Stern-Gerlach Interferometers with Dual Sensing: Probing Recoherence and Lifecycles of Islands of Coherence

Abstract

The Branched Hilbert Subspace Interpretation (BHSI) addresses the quantum measurement problem by preserving unitary quantum evolution within a single world. Its central concept is the Island of Coherence (IOC), an operationally isolated, inseparable quantum system mathematically described by a Local Hilbert Space (LHS), which carries no intrinsic spacetime metric and coexists with the spacetime in which the IOC is embedded, a dual structure implicated by the first quantization. This paper advances BHSI on both experimental and conceptual frontiers. Experimentally, we propose a three-stage dual-sensing Stern-Gerlach interferometer (SGI) designed to probe the fuzzy spatiotemporal boundaries associated with IOC transitions. Stage 1 targets uncommitted timing events, manifested as sensor-detector mismatches; Stage 2 investigates conditional recoherence, a signature of local, time-extended branching; and Stage 3 employs controlled electromagnetic phase shifts to discriminate between unitary and retrocausal recoherence mechanisms. Conceptually, we introduce the lifecycle of IOCs, describing how coherent domains emerge, persist, and fragment across scales. We draw structural analogies between fuzzy IOC boundaries and phenomenological bag models in quantum field theory, and between primordial global Hilbert space fragmentation and Hilbert space fragmentation in many-body systems. Altogether, BHSI offers a consistent and experimentally testable approach to resolving the quantum measurement problem.