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Cohesion Dynamics (CD)

Paper B2 — Non-Factorisable Composition and Entanglement

Paper B2 demonstrates that non-factorisable composite states (entanglement) are a representational necessity for cohesive substrates when multiple subsystems are subject to joint admissibility constraints under finite tolerance WW. Building on the linear amplitude framework (B1), it derives that subsystem separability is conditional, not fundamental.

Key Results:

  • Five-step necessity chain: (1) conditional separability holds only when joint constraints decompose additively, (2) joint admissibility generically produces non-decomposable cross-terms, (3) factorized representations cannot encode cross-terms without conflating distinct substrate states, (4) faithful representation forces non-factorisable coefficients, (5) this is precisely quantum entanglement
  • Any linear representational scheme faithful to joint admissibility must either encode non-factorisable coefficients (entanglement) or discard admissible substrate distinctions (information loss)—no third option
  • Entanglement is not a physical interaction but a representational consequence of joint constraint bookkeeping

Epistemic Status: No quantum postulates, non-locality assumptions, or measurement axioms imported. Derivation proceeds purely from substrate mechanics (A), finite tolerance (AX-TOL), joint admissibility (AX-ADM), and linear amplitude structure (B1). Establishes why composite quantum systems exhibit entanglement as unavoidable representational feature.

Scope: Does not yet address spectral discreteness (B3), dynamics (B4), or outcome probabilities (B5). Does not import tensor products, Hilbert spaces, Bell inequalities, measurement postulates, or probabilistic interpretation as primitives—these emerge or follow in subsequent papers.

Paper ID: CD-B2 | Series: B-series (Derived Physics) | Status: Draft | Dependencies: A, M2 (refines), M4 (refines), B1, AX-TOL, AX-ADM; informed by R-DCC