Electroweak Theory: A Research Direction

UCF/GUTT has formally verified recovery of quantum mechanical wave function formalism (UCF_Subsumes_Schrodinger_proven.v) and general relativistic field equations (UCF_Subsumes_Einstein.v, GR_Necessity_Theorem.v). The natural question is whether the framework can extend to Standard Model physics, beginning with electroweak unification.

This work is not yet proven. The content below represents a research program, not established results. Formal verification targets include Electroweak_Recovery_proven.v and Gauge_Symmetry_proven.v.

Electroweak Theory unifies electromagnetic and weak nuclear forces through SU(2) × U(1) gauge symmetry, with mass generation via the Higgs mechanism. It has been experimentally validated to extraordinary precision, including prediction of W and Z boson masses before their discovery.

Any framework claiming relevance to fundamental physics must either recover electroweak predictions as a special case, or explain why electroweak theory works despite being incomplete. UCF/GUTT pursues the first path: demonstrating that electroweak structure emerges from relational dynamics.

The following verified results provide the starting point:

Wave Function Recovery (UCF_Subsumes_Schrodinger_proven.v): Schrödinger formalism emerges from relational tensor evolution, establishing that quantum mechanical structure is compatible with UCF/GUTT.

Conservation Laws (UCF_Conservation_Laws.v): Energy-momentum conservation across relational scales, required for any viable particle physics.

Multi-scale Structure (NRT_Structure_Uniqueness.v): Nested Relational Tensors handle hierarchical dynamics, potentially relevant to symmetry breaking.

Conjecture 1: Relational Invariance as Gauge Symmetry

We hypothesize that gauge symmetry emerges from relational invariance—transformations that preserve relationships between entities while changing their individual descriptions.

Proposed formalism: Relational tensors transform as T'(p) = C · T(q), where C is a coupling tensor preserving relational structure.

Proof target: Show that SU(2) × U(1) structure emerges necessarily from relational constraints on NRT transformations.

Status: Conjectured, not proven.

Conjecture 2: Mass from Relational Density

Rather than the Higgs mechanism as fundamental, mass may emerge from relational coupling strength and network density, where effective mass depends on how densely connected an entity is within the relational network and the sum of its coupling strengths to other entities.

Proof target: Derive Higgs mechanism as a special case of relational mass emergence, recovering correct boson mass ratios.

Status: Speculative. No formal work begun.

Conjecture 3: Force Mediators as Relational Patterns

Gauge bosons (photon, W, Z) may be patterns within relational tensors rather than fundamental entities.

Proof target: Show that photon-like, W-like, and Z-like interaction patterns emerge from NRT dynamics with correct coupling constants.

Status: Conceptual proposal only.

For UCF/GUTT to legitimately claim electroweak recovery, formal verification must establish:

First, gauge group emergence—that SU(2) × U(1) structure arises from relational constraints rather than being imposed. Second, coupling constant relationships—that the Weinberg angle emerges from relational geometry. Third, mass generation—that W/Z masses and the massless photon follow from symmetry breaking in NRTs. Fourth, interaction vertices—that correct Feynman rules for electroweak processes can be derived. Fifth, anomaly cancellation—that quantum consistency conditions are preserved.

None of these have been formally verified.

This research program fails if relational invariance cannot produce non-Abelian gauge structure, if no natural mechanism generates the observed mass hierarchy, if coupling constant ratios cannot be derived from relational geometry, or if the framework predicts phenomena contradicted by precision electroweak measurements.

Electroweak Theory is experimentally validated with precise, confirmed predictions. It achieves unification through SU(2) × U(1) gauge symmetry, explains mass through the Higgs mechanism, and treats W, Z, and photon as fundamental force-carrying particles.

UCF/GUTT's approach remains a research program with no experimental predictions yet. It proposes that gauge structure emerges from relational invariance (conjectured but unproven), that mass arises from relational density (speculative), and that force mediators are patterns within relational tensors rather than fundamental particles (conceptual only).

The asymmetry is stark: Electroweak Theory has decades of precision confirmation. UCF/GUTT has suggestive conceptual parallels but zero formal verification of electroweak recovery.

Phase 1: Gauge Structure (Target: 2025-2026)

Formalize relational invariance in Coq. Prove or disprove emergence of Lie group structure from NRT constraints. Deliverable: Gauge_Symmetry_proven.v or documented failure.

Phase 2: Electroweak Recovery (Target: 2026-2027)

If Phase 1 succeeds, extend to SU(2) × U(1) specifically. Derive Weinberg angle from relational geometry. Deliverable: Electroweak_Recovery_proven.v or documented obstacles.

Phase 3: Experimental Predictions (Target: 2027+)

If recovery succeeds, identify where UCF/GUTT predictions diverge from Standard Model. Propose testable differences.

Electroweak Theory is among the most precisely tested theories in physics. UCF/GUTT has not yet demonstrated it can reproduce these results. The conceptual parallels between relational invariance and gauge symmetry are suggestive but unproven.

This page documents a research direction, not an achievement. The formal verification work remains ahead.

Proven foundations are available at the GitHub repository github.com/relationalexistence/UCF-GUTT.

Current proof files do not yet include electroweak recovery. This page will be updated as formal verification progresses.