T26 — Coupled Spin Network + Matter
Arrow-of-time emergence
Objective
Couple Z₂ gauge field to a scalar field and study symmetry breaking that selects a global arrow of time.
Status
🔴 Blocked on T20 + T24
Theory
Combined action:
\[ S = S_{Z_2} + S_\phi + S_{\text{int}} \]
where S_int = λ Σ_v φ_v τ_v
Expected Outcome
⟨φ⟩ ≠ 0 spontaneously breaks remaining Z₂ symmetry, completing “orientability → arrow.”
References
- Paper: Section 6 (Discussion)