dark matter (Section 4.2) faces a factor-of-2 discrepancy in the Bullet Cluster lensing offset relative to the normal ether fraction. A full hydrodynamic simulation with the two-fluid ether model is needed.
Reference: Section 4.2.7e. Difficulty: 6–12 person-months.
I5. Derivation of \alpha_{bp} = 1/\sqrt{2}.
Proposition 4.4 (§4.7) derives the MOND acceleration scale a_0 = \Omega_{\text{DM}} c H_0 / \sqrt{2} with 0.5% numerical agreement, but the dimensionless baryon-phonon coupling \alpha_{bp} = 1/\sqrt{2} is empirically determined. Deriving this value from the relativistic phonon field equation on an FRW background would elevate Proposition 4.4 to a theorem.
Reference: Section 4.7. Difficulty: 3–6 person-months.
I6. Multi-Particle Pilot Wave in Configuration Space.
Proposition 7.3 derives the de Broglie–Bohm guidance equation for a single particle from ether dynamics. For N particles, Bohmian mechanics requires a pilot wave in 3N-dimensional configuration space. The 3-dimensional ether does not straightforwardly support a 3N-dimensional wave. Possible resolutions include emergent configuration space from non-local ether correlations and Valentini’s quantum non-equilibrium approach.
Reference: Sections 7.6, 7.7. Difficulty: 6–12 person-months.