Einstein's Electron and Local Unitary Branching: Boundaries of Islands of Coherence and Quantum Nonlocality

Abstract

The Branched Hilbert Subspace Interpretation (BHSI) aims to provide a unitary account of quantum measurement while maintaining a single-world ontology. The framework reexamines scenarios such as Einstein 1927 electron-diffraction thought experiment by treating measurement as a finite dynamical process of information recording, comprising a sequence of unitary operations: branching, engaging, and disengaging. This perspective motivates a testable proposal: a dual-layer experiment in which the particle transit time between layers is shorter than the sensor response time, enabling a direct probe of measurement timing and potentially uncommitted outcomes. We introduce the Island of Coherence (IOC) as an operationally isolated quantum system, mathematically described by a Local Hilbert Subspace (LHS), which coexists with the background spacetime and within which unitary branching occurs. Historically, the first quantization already implies this dual structure. Applying the Gleason and Busch theorems to local unitary branching, the Born rule follows from the amplitudes given in the initial state. Moreover, quantum nonlocality (e.g., in Bell tests or tunneling) arises naturally from the inner-product structure of the LHS, which possesses no intrinsic spacetime metric. BHSI thus provides a coherent framework in which relativistic causality and quantum correlations remain structurally compatible.