B-Series: Quantum Representation in Cohesion Dynamics
The B-series explains why quantum-mechanical structure emerges as the stable representational calculus for systems embedded in a branching, reconciling informational substrate.
These papers do not introduce stochastic laws or collapse. Instead, they show how amplitudes, interference, entanglement, and Born-like weighting arise as structural necessities for coherent self-location and prediction.
How the Papers Fit Together
The papers are intended to be read in order:
- B1 — Why amplitudes are the correct representational objects
- B2 — Why entanglement and non-factorisable structure are unavoidable
- B3 — Why outcome weighting is required at all
- B4 — Why norm-preserving, reversible structure is selected
- B5 — Why Born-like quadratic weighting is the uniquely stable calculus
This prevents people jumping straight to B5 and misunderstanding it.
Papers
B — Continuum Physics in Cohesive Phases
Continuum-level behavior and foundations
Establishes the continuum-level behavior that emerges from substrate mechanics. Provides the foundation for understanding how effective physical theories arise.
Status: v0.9
B1 — Emergence of Quantum State Representation
Why amplitudes are the correct representational objects
Demonstrates that linear amplitude-based state representation is a representational necessity for cohesive substrates exhibiting mergeable divergent histories under finite tolerance W. Shows that any representational calculus capable of faithfully tracking substrate evolution through branching constraint resolution paths must employ a linear composition rule.
Amplitudes emerge as bookkeeping objects for compatibility and provenance relationships. Linearity is forced by consistency requirements: regrouping, associativity, and invariance under history reordering.
Status: Draft
B2 — Non-Factorisable Composition and Entanglement
Why entanglement and non-factorisable structure are unavoidable
Shows that joint admissibility forces composite structure and that non-factorisable cross-terms (entanglement) are forced by joint constraints under finite tolerance W. Demonstrates that once composite systems exist, entanglement is unavoidable.
Status: Draft
B3 — Spectral Discreteness from Closure Stability
Why outcome weighting is required at all
Explains how closure stability selects discrete modes while continuous configurations fail closure. Shows that only discrete families satisfy commit-cycle closure within tolerance W. Quantisation emerges as a selection effect, not a boundary condition.
Status: Draft
B4 — Quantum Dynamics from Commit-Based Evolution
Why norm-preserving, reversible structure is selected
Demonstrates that closure-preserving transport uniquely determines Schrödinger-class dynamics. Shows that unitary evolution emerges from representational consistency and that Hamiltonians are bookkeeping devices for stable transport, not fundamental operators.
Status: Draft
B5 — Measurement and the Born Rule
Why Born-like quadratic weighting is the uniquely stable calculus
Explains why, in a deterministic branching substrate, only a quadratic (Born-like) weighting scheme remains stable under interference, recomposition, and self-location.
Shows that probability is an emergent representational necessity, not a fundamental postulate. Measurement is shown to be substrate commit (partition), not a collapse postulate.
Status: Draft
Who Should Read This Series?
This series is for you if:
- You have a background in quantum mechanics or foundations
- You want to understand why the quantum formalism has its structure
- You are comfortable with conceptual (not computational) arguments
This series is not:
- A quantum mechanics textbook
- A proposal of new quantum dynamics
- An interpretation of QM independent of substrate structure
Additional Resources
For a comprehensive technical overview of the B-series, including assumptions, derivations, boundaries, and reviewer audit maps, see the B-Series Overview Guide.
For context on how the B-series fits into the broader research programme, see the Research Programme page.