Paper4Quantum entanglement from the linearized visible action in the B framework

This research investigates whether a Heisenberg-type uncertainty structure can be derived, in a controlled effective sense, from the visible action of the alpha-beta-phi framework. Starting from the already established visible action, the study reduces the linearized visible sector to a single normalized mode and identifies a natural branch-observed coordinate Q = qbeta + eta*qₚhi, together with its conjugate momentum PQ = pbeta. Key Developments: Quantization: The work yields the effective canonical relation Q, P = i*hbar and the corresponding uncertainty inequality deltaQ * deltaPQ >= hbar/2. Diagonalization: The coupled visible oscillator is diagonalized to derive explicit ground-state expressions for the uncertainties. Open-System Dynamics: By coupling the observed coordinate to an external environment, the study derives a master equation where the environmental term that suppresses interference also generates diffusion in the conjugate momentum. Conclusion: The results demonstrate that uncertainty, decoherence, and branch selection descend from the same visible action-based structure. This connection is established within the reduced linearized visible sector and its open-system extension, serving as a foundational step toward the full interacting theory.