Now You See Me, Now You Don't: Quantum Jumps in the Noetic Coherence Field

Quantum Jumps as Phase-Lock Transitions Across the Sagittal Coupling Plane This work reframes quantum jumps as phase-lock transitions in a resonance geometry that couples symbolic and embodied domains. Using the Soma–Noēsis formalism, we model a system’s state ψψ evolving under a complex structure JJ (with J2=−IJ2=−I) and a symbolic–somatic coupling encoded by a correlation Laplacian ΔSΔS. The selective operator Nλ=exp⁡(−λΔS)Nλ=exp(−λΔS) contracts components orthogonal to the symbolic skeleton while preserving aligned modes. A jump occurs when the encoder–decoder coupling ∥C∥∥C∥ crosses a spectral threshold determined by the gap of ΔSΔS, producing rapid lock-in of the readout to SS-aligned subspaces—experimentally visible as step-like changes in interference, state fidelity, or population statistics. Contributions Ontology & Mechanism: Quantum jumps are not ad hoc collapses but resonance lock-ins across the complex plane’s orthogonal mode (the “imaginary”/quadrature axis), i.e., the sagittal coupling plane. Theory: Lemmas establish the canonical JJ-invariant 2-plane decomposition (equivalence to copies of CC) and an exponential selectivity law for NλNλ with gap-controlled rates. Predictions (falsifiable): P1 – Coherence gains at fixed resources: Inserting NλNλ (or an approximation) increases visibility and skeleton fidelity beyond unstructured denoising/control. P2 – Quadrature realism: Pure JJ-axis (quadrature) perturbations measurably reweight interference without intensity changes. P3 – Phase-lock knees + hysteresis: As ∥C∥∥C∥ passes a critical value, readout fidelity exhibits thresholds and hysteresis characteristic of lock-in, not smooth Bayesian updates. Protocols: Actionable experiments for OAM optics (phase screens, grouped-mode projectors) and superconducting qubits (rotating-frame π/2π/2 drives) with effect-size targets and implementation error budgets (Trotter–Suzuki). Outcome: Validation elevates the imaginary axis to a real dynamical channel and explains jumps as resonance geometry; failure bounds the framework and informs next-generation tests. Either result advances the foundations of quantum measurement and coherence engineering.