In the Asymmetric Source Field Model (ASFM), light is described as a field of interference nodes, which in physics would correspond to light quanta. This work examines whether the correlations of polarization-entangled light pairs arise because both nodes of a pair lie on the field of the same short-lived null-field sources. For point-symmetric source arrangements the orientations of both nodes agree at all times, and mixing two perpendicular source planes sets the shared orientation continuously to any angle while the partner node follows exactly. Under the principle that the sources and their carrier wave respond to a measurement as a whole, the setting at one node is fully transferred to the other. A readout from the independent fine structures of the two polarizer outputs yields Malus's law. In the limit of many contributions the Tsirelson bound 2√2 is the upper limit of the model for every transfer strength. The seven data points of Aspect, Grangier and Roger (1982) are reproduced with χ² = 2.1 without freely fitted parameters. The signed outcomes at each node remain balanced. The field power in the detector cone of the other node depends by a few per cent on whether a measurement takes place, but not on the setting, which is a testable prediction beyond quantum mechanics. The English and German manuscripts are included.
In the Asymmetric Source Field Model (ASFM), light is described as a field of interference nodes, which in physics would correspond to light quanta. This work examines whether the correlations of polarization-entangled light pairs arise because both nodes of a pair lie on the field of the same short-lived null-field sources. For point-symmetric source arrangements the orientations of both nodes agree at all times, and mixing two perpendicular source planes sets the shared orientation continuously to any angle while the partner node follows exactly. Under the principle that the sources and their carrier wave respond to a measurement as a whole, the setting at one node is fully transferred to the other. A readout from the independent fine structures of the two polarizer outputs yields Malus's law. In the limit of many contributions the Tsirelson bound 2√2 is the upper limit of the model for every transfer strength. The seven data points of Aspect, Grangier and Roger (1982) are reproduced with χ² = 2.1 without freely fitted parameters. The signed outcomes at each node remain balanced. The field power in the detector cone of the other node depends by a few per cent on whether a measurement takes place, but not on the setting, which is a testable prediction beyond quantum mechanics. The English and German manuscripts are included.
The Asymmetric Source Field Model (ASFM) is a general real-space residual-field theory that addresses multiple open questions in quantum and nuclear physics. The present work applies this framework specifically to quantum correlation structure. Observable structures are modeled as spatially bounded residual-field interference organizations with resonance structure arising from harmonically scaled spherical source-field superposition. Constructive and conjugate-modulating sectors generate spatially bounded, nonzero, spatially persistent coherence nodes characterized by phase coherence, amplitude ordering, eigenmode structure, resonance capability, and node-to-node coupling response. In the Bell/CHSH reconstruction, the two measurement sites are not treated as independent carriers of pre-existing local values. They are local eigenmode readouts of one shared, spatially bounded residual-field interference topology with resonance structure. ASFM is therefore not a Bell-local hidden-variable model; the Bell assumption not satisfied by ASFM is local separability, equivalently local factorization. Bell-type correlations arise from non-separable residual-field topology, not from detector unfairness, sample rejection, or post-selection. The present work formulates the corresponding norm-preserving CHSH ring structure. The four CHSH configurations are interpreted as linked readout states of a closed resonance ring in the joint residual-field eigenmode space. A physically admissible closed ring may redistribute phase, frequency, amplitude, and eigenmode orientation, but it may not create residual-field readout norm. The associated normalized ring coherence represents the closure fraction of the conserved ASFM ring-norm class. The Bell-local boundary corresponds to the absence of an additional nonclassical ring-closure contribution, whereas complete norm-preserving closure corresponds to the Tsirelson limit. The paper distinguishes effective and direct Noether-ring coherence. Effective coherence is extracted from the simulated CHSH value. Direct coherence is predicted independently from phase closure, frequency compatibility, amplitude balance, and residual-node eigenmode coherence. Agreement between these quantities and their stable positive correlation constitute the principal non-circular validation criterion. The numerical reconstruction reports stable interference-resonance windows in which fixed-ring bounded readouts are Bell-violating and Tsirelson-safe. The leading confirmed window at a grid resolution of 65 cubed and harmonic range K6-K24 reaches a mean absolute CHSH value of 2.8118, with no Class-III seed in high-statistics confirmation. Across all confirmed interference-resonance windows, fixed-ring component tests show that phase, frequency compatibility, amplitude readout, eigenmode transport, coupling, and CHSH angular geometry are necessary. Controlled degradation of each component monotonically reduces the absolute CHSH value and produces no super-Tsirelson outcomes. The strongest near-Tsirelson windows form a more specific structural subclass characterized by compact pair topology, stable bounded readout, favorable amplitude response, and stable two-axis eigenmode structure. Direct structural coherence is retained as a global classifier. The principal non-circular refinement is an independently computed CHSH-mode anisotropy factor that incorporates the local orientation, transport, and angular dependence of the eigenmodes before CHSH evaluation. Within this application of the broader ASFM theory, quantum entanglement is interpreted as the effective readout of coupled, spatially bounded residual-field interference nodes with resonance structure embedded in a shared field topology, rather than as a connection between isolated particles. The Tsirelson bound is reconstructed operationally as the fixed, norm-preserving closure limit of an admissible CHSH residual-field readout ring.
This record provides the short manuscript of the Asymmetric Source Field Model (ASFM), a deterministic interference-field approach in which atomic structure is described by stable residual coherence nodes formed by superposed spherical-wave sources. The manuscript is included in English and German versions. The work focuses on a field-based interpretation of valence as an emergent node topology and outlines a parameter-sweep and node-detection workflow for selected elements. Note on code: A standalone reference implementation exists, but it is not included in this record version because it has not been re-tested in the current environment. A tested snapshot can be provided in a later Zenodo version.
What quantum mechanics calls "observation" has lumped together three interactions of different character: one that switches the discrete state of the partner, one that leaves the partner's state unswitched and shifts only the internal phases, and one that severs the mutual phase relation. This paper places the substance of observation in the second, the readout of the interference of a phase difference, and adopts only three premises. (P1) The distance between two parties is set by the ratio of a shared viewing angle to the partner's size; only ratios are readable and the absolute scale is not. (P2) An interaction is a single relation in which emission and absorption hold simultaneously; the speed of light appears on the readout side as a conversion factor between local clocks. (P3) The phase of a relation carries a harmonic order n that depends on the kind of wave. From these, the fact that a probability is the product of an amplitude and its conjugate (the form of the Born rule), the two-party correlation E = ∓cos nθ, the upper bound 2√2 of the CHSH quantity (the Tsirelson bound), and no-signaling follow in a few lines. The normalization that turns this into a probability is the division that discards the size ratio, i.e. the choice of the η = 0 section. As a consequence, the bound is 2√2 independently of the kind of wave, and the detector angle giving the maximal violation shrinks in proportion to 1/n (45° for spin-½, 22.5° for photons, 11.25° for gravitational waves). For a localized relation that is a sum of harmonics the correlation is the autocorrelation of the pulse shape; the bound holds for any weights, equality is attained only for a single harmonic, and a rectangular pulse reduces to a local hidden-variable model with S ≤ 2. Japanese original (authoritative) and English translation, with TeX sources, PDFs, five figures (Japanese and English labels) and the figure-generating program.
This paper examines a local deterministic model of an experiment involving correlated photons. The experimental setup involves a source that emits two linearly polarized photons in each act, two two-channel analyzers, and detectors included in the coincidence scheme. The orientation angle of the photon polarization plane is a random variable with a uniform distribution, and it is the same for simultaneously emitted photons. The model presented here is a generalization of the “naive example of hidden variable theory” described in A. Aspect's article ‘Bell's Theorem: The Naive View of an Experimentalist. In our model, the outcome of the photon interaction with the analyzer (hit in one of the two channels) is uniquely determined by the angle between the photon polarization plane and the analyzer axis and is described by a step function. The difference in our model is that the step function contains a large number of segments of different lengths. The location and lengths of the segments are set so that the probability of a photon hitting a specific channel of an ideal analyzer, determined by averaging the outcomes over small neighborhoods of angles, approaches the Malus law when the maximum length of a segment decreases. This ensures that the classical model is self-consistent. When ideal analyzers are used, the absolute value of the correlation coefficient of detector readings mainly does not exceed the values from Aspect's ‘naive example’. However, when analyzers with absorption are used, the calculated correlations for some orientations of the analyzers exceed the quantum mechanical values. Key words: linear polarization of photons, Malus law, entangled photons, correlations, hidden parameters.
Photon polarization is one of the cleanest physical settings in which two-state quantum structure, superposition, interference, and Bell-type entanglement are experimentally realized. This paper asks a narrow structural question: does the tholonic N-D-C geometry contain a native mathematical structure that can represent the polarization degrees of freedom of a photon and the non-factorizable correlations of an entangled photon pair? The answer developed here is qualified but affirmative. The tholonic role space begins with three coordinates, (N, D, C), but its common-mode direction (1,1,1) carries no information about relative role differentiation. Removing that common mode leaves a two-dimensional zero-sum plane V, singled out by the model's own cyclic role symmetry N → D → C → N rather than by convenient axis-dropping. That plane is already implicit in the framework's cube-root-of-unity representation, and a pair of orthogonal directions in it can represent the linear-polarization basis of a photon without declaring the tholonic roles D and C themselves to be orthogonal. For a non-factorizable antisymmetric two-photon state, the corresponding binary observables yield the standard photon-polarization correlation E(a,b) = -cos 2(a-b), with the usual CHSH settings giving |S| = 2√2. Beyond reproducing the standard result, the construction has one feature not visible in the quantum formalism alone: the three roles occupy three fixed directions 120° apart in the relational plane, which as polarization axes form an equiangular trine at 60° spacing. Evaluating CHSH on these native settings, with no angle tuning, gives |S| = 5/2, so the triad's own role directions already violate the classical bound, reaching 88.4% of the Tsirelson bound, while provably falling short of saturation. The construction is not a derivation of quantum mechanics from tholonic first principles. Tensor-product composition and the Born interpretation of squared amplitudes remain quantum postulates, and the full polarization qubit requires complexifying the relational plane. The result is presented as a structural embedding with one quantitative signature, together with a proof, restated from first principles, that no tholonic construction built from two children reading one shared object (fixed, cyclic, or a deterministic parent-to-child pipeline) can exceed the classical CHSH bound of 2. Paper 38 in the Tholonic N-D-C series (Clarity Coalition).