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.
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.
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.
We develop an explicit configuration-space formulation of EPR-Bell experiments within the framework of de Broglie-Bohm theory, in which joint measurement outcomes arise from a deterministic mapping from initial particle configurations to outcome pairs. This construction induces a partition of the hidden-variable configuration space into domains associated with the different measurement outcomes. Using a reduced-dimensional Stern-Gerlach model, we derive the structure of these domains and identify the corresponding separatrices that define their boundaries. We show that Bell correlations emerge from the geometry of these partitions: the domain boundaries depend nonlocally on the measurement settings, while the marginal outcome distributions remain invariant, providing a direct dynamical realization of no-signaling. Analytical results are supported by numerical simulations, which exhibit quantitative agreement with the predicted domain structure as a consequence of the underlying partition of configuration space induced by the measurement dynamics. This approach provides an explicit configuration-space representation of nonlocal correlations in Bohmian mechanics, linking trajectory dynamics, measurement processes, and statistical predictions within a unified framework.
This work presents an elegant and conceptually clean geometric bridge between Pauli algebra and the topology of the Hopf fibration. It shows that the well-known Bell singlet correlation E(a, b) = −a·b is not an additional mystery of quantum theory, but is already fully encoded in the standard spinor geometry S³ → S² and in the non-commutative structure of SU(2). The main result can be understood as a representation statement: the Bell correlation admits a natural formulation as the real part of a U(1) holonomy on the Hopf bundle, namely E(a, b) = Re exp(i(π − θ)), where θ is the angle between measurement directions on the Bloch sphere. This holonomy arises from the Berry–Pancharatnam phase defined on the projective space CP¹ ≃ S², and depends only on the associated oriented solid angle. Importantly, this work does not introduce new physical laws and does not modify quantum mechanics. Instead, it demonstrates that the standard result E = −a·b already admits a rigorous geometric interpretation in terms of connections, curvature, and parallel transport. In this sense, the contribution is not a new theory, but a precise geometric reformulation of existing quantum structure. A key clarification concerns interpretation. The non-abelian SU(2) structure appearing here is not a hidden variable in the sense of Bell’s theorem. It describes the geometry of the quantum state space S³, not a set of pre-existing measurement outcomes. The reduction to U(1) reflects the fact that projective measurements access only equivalence classes on S², discarding the global phase. Accordingly, the violation of Bell inequalities arises from non-commutativity of observables, not from hidden parameters or signalling. The value of the work lies in structural unification. It brings together three standard but often separately presented elements: (i) the algebraic form of entangled correlations, (ii) the geometry of spinor space S³ and the Bloch sphere S², and (iii) the holonomy/phase nature of quantum quantities. In this formulation, Bell correlations appear not only as probabilistic objects, but as global geometric features of the underlying state space. This perspective is particularly useful for geometric quantum mechanics, quantum information theory, and pedagogy, where it provides a clear and rigorous insight into the origin of the cosine correlation law. At the same time, the scope is deliberately modest: the construction is fully consistent with standard quantum theory and does not attempt to extend it. The main risk lies in interpretational overreach. While the geometric picture is compelling, it should not be mistaken for an alternative to quantum mechanics or for a hidden-variable completion. Rather, it reveals an internal geometric layer that is already present in the theory. In summary, this work represents a high-quality incremental advance in quantum foundations: not a paradigm shift, but a compact and illuminating reconstruction of a fundamental result in the language of topology and geometry.
We revisit the Bell--CHSH scenario for two spin-21 particles and isolate the precise algebraic origin of the Bell contradiction. On the quantum side, spin-21 is described by a noncommutative spinor (Clifford) algebra acting on the Hilbert space of two spin-21 particles, with the singlet state yielding the usual correlation E(a,b)=−a⋅b and Tsirelson's bound 22. On the classical side, the standard Bell assumptions amount to describing all measurement outcomes as {±1}-valued random variables on a single Kolmogorov probability space, i.e.\ elements of a commutative algebra C(Λ).
We show that there is no representation of the spinor algebra of spin-21 (with its singlet state and locality structure) into any such commutative Kolmogorov algebra that preserves the {±1} spectra of local spin components and the singlet correlations entering the CHSH expression, under the standard Bell assumptions of locality (factorization) and measurement independence. In this sense, the Bell--CHSH contradiction is exhibited as an algebraic mismatch between a noncommutative spinor/Clifford description of spin and the classical assumption of a single global Kolmogorov space supporting all outcomes. In the language of quantum probability, this is a C∗-algebraic reformulation of the known fact that the singlet correlations admit no local hidden-variable model with jointly distributed outcomes on one probability space.
We also give an explicit realization of the same spinor structure within the author's Quantum Index Algebra (QIA) framework, where locality appears as disjoint index slots and the singlet state as a simple index cocycle.
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
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to the customary a priori given frame of reference of the laboratory when describing real EPR experiments. J.S. Bell has argued that local hidden parameter theories that reproduce the predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning leading to Bell's conclusion is physically meaningless if the frame of reference that is based on EPR-correlations is accepted as the backdrop for EPR-type experiments. The refutal of Bell's proof opens up for the construction of a viable hidden parameter theory. A model of a spin h/2 particle in terms of a non-flat metric of space-time is shown to be able to reproduce the predictions of quantum mechanics in the Bohm-Aharonov version of the EPR experiment, without introducing non-locality.