Paper B5 — Measurement and the Born Rule
Paper B5 demonstrates that the Born rule and quantum outcome probabilities emerge as a representational necessity once branching dynamics (B1–B4), discrete spectral structure (B3), and deterministic commit semantics (Paper A) are taken seriously. Quantum probabilities are not stochastic laws of nature, but epistemic weights over deterministically branching commit histories, forced by compatibility accounting under finite tolerance .
Key Results:
- When multiple mutually incompatible post-commit states exist after closure, an embedded observer cannot determine which branch they will occupy—structural uncertainty requires conserved branch measure
- Only quadratic weighting satisfies all constraints: additivity under branch refinement, conservation under unitary evolution (B4), correct reduction under coarse-graining
- Any other weighting rule breaks compatibility conservation, accumulates mismatch, or violates closure under repeated commits
- Measurement is not a new process but commit (substrate resolution from Paper A); “collapse” is deterministic commit to one branch, not stochastic wavefunction reduction
Epistemic Status: Establishes structural origin of Born rule without importing probabilistic axioms, measurement postulates, or collapse mechanisms. Outcome weighting is representationally necessary, not empirically postulated. Completes B-series recovery of quantum mechanics: entire quantum formalism derived from substrate mechanics without importing quantum axioms.
Substrate Assumption: Quantum-capable substrate (DCC-QM) with finite tolerance, coherence, admissibility, partition semantics. Cites AX-TOL (tolerance), AX-PAR (partition on violation), AX-REL (relational evolution).
Paper ID: CD-B5 | Series: B-series (Derived Physics) | Status: Draft | Dependencies: A, M4 (refines), B1–B4, AX-TOL, AX-PAR; informed by R-DCC