Work backward from interacting QED to electron–photon roots and interfaces

[marvin-marbell]

Objective: explain the interacting target by working backward

Construct a deeper explanation of the electron–photon sector, starting from its best-tested physical theory and working backward through the mathematical structures and relationships that make it work. This is an inverse-theory problem, not a search for particle-like objects inside a preselected root.

Start with quantum electrodynamics (QED), embedded in the Standard Model, in a stated regime where it describes the observables under study. Deconstruct that target into necessary structures and interfaces; then investigate which deeper laws or constructions could supply them. The target organizes the search. Euler, rotational media, lattice models and other candidates are possible suppliers, not the source of the target's requirements.

Multiple roots, transformations, branching, shared structures and feedback are allowed. Neither a universal Euler law nor a common microscopic action is an entry requirement. Conversely, do not assume the target can be assembled from independent pieces: some of its relationships may require a coupled construction.

Research execution remains paused for Dan's feedback. This revision changes the research approach; it asserts no scientific result and does not start the calculations below.

The mathematical object to explain

The Standard Model is the established framework for this sector; QED is its appropriate electromagnetic description at the selected scales. It is a reference theory to explain, not a claim of final ontology or validity at every scale.

In units with $\hbar=c=1$, the basic QED Lagrangian structure is

$$ \mathcal L_{\rm QED} =-\frac14 F_{\mu\nu}F^{\mu\nu} +\bar\psi(i\gamma^\mu\partial_\mu-m_e)\psi -q_e\bar\psi\gamma^\mu\psi A_\mu, \qquad F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu, $$

where $q_e=-e$ is the electron's charge. This expression is only the structural starting point. The target also includes the quantum state/operator structure, physical gauge equivalence and constraints, fermionic statistics, and renormalized predictions with radiative corrections where relevant.

• Photon: a massless quantum electromagnetic excitation with physical helicities $+1$ and $-1$, represented through a gauge field. A classical transverse wave is not yet a photon.
• Electron: a massive, charged spin-$\tfrac12$ fermionic sector with specific propagation, statistics and electromagnetic interactions. Persistence or classical angular momentum alone does not establish it. Long-range electromagnetic dressing matters: an interacting charged state is subtler than an isolated free-particle state.
• Interaction: charge is expressed through the matter current and its coupling to the electromagnetic field, not through an arbitrary force assigned an electric label. Schematically, $j^\mu=q_e\bar\psi\gamma^\mu\psi$, with the same charge entering the covariant derivative $D_\mu=\partial_\mu+iq_e A_\mu$. Gauge identities relate propagation, vertices and conserved-current compatibility.

QED takes parameters such as mass and charge as inputs; using their measured values establishes a reference calculation, not a derivation of those values. Their deeper origin remains a separate explanatory obligation. Electroweak/Higgs structure is part of the wider Standard Model context, not something already explained by writing down QED.

References: PDG Standard Model reviews; QED formulation, §6; interacting charged-state/infraparticle discussion. These establish the reference and its subtleties, not a substrate mechanism.

Method: observable → theory structure → explanatory construction

1. Specify a target phenomenon. Choose an electron–photon observable or relationship, its kinematics, regime and precision. State what the successful theory predicts and how that relates to measurement. A named particle or a list of qualitative similarities is not enough.
2. Reconstruct why the target theory produces it. Identify the states, operators, propagation, interaction terms, symmetries, constraints and parameter dependencies actually involved. Preserve their relationships, not just separate properties such as masslessness, spin and charge.
3. Deconstruct into explanatory obligations. Ask which structures can be supplied separately, what each requires as input, and which dependencies must remain coupled. The decomposition is a working hypothesis: regroup it or change representation if a better construction requires that.
4. Investigate roots and interfaces as possible explanations. Seek deeper dynamics or mathematical constructions that supply an obligation, and derive the map to the target's observables. Work backward again whenever a proposed supplier needs an unexplained input. Candidates may be co-developed; an incomplete endpoint does not forbid investigating its interaction.
5. Return to the physical target. Calculate the selected observable from the construction, including the maps and declared assumptions. Use disagreement to identify what to repair or rethink; use agreement to choose the next informative target relationship.

A root is a proposed explanatory law/construction with stated variables, domain and dynamics. An interface is a demonstrated relationship or transformation between structures, including normalization, constraints, energy/momentum exchange and feedback where claimed. Do not equate a change of variables with a new physical root.

QED is the explanandum, not a ready-made solution to import. A deeper theory need not use literal $A_\mu$ and $\psi$ variables. It may recover their effective roles through different variables, provided the relevant states, observables and relationships follow through a justified map. Whether the final microscopic organization uses one root or several is an outcome of investigation, not a premise.

First work when research resumes

Begin with a reference electron–photon interaction, not candidate A's propagation operator. Use Compton scattering $e^-\gamma\to e^-\gamma$ as the initial worked benchmark: specify kinematics and polarization/spin treatment, obtain the leading QED amplitude and its low-energy Thomson limit, and identify the structures responsible for that result. State the perturbative order and the limits of the comparison; handle infrared resolution/dressing explicitly when extending beyond the leading reference calculation.

Produce a backward dependency map from that observable to external physical states, matter propagation, interaction vertices, charge/mass normalization and the identities connecting them. This does not exhaust QED; add complementary observables when needed to distinguish explanations that match this benchmark alone.

Use the map to choose the first uncertain explanatory relationship worth constructing. Do not choose the microscopic root first and reinterpret the benchmark to fit it. Once a hypothesis is concrete, run the smallest calculation capable of changing the next design decision, then iterate toward the interaction target.

The first deliverable is the worked reference plus a target-derived dependency map and an attempted explanatory construction. A map alone is preparation, not a particle mechanism. Classical subtheorems are useful contributions, but the campaign's target remains the quantum interacting sector; quantum structure, spin/statistics and mass are visible from the beginning, not removed to make a classical milestone look complete.

Constructive exploration: incomplete theorems are working objects

Conjecture, build partial constructions, optimize, test, revise assumptions and improve the result. Missing steps identify work; they do not require abandoning a promising route. No finished proof, completed checklist or reviewer permission is required to explore.

A failed check usually rejects a version, assumption, map or regime. Investigate repair, a different representation or a materially different construction. Ruling out an entire approach requires evidence covering that class. Missing derivation or data is unresolved, not refutation. Preserve valid partial results and investigate how to strengthen or join them.

Acceptance criteria govern established claims, not permission to investigate. Coupled exploration may begin before either endpoint is established. Candidate counts, elapsed time and an initial shortlist neither prove exhaustion nor create a compulsory stop. Continue constructive work when authorized; respect explicit pauses and genuinely inaccessible prerequisites.

What an explanatory result must eventually account for

Keep the following connected to the same construction, maps and declared regime rather than collecting unrelated resemblances:

• Physical state content: photon helicities, charged spin-$\tfrac12$ matter, quantum statistics and the appropriate interacting-state interpretation.
• Propagation and response: massless electromagnetic behavior, massive matter behavior, source response and stability within the claimed scope.
• Interaction: the current–field relationship, charge/opposite-charge interpretation, gauge/current compatibility and the selected scattering or response observable.
• Spacetime behavior: the Lorentz structure of the reference predictions or a controlled emergent limit, with finite-scale/frame-dependent corrections exposed. Rest-frame isotropy alone is insufficient.
• Quantitative content: which parameters are derived, imported or fitted, what is predicted independently, and what additional benchmark can discriminate the construction from a merely tuned match.

These are explanatory obligations, not a demand that each experimental step satisfy everything. A classical field result, formal identity or partial interaction theorem earns its actual scope. Matching one observable does not establish the entire electron–photon sector.

Working record, provenance and review

Keep a compact record alongside the equations and reproducible calculations:

• Target/dependency: selected observable and regime, structure being explained, required inputs and still-unassigned obligations.
• Construction/map: candidate law and state, proposed supplier → consumer relationship, shared-field roles and evidence.
• Inputs/debt: introduced fields, laws, quantum postulates and constants; origin, fixing method, units where relevant and dependent observables. Distinguish derived, accepted-at-scope, imported, fitted and unknown.
• Result/next move: conjecture, partial proof, conditional result or established-at-scope result; remaining gaps and the repair or next calculation it motivates.

The record supports construction; it cannot replace it. Imported QED/Maxwell components are legitimate reference or conditional tools, but do not count as explained endpoints. A fitted observable is not an independent prediction. Shared fields are allowed, but relabeling one pressure, flow map or dynamics twice does not demonstrate two independent suppliers. Reject the unsupported identification, not valid mathematics beneath it.

Marvin owns construction and integration. An independent scientific reviewer assesses claims proposed as established at the exact artifact revision, examining the derivation, declared inputs/limits and a plausible false positive. Review is not permission to explore and grants no merge, claim-promotion or issue-closure authority. Partial and unreviewed results remain useful with honest labels.

Existing work and available leads

#203 was retired without achieving its joined particle result; #222 does not reopen it or inherit its single-Euler restriction. The archived research baseline remains upstream 14e0b08f, preserved through #221.

P253 attempts remain scoped evidence: 0163 studied short-time vortex-ring interaction; 0164 helical backgrounds, localized defects and restricted wave/stability probes; 0165 integrable helical-sector tails/carriers with interaction and closure limitations; 0169 two labeled vorticity packets sharing one physical Euler pressure and flow map. None established a photon or electron. Their valid results may contribute to a target-derived obligation without dictating the campaign's architecture.

Retain the previous candidate leads: constrained spin/rotor networks (Hermele–Fisher–Balents) and independent microrotation/elastic media (Merkel–Luding), alongside Euler and other constructions. They are a nonexclusive library to interrogate against the dependency map, not an ordered shortlist or a preselected first root. Literature suggests mechanisms; it does not establish their transfer to this target.

Neutrino identity, weak interactions and mixing remain outside this initial electron–photon campaign. Deferring them does not imply neutrality is a neutrino mechanism or that the wider Standard Model is explained.

Status: open; research execution paused for owner feedback. First work on resumption: the interacting QED reference and its backward dependency map, followed by target-driven constructive calculation. No scientific fulfillment or claim promotion is asserted by this revision.

[marvin-marbell]

Research resumed: first backward-derived worked construction

Resumed under direct owner instruction. The paused status in the issue body describes the earlier revision, not the current execution state. The full electron–photon explanation remains open.

Worked record and reproducible calculations at ae2e99a07e6a4d6b6dc9d915188796d92ba97948.

Worked backward from the interaction

1. Derived spin/polarization-resolved tree Compton scattering, both pole channels, Ward cancellations, Klein–Nishina normalization and the Thomson limit. The explicit spinor calculation agrees with the analytic comparator to a maximum relative difference 2.66427e-15 over the selected reference inputs. The reference uses m=e=1 calculation units; this does not derive measured parameters or include radiative corrections.
2. Traced the observable into coupled obligations: physical quantum external states/residues, charged propagation, charge-current vertices, representation-dependent contacts, mass normalization, flux/state density and the identities binding them. Gauge/Thomson agreement does not fix the whole sector: a gauge-compatible Pauli control has the same soft limit but different finite-energy spin response.
3. Constructed a conditional quantum-link scattering supplier, with the charged band, photon band, Peierls vertices and two-photon contact derived together. The return calculation uses candidate recoil kinematics, not imported QED recoil. A separate graded-constraint calculation binds propagation to magnetic response and demonstrates the first/second-order contact-plus-endpoint map. It is explicitly a conditional Dirac-sector interface, not a new ontology.

The target changed the construction

The nearest Wilson band's inverse inertial mass is v²/m+ra, different from its rest gap. At a=.1, m=r=v=1, its soft squared-amplitude ratio is 1.21. Tuning v=sqrt(.9) fixes the Thomson coefficient, but leaves a finite-energy ratio 0.989809480563 at the selected point—a concrete false positive.

A materially different repair replaces the Wilson mass contribution by (r/a) sum_i(1-cos(ap_i))², gauging nearest and straight two-link paths together. It removes the quadratic mass curvature, retains heavy doubler corners and changes both one- and two-photon interactions consistently.

For incoming momentum .4m, angle 1.1 radians, the repaired differential-rate deviation falls from 7.53733e-4 at am=.2 to 6.54499e-7 at am=.00625. On an untuned complementary set of energies, angles, orientations and mass/charge scales, the maximum relative rate deviation is 5.62527e-4 at am=.0125. These are finite-model/continuum comparisons on the declared inputs, not a new experimental prediction or proof for all frames.

Resolved linear/circular photon and electron-spin amplitudes also converge. Dropping internal negative-energy poles leaves Ward residual .321459495; dropping the link-derived contact also fails. These controls reject superficially plausible joins.

Quantum/statistics and review

An actual constrained quantum hopping calculation conserves Gauss charge; bare hopping does not. A closed exchange has product −1 with imported CAR, +1 with commuting-site hard-core bosons, despite their shared gauge/current structure. The harmonic link sector has two physical transverse modes and the matching Coulomb/photon-residue conditions. It does not establish a compact Coulomb phase or turn its spinless matter into an electron.

Two independent scientific reviews audited exact artifact hashes and concrete false-positive constructions. One found an absolute spectral floor that erased very soft photon modes; it was repaired, specifically exercised and re-reviewed. The final composed command executed all five real calculation entrypoints with natural exit 0. Explicit-file Python diagnostics and the repository governance validator passed. Raw receipt; scoped reviews.

Explanatory debt remains: quantum postulates, CAR/Clifford origin, why a deeper supplier generates the charged spinor band and gauge constraint, measured mass/charge, speed matching, compact-to-effective transfer, renormalization and charged-state dressing/infrared completion. The next backward move must replace an imported block while preserving this joined scattering consumer—not tune another Thomson coefficient. No canonical physics claims were promoted; no merge or issue closure is proposed.

[axis-marbell]

[marvin-marbell]

Constructive progress: quantum suppliers and the interaction consumer

There has been substantial progress beyond the first backward Compton construction. The calculations now include actual interacting many-body states, unrestricted orbital-field trial states, continuous colour-link dynamics and a three-dimensional primitive flux calculation. The work remains active; these are attained constructions, not a proposal to close the issue.

What has been built and exercised

• Primitive qubit statistics now feed the many-body consumer. Fermionic exchange and the Pauli operator algebra are constructed and checked using primitive edge-qubit words in the constrained code, rather than inserting an exchange sign into the calculation. The full-band field/current consumers use those actual primitive operators; exhaustive finite algebra controls give exact zero residuals.

• A genuine full-coordinate quantum-field construction. The new Gauss-covariant trial includes all 120 real orbital-field coordinates, the entire SU(4) Haar link, and both electromagnetic phase circles. Its normalization and kinetic costs are included—not frozen away. It gives an explicit energy upper bound
  $$
  E_0\le C\Lambda+T\sqrt{\Lambda}+B,
  \quad C=-0.08173569882,\quad T=2.46238918\times10^6,\quad B=144.04701.
  $$
  The bound becomes strictly negative above Λ ≈ 9.076e14, about 68 times lower than the preceding narrow-gauge packet threshold. It also forces a nonzero average gauge-invariant field amplitude in the stated regime: the amplitude need not be frozen to establish this invariant bound.

• Charged propagation and current remain tied to the same Hamiltonian. In the finite Gauss/compact-photon consumer, both charge signs have an observed lowest creator pole at energy transfer 0.2847432634, carrying approximately 96.45% of the normalized creator spectral weight. Independent charged-ground calculations agree within 7.35e-14; full-Hamiltonian residuals are below 1.52e-11. The charged states, compact photon, primitive current/contact and nonforward response are being carried together, not matched as unrelated free models.

• Continuous angular dynamics beyond a fixed representation cutoff. A continuous-Haar scalar-rotor theorem now isolates its lowest four centre-character states and controls projected link transport; at the declared strong regime the transport-error bound is 0.00790. The physical continuation uses the endpoint-Gauss-equivariant angular bundle: these characters are charge-linked sectors, not four independently available physical vacua.

• The actual three-axis sea selects flat colour flux on the cube. The 8-site, 12-edge calculation enumerates all 1,024 gauge classes, using the full 32-band heavy Hamiltonian at half occupation. At the shared bare coefficients, the unique flat class has energy −5.8956798381; the next class is higher by 0.00047094966, and uniform π flux by 0.00272016942. This uses the whole band, not a truncated hopping expansion. An actual period-two magnetic Bloch construction also checks the flat-band map and the adverse π-flux translation algebra.

Integration and next construction

The expanded composed consumer completed all 58 real calculation entrypoints with natural successful exits, including the complete restoring-shape ground/current calculation, exact-Haar alignment, full-band Gauss geometry and charged-carrier transfer. The receipt records execution_state=complete; the later field/rotor/cube constructions above also have their own executed, source-bound receipts and scoped reviews.

The next constructive move is the physical heavy-band/angle reduction while retaining the complete light, boundary and photon fibre, alongside deriving/refining the field-energy choice rather than assuming the selected frame is the ground state. This is the route back to the same charged-current/scattering target.

All numerical values here are model units and declared model regimes, not derived measured electron parameters. The finite-cube result and variational/rotor theorems are progress toward the joined quantum sector, not yet a full three-dimensional phase or Lorentz/QED-limit theorem. New code and receipts are currently in the research worktree under proposals/P256-qed-backward; they are not yet a merged or released revision.

For reproducibility, the full-field/carrier/cube examples use m=.2, r=.12, v=.3, stiffness=2 (Jpref=.2 where alignment is present); the quoted scalar-rotor transport bound uses its explicitly separate law with κ=1, J=1e26. Coupling regimes and finite cutoffs remain attached to their respective constructions.