We introduce a local phase-field framework for spin-entanglement correlations. In this framework, the relevant hidden variable is an internal scalar phase associated with each fermion and derived from two underlying real fields. The fields are assumed to evolve locally in ordinary spacetime. When a particle pair is produced at a common spacetime event, the pair acquires a shared phase-locking condition at creation; after separation, the two internal phases evolve independently and no nonlocal interaction is introduced. Spin measurements by Stern–Gerlach analyzers are modeled as local filtering operations. Each local response depends only on the internal phase carried by the particle and on the orientation of the local analyzer. The local response function A(α,λ) = cos(λ − 2α) is derived from the spinorial transformation law of the underlying real field pair and the projection geometry of the detector interaction; it is not a phenomenological ansatz. From these deterministic local responses we derive an analog correlator. The raw product moment of the continuous detector outputs evaluates to ⟨AB⟩ = −½ cos 2(α − β), which satisfies classical Clauser-Horne-Shimony-Holt (CHSH) bounds. After Pearson normalization—the operationally appropriate correlation measure for continuous analog detector outputs, justified by channel-contrast physics and scale invariance—the normalized correlator yields E(α,β) = −cos 2(α − β), matching the quantum singlet correlator in functional form. When this normalized correlator is inserted into the CHSH expression, it yields the numerical value 2√2. This result is a structural consequence of the reduced marginal variance of continuous response functions relative to the unit-variance dichotomic observables assumed in Bell’s derivation; it does not constitute a violation of Bell’s inequality. The model does not reproduce quantum singlet statistics at the level of binary detector outcomes, where the correlator takes a triangular rather than cosine form. The contribution is therefore ontological and conceptual rather than predictive. The framework preserves parameter independence and no-signaling throughout. It provides a concrete real-field ontology for spin correlations based on internal phase structure, and it demonstrates that the functional form of the quantum singlet correlation can be obtained from a strictly local deterministic description, provided that the detector responses are treated as continuous analog quantities and normalized accordingly. We compare the model with earlier phase-based approaches and discuss experimental configurations—including time-resolved and multi-stage Stern–Gerlach measurements—that could in principle probe the proposed internal-phase dynamics at the pre-registration level.
Doron Kwiat (Fri,) studied this question.