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

TL;DR

This paper introduces the Branched Hilbert Subspace Interpretation (BHSI), a novel framework that models quantum measurement as a unitary process involving branching, enabling a unified view of quantum coherence, nonlocality, and relativistic causality.

Contribution

It proposes a dual-layer experiment to test measurement timing and develops a mathematical structure linking quantum nonlocality with local Hilbert subspaces within BHSI.

Findings

Born rule derived from initial state amplitudes

Quantum nonlocality explained via inner-product structure of LHS

Proposes experimental test for measurement timing

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.