We present a complete and rigorous model of an EPR--Bell-type experiment within the framework of the de Broglie--Bohm theory. The purpose of this work is to show explicitly how a deterministic hidden-variable theory can reproduce all quantum-mechanical predictions, including the violation of Bell inequalities. Combining analytical arguments with numerical simulations, our approach offers a unified and transparent illustration of the central ingredients of de Broglie--Bohm theory, including particle trajectories, spin dynamics, and quantum entanglement. The model is designed to be pedagogical and self-contained, making it suitable for readers seeking a concrete understanding of how a nonlocal hidden-variable theory can describe the EPR--Bell experiment and illustrate Bell's theorem.
We present a geometric representation of bipartite quantum correlations based on a global spinorial structure. The framework provides an explicit mapping between measurement interaction and observed detector outcomes via a deterministic projection–threshold mechanism. The construction reproduces the singlet correlation form and clarifies how correlation structure can arise from geometric constraints on a global configuration rather than from pre-assigned subsystem properties. Probabilistic descriptions are treated as emergent at the level of repeated experiments, not as fundamental primitives. The framework is not formulated in terms of joint counterfactual assignments and is therefore not naturally expressed within the standard Bell–CHSH representation. The model yields a concrete experimental signature through threshold-dependent corrections to observed correlations.
AbstractWe present a geometric representation of bipartite quantum correlations based onglobal spinor structure rather than probabilistic hidden variables. The constructionreproduces the singlet correlation and provides an explicit mapping between mea-surement interaction and observed outcomes. The framework does not modify theempirical predictions of quantum mechanics, but supplies a non-factorisable mathe-matical representation in which outcomes arise through structural compatibility ratherthan sampling over counterfactual assignments. The analysis clarifies why Bell–CHSHfactorisations cannot be constructed within this representation and identifies the ob-struction as structural. The work addresses the representation of measurement andcorrelation structure within quantum theory.
This paper presents a structural interpretation of quantum measurement within the Scalar Drag Emergence Framework (SDEF), in which physical systems are described in terms of corridor morphology and an ancestry field governing coherence and constraint. In this formulation, measurement is defined as a mapping from an underlying structural configuration to observable outcomes under imposed constraints. Particles are interpreted not as fundamental entities, but as localized realizations of this mapping. Observable probabilities arise from the geometry of projection between structure and constraint, rather than from intrinsic randomness of independent objects. Entanglement is reinterpreted as the non-separability of corridor morphology, and Bell correlations emerge naturally from the non-factorizability of the mapping process. The framework reproduces standard quantum predictions, including the cosine correlation law and maximal Bell violation, as a consequence of symmetry. Quantum mechanics is identified as a symmetry-dominant regime corresponding to spatially uniform ancestry, in which transport remains non-selective and structural selection is inactive. Beyond this regime, the framework predicts structured, anisotropic deviations from ideal behavior in non-equilibrium or high-energy environments. This work does not modify quantum mechanics, but provides a coherent structural basis for understanding measurement, entanglement, and correlation within a unified conceptual model.
Bell’s theorem is a foundational result in quantum theory, demonstrating that no local hidden-variable model satisfying certain assumptions can reproduce quantum correlations. While mathematically correct within its formal framework, the theorem implicitly relies on a specific representational choice: measurement outcomes are modeled as scalar, commutative variables (±1). This assumption, though natural for flat and static configurations, is not mandated by physical necessity. In this work, we examine the consequences of relaxing this representational constraint when measurement outcomes arise as projections of states with nontrivial topology. We show that when physical correlations are naturally organized as elements of an S³-valued structure — such as those associated with spin and rotational degrees of freedom — the induced measurement algebra becomes noncommutative. Under these conditions, the key algebraic factorizations employed in Bell-type derivations no longer apply. We construct an explicit local, realistic model in which observable correlations reproduce the quantum expectation E(a, b) = − cos θ and violate the CHSH bound S ≤ 2, without invoking non-local interactions or superluminal influences. The effective S³×I structure arises not as a fundamental substrate, but as the natural geometric form taken by the actualization of physical processes within an underlying relational framework. Importantly, this structure was not introduced to address quantum entanglement specifically; it emerged independently in the study of cosmological expansion, emergent gravity, and mass generation. Its relevance to Bell-type correlations follows as a consequence of geometry, not as an ad hoc modification. These results suggest that quantum entanglement may reflect topological features of physical realization rather than intrinsic non-locality. Possible experimental implications and connections to geometric and substrate-based approaches to fundamental physics
de Broglie-Bohm theory (dBBT), treating quantum particles as point objects moving along well defined (Bohmian) trajectories, offers an appealing solution of the measurement problem in quantum mechanics; it has, however, problems relating to spin, relativity and lack of proper integration with the Hilbert space based framework. In this work, we present a consistent formalism which has the traditional state-observable framework integrated with the desirable features of dBBT. We adopt ensemble interpretation for the Schrodinger wave function
ψ. Given a Schrodinger wave function
ψ, we use its value
ψ0 at some fixed time (say,
t=0) to define the probability measure
∣ψ0∣2dx on the system configuration space
M (
=Rn). On the resulting probability space
M0, we introduce a stochastic process
ξ(t) corresponding to the Heisenberg position operator
XH(t) such that, in the Heisenberg state
∣ψh⟩ corresponding to
ψ0, the expectation value of
XH(t) equals that of
ξ(t) in
M0. This condition leads to the de Broglie-Bohm guidance equation for the sample paths of the process
ξ(t) which are, therefore, Bohmian trajectories supposedly representing time-evolutions of individual members of the
ψ0-ensemble. Stochastic processes and Bohmian trajectories corresponding to observables with discrete eigenvalues (in particular spin) are treated by extending the configuration space to the spectral space of the commutative algebra obtained by adding appropriate discrete observables to the position observables. Pauli's equation is treated as an example. A straightforward derivation of von Neumann's projection rule employing the Schrodinger-Bohm evolution of individual systems along their Bohmian trajectories is given. Some comments on the potential application of the formalism developed here to quantum mechanics of the universe are included.
In many-particle quantum mechanics the wave function is irreducibly defined on configuration space. In the de Broglie–Bohm theory this fact is made explicit: both the wave function and the actual motion are naturally described as evolving in configuration space, while the familiar three-dimensional motions of particles arise only as projections of this higher-dimensional dynamics. In this paper we argue that configuration space should be regarded as the fundamental arena of quantum dynamics. On this view, the nonlocal correlations observed in ordinary three-dimensional space are not mysterious dynamical influences but direct consequences of local evolution in configuration space. This perspective is developed and illustrated through a detailed analysis of momentum measurement and which-way detection in the iconic two slit experiment, in the two-particle interferometry experiment of Horne–Shimony–Zeilinger and in the Einstein–Podolsky–Rosen experiment.