Open Problems

September 2026

This project publishes what it can defend and marks plainly what it can’t. The list below is a working board, not a roadmap promise — see Purpose & Goals for why that distinction matters here.

Live / established on this site

• Bell’s theorem / entanglement (interpretive track). Local hidden-variable accounts of PBT’s own entanglement mechanism are closed for the published CHSH construction (ruled out by Fine’s theorem, not just this site’s own test). Site language treats an infinite-speed correlation structure as something that can be experienced in the correlation sector, never detected as a usable faster-than-light telegram. Live: Bell’s Theorem & Quantum Entanglement.
• Light / Fresnel drag. The partial-drag coefficient $f=1-1/n^2$ is inheritance from unmodified Lorentz electrodynamics in a moving medium, not a fresh derivation from PBT’s own aether action. The Light page carries this distinction directly rather than letting a real, 175-year-old result be mistaken for a new PBT prediction.
• Paper 2 — candidate light-sector extension (research, not yet adopted). A separate photon-aether coupling, $L_{\mathrm{wave}}$, is documented on Paper 2 as a research candidate, with its own bound hierarchy and an explicit warning not to equate its $\kappa$ with the SME literature’s $\tilde\kappa_{\mathrm{tr}}$. It is not part of the paper’s published gravity-sector coefficients. Live: Paper 2 — Candidate Light-Sector Extension.

Stalled

• Derivational Bell / non-locality with realism. A 2026-07-21 standing project decision set the actual target: non-locality with realism intact (the Bohmian-mechanics direction), after rejecting both standard quantum mechanics’ imprecision and superdeterminism’s denial of free measurement choice — not generic Kochen-Specker contextuality, an earlier and less precise framing. An asymmetric, Toner-Bacon-style construction reproduces the full Tsirelson-bound correlation without signaling, but the probability rule driving it is imported from the known quantum answer, not derived from PBT’s own vortex/pressure mechanism. Four distinct categories of non-local model — pre-shared structure fixed before either measurement, one-way communication, retrocausality, and a screened dynamical law — have all now been tried; each either leaks signaling, collapses back into the imported rule, or (the screened case) reduces to a mixture of the other two rather than deriving anything new. This track stays open, genuinely unresolved. Reopening it requires either a genuine PBT-native derivation of the probability rule, or a named new postulate with a concrete mechanism behind it — not another import dressed up as a solution.

Benchmarks run in September 2026 (gravity and atoms)

This section is a failure log: four benchmarks the project ran against measured numbers, and what each returned. It is kept because the site’s rule is that a failed fit is reported with the same care as a pass.

• A fluid medium at rest, fitted to the clocks, fails the light (twenty-ninth calculation, 2026-09-14). A barotropic medium in hydrostatic equilibrium in an imposed Newtonian potential, with a clock’s rate and light’s speed both tied to its sound speed by postulate, reproduces the gravitational clock shift by one fitted amplitude and then bends starlight at half of general relativity: $\gamma = 0$, some 43,000 of Cassini’s standard deviations away. Ruled out as a complete model of that class (a barotropic medium responding to an imposed potential, with one sound speed setting both clock and light); the clock rows are a calibration, not evidence. Published with its script in The Balloon and the Planet.
• Frame dragging can be fitted, not derived (thirty-first calculation, 2026-09-15). A vortex in the medium reproduces the measured Lense-Thirring coupling only when its strength is set to general relativity’s own; the flows a fluid supplies on its own, an irrotational vortex and the boundary-layer flows, fail by shape or by size. Working notes only (unpublished); summarised in The Balloon and the Planet.
• The working model’s gravity sector fails the preferred-frame tests (thirty-second calculation, 2026-09-16). The working model is the one in How It Could Work, a different construction from the fluid above: its light bending is fitted to the measured value, $\gamma = 1$, and its gravity has no velocity dependence. Under the project’s map from that sector to the parametrised post-Newtonian framework, those two facts give $\alpha_1 = -8$ and $\alpha_2 = -1$; lunar laser ranging, the Sun’s spin axis and pulsar timing exclude those by four and by six to nine orders of magnitude. Working notes only (unpublished); summarised in The Balloon and the Planet.
• The periodic table’s period lengths as a benchmark for the atom model (article dated 2026-09-23). Any model of the atom has to reproduce 2, 8, 8, 18, 18, 32, 32 in the order the real table records. The equilibrium-shell picture inherits the angular degeneracies from spherical geometry, borrows the exclusion principle, and has not produced the filling order; the one radial scale attempted needed a wave speed the program no longer uses for the atom, and the radial mode count is an order-of-magnitude bracket. Status: open, path not specified. Set out in Two, Eight, Eight, Eighteen.

What stands after these four: the clock-sector kinematics validated in How It Could Work, and the angular degeneracies any spherical standing-wave model inherits. What does not: no complete medium model of gravity survives the light and preferred-frame tests, the gravity and atom threads use different media and are not one model, and the atom sector is exploratory.

Gravity / Paper 2 action (research status)

• Paper 2’s covariant action, the phenomenological shadowing/$G_{\mathrm{eff}}$ formulas (Papers 1/13/14), and Paper 2’s own refractive light-bending treatment are three independently developed pieces that have not been shown to follow from one another. Paper 2 itself states that its bending calculation is a phenomenological refractive-index treatment, not derived from the action $S$. The named slot where that connection was supposed to live, $L_{\mathrm{push}}$, remains undefined in the published corpus. An overnight research pass on an attenuation/optical-depth candidate for $L_{\mathrm{push}}$ produced a dual result (mailbox research notes, not adopted site physics): if the flux stress-energy itself sources spacetime curvature, light bending comes out wrong by about one-third (a mathematical consequence of the flux’s own equation of state); if the flux only mediates a force on ordinary matter, with matter’s own rest-mass sourcing curvature the usual way, bending can stay consistent — but that branch inherits this project’s already-documented Le Sage drag/heating tension (Paper 14), which continuum embedding does not remove and which tachyonic escapes remain rejected for Lorentz/causality reasons. Two specific follow-up mechanisms were checked and closed: a resonant/optical-gradient coupling to the shadow-deficit intensity (wrong distance scaling), and near-frictionless elastic scattering at PBT’s own stated corpuscle mass (no heating improvement at the microscopic scale that actually matters; a bulk-body estimate was tried and retracted as the wrong mass for the question). Until a concrete mechanism is shown to work at the right scale, gravity/light unification via $L_{\mathrm{push}}$ stays an unresolved research track, parallel to and separate from the Bell derivational track above.

Parked / lowest priority

• Correlation-sector speed, standalone. Whether the non-local correlation sector is truly unbounded in speed or merely very large and finite remains an open, exploratory question in its own right. The site-relevant consequence is already folded into the Bell’s Theorem page’s language; resolving the standalone physics question isn’t blocking anything else here.

Explicitly not claimed

• That $L_{\mathrm{wave}}$ is already adopted physics within Paper 2’s published gravity sector.
• That Paper 2’s Newtonian/$G_{\mathrm{eff}}$ phenomenology or refractive bending have been derived from the published action $S$.
• That an attenuation-based $L_{\mathrm{push}}$ currently solves both bending and Le Sage drag/heating together.
• That elastic corpuscle–matter scattering escapes historical Le Sage heating at PBT’s stated finest-scale corpuscle mass.
• That a PBT-native derivation of the Bell correlation’s probability rule exists today.
• That infinite propagation speed has been laboratory-detected. Finite experiments only ever raise a lower bound; detection itself stays with finite-$c$ light and ordinary signals.
• That a barotropic fluid medium reproduces light bending, or that its clock match is evidence rather than calibration.
• That the working model’s gravity sector passes the preferred-frame tests.
• That this project’s shell model reproduces the periodic table’s period lengths, or has a stated path to the exclusion principle.