Quantum mechanics and modern artifcial intelligence belong to profoundly diferentscientifc domains. Nevertheless, both exhibit behaviors whose conceptual interpretationbecomes difcult when one attempts to attribute the observed outcome exclusively to isolatedobjects.In Young’s double-slit experiment, the observed behavior depends on the global exper-imental arrangement, including whether or not an interaction is introduced that providesinformation about the path followed by the quantum system. In modern artifcial intelligencesystems, the generated response depends not only on training data and algorithms, but alsoon context, internal representations, constraints, interaction history, and the prompt providedby the user.In this work, we extend a discrete relational framework based on the additive group(nZ, +). The central hypothesis is that certain behaviors described as probabilistic, emergent,or unexpected may be interpreted as observable manifestations of a deeper global relationalorganization.In this perspective, probability is not removed from scientifc formalism. Instead, weinvestigate the possibility that probability may not necessarily be fundamental, but couldconstitute an efective description of the uncertainty of an observer having access only to partof the complete relational scene.We introduce the notions of relational scene, admissible confgurations, relational coherence,and a hypothetical relational selection operator. We then show how these concepts mayprovide a common conceptual language for discussing quantum measurement and responseemergence in artifcial intelligence systems without identifying artifcial intelligence with aquantum system.Finally, we formulate the minimum requirements that a relational theory must satisfyin order to move beyond the status of a conceptual interpretation: it must recover knownquantum probabilities, yield quantitative results, and identify at least one empirically testableprediction that distinguishes it from existing descriptions
Quantum mechanics and modern artifcial intelligence belong to profoundly diferentscientifc domains. Nevertheless, both exhibit behaviors whose conceptual interpretationbecomes difcult when one attempts to attribute the observed outcome exclusively to isolatedobjects.In Young’s double-slit experiment, the observed behavior depends on the global exper-imental arrangement, including whether or not an interaction is introduced that providesinformation about the path followed by the quantum system. In modern artifcial intelligencesystems, the generated response depends not only on training data and algorithms, but alsoon context, internal representations, constraints, interaction history, and the prompt providedby the user.In this work, we extend a discrete relational framework based on the additive group(nZ, +). The central hypothesis is that certain behaviors described as probabilistic, emergent,or unexpected may be interpreted as observable manifestations of a deeper global relationalorganization.In this perspective, probability is not removed from scientifc formalism. Instead, weinvestigate the possibility that probability may not necessarily be fundamental, but couldconstitute an efective description of the uncertainty of an observer having access only to partof the complete relational scene.We introduce the notions of relational scene, admissible confgurations, relational coherence,and a hypothetical relational selection operator. We then show how these concepts mayprovide a common conceptual language for discussing quantum measurement and responseemergence in artifcial intelligence systems without identifying artifcial intelligence with aquantum system.Finally, we formulate the minimum requirements that a relational theory must satisfyin order to move beyond the status of a conceptual interpretation: it must recover knownquantum probabilities, yield quantitative results, and identify at least one empirically testableprediction that distinguishes it from existing descriptions
This article proposes a conceptual bridge between artifcial intelligence, theYoung double-slit experiment, and a discrete relational framework based on theadditive group (nZ, +). Artifcial intelligence is usually described as a system builtfrom data, algorithms, learning procedures, internal representations, and computa-tional architectures. This description is technically necessary, but it may remainconceptually incomplete. A response produced by an artifcial intelligence systemdoes not arise from isolated data alone. It emerges from a global organization ofrelations between data, context, constraints, internal structures, user interaction,and representational patterns.A comparable relational interpretation can be proposed for the Young double-slitexperiment. In this experiment, the introduction of a measurement device changesthe observed behavior of photons, electrons, or matter. This change does not requireattributing consciousness to the particle. Instead, it can be understood as thetransformation of the global relational scene. The source, the slits, the detector,the screen, and the experimental conditions form a relational structure. Whena detector is introduced, the structure is no longer the same, and the observedbehavior changes accordingly.By analogy, interaction with artifcial intelligence can be viewed as an informa-tional form of measurement. A prompt, a discussion, a reformulation, or a con-straint introduced by the user changes the relational confguration from which theresponse emerges. Therefore, artifcial intelligence should not be understood onlyas a machine that retrieves stored data or executes explicit algorithms. It can alsobe understood as a relational system in which new associations, new formulations,and new conceptual organizations may emerge through interaction.The goal of this article is not to claim that artifcial intelligence is conscious, norto identify artifcial intelligence with quantum physics. Rather, the goal is to showthat both domains can be examined through a common relational principle: observ-able behavior may arise from the organization of relations rather than from isolatedentities. The discrete relational framework based on (nZ, +) is presented as a con-ceptual candidate for studying information, interaction, measurement, coherence,and emergent behavior.
For centuries, science has attempted to understand reality by identifying its most fundamen-tal objects. Atoms, particles, molecules, felds, neurons, symbols and data have progressivelybecome the elementary building blocks through which natural phenomena are described.This object-centered view has produced remarkable scientifc achievements. Nevertheless,many phenomena observed in physics, mathematics, language, biology and artifcial intelligencesuggest that the behavior of a system cannot always be understood by studying its componentsindependently.The central idea developed throughout this book is that relations may be more fundamentalthan the objects themselves.Objects acquire meaning through the network of relations in which they participate. Observ-able behavior emerges from coherent relational organizations rather than from isolated entities.This book proposes a discrete relational framework based on the additive group(nZ, +)as a possible mathematical foundation for describing relational organization, emergence,measurement, artifcial intelligence and several conceptual questions arising in modern quantumphysics.The objective is not to replace existing theories but to explore a complementary perspectivein which relations become the primary elements of scientifc description.
Quantum mechanics is based on fundamental notions such as the wave function,superposition, probability, measurement, entanglement, and nonlocality. These no-tions are remarkably successful from both mathematical and experimental points ofview, yet they raise deep conceptual questions. Is the wave function a real physicalobject or only a computational tool? Does superposition mean that an object reallyexists in several states at once? Does entanglement imply an instantaneous actionat a distance? Is probability fundamental, or does it arise from partial information?In this article, we propose an exploratory relational interpretation of these no-tions within a discrete framework based on the additive group (nZ, +). In thisframework, the fundamental entities are not isolated objects, nor points of a pre-existing spacetime, but indexed relational degrees of freedom. A physical confgura-tion is described by a global relational scene, and admissible scenes are selected bya relational master equation derived from a coherence functional.The aim is not to deny the empirical success of quantum mechanics, but topropose a conceptual dictionary in which the wave function is interpreted as anefective representation of a deeper relational structure. In this perspective, su-perposition becomes a composition of compatible relations, entanglement becomesrelational non-separability, measurement becomes relational selection, and probabil-ity becomes an efective description associated with the observer’s partial access tothe global structure.
Quantum mechanics is the study of uncertainty. But what does uncertainty mean within the structure of physical reality? From Newton onward, mathematical physics has largely approached motion by specifying a state, identifying the laws governing its evolution, and determining the subsequent behavior of the system. Fourier extended this program to heat, Maxwell to electromagnetic fields, Navier and Stokes to fluids, Hamilton and Lagrange to variational and canonical mechanics, Einstein to spacetime, and quantum mechanics to the evolution and measurement of the quantum state. Across these theories, increasingly powerful mathematics has described what a physical system may do and how its state may evolve. This work asks a logically prior question: Does everything that is mathematically accessible participate equally in physical realization? We propose that it does not. The central distinction developed in this work is between accessibility, admissibility, participation, and realization. A mathematical representation may contain a large space of possible states, trajectories, modes, or outcomes. Physical realization, however, need not occupy that space uniformly. We propose that relational structure establishes an admissible geometry within the accessible space; that geometry determines which possibilities participate strongly or weakly; and probability subsequently quantifies the residual uncertainty among physically supported realizations. The resulting ordering is: Potentiality → Relations → Structure → Geometry → Admissibility → Participation → Realization → Evolution. Under this interpretation, probability is not abolished. Superposition is not abolished. Quantum mechanics is not rejected. Rather, their physical ordering is reconsidered. Superposition describes what the mathematical representation can contain; relational geometry determines how strongly those possibilities can participate; probability describes the uncertainty remaining within that structured support; and observation records the realization that occurs. The NIST loophole-free two-photon Bell experiment provides the principal empirical test developed in this work. Beginning from the experimentally characterized entangled state—not from subsequently observed outcome counts—we construct a relational geometry and the corresponding outcome-dependent participation and information-cost landscapes. The NIST measurement configurations then become experimental sampling coordinates on a geometry determined independently from the later event records. The resulting analysis identifies several mutually reinforcing features: strong inequality among the participation of mathematically accessible Bell outcomes; a corresponding hierarchy of geometric information cost; concentration of experimental variation into reduced effective dimensions; agreement between predicted geometric support and held-out experimental records; preservation of Bell-inequality violation on the reduced realization geometry; compatibility with no-signalling; and robustness tests against multinomial, temporal, detector, and other alternative explanations. The interpretation is not a restoration of Bell-local hidden variables and does not require superluminal signalling. Bell's theorem continues to exclude the relevant locally factorized descriptions. Instead, the observed correlations are interpreted as local measurements of a common non-separable relational structure. Spatial separation does not imply relational or informational separability. This distinction also reframes the quantum measurement problem. Wave-function collapse need not be regarded as the event that creates the physical structure responsible for an outcome. The framework instead proposes that admissibility constrains participation prior to observation, with measurement revealing a realization from an already structured physical domain. A definitive replacement for the standard measurement postulate will require discriminating predictions beyond those already shared with conventional quantum mechanics. The broader implication concerns the theory of motion itself. Newtonian mechanics, Hamiltonian dynamics, Maxwell's equations, Fourier transport, Navier–Stokes flow, relativity, and quantum mechanics employ very different evolution equations, yet all operate upon structured physical domains. The admissibility framework proposes that their deeper commonality lies not in a single dynamical equation but in an ontological ordering: the laws of motion govern how reality evolves; admissibility governs the structure within which reality can become realized. This has consequences beyond quantum foundations. In engineering and computational physics, enormous mathematical state spaces are routinely explored through CFD, finite-element simulation, optimization, Monte Carlo methods, and digital twins. If physically significant behavior occupies a substantially smaller admissible geometry, computation can be redirected from exhaustive exploration toward the structures in which realizable behavior is concentrated. This provides a theoretical basis for reduced-order physical prediction, targeted simulation, transport localization, and deterministic Physics Intelligence. In AI infrastructure and high-performance computing, the same principle suggests that workloads, thermal transport, energy utilization, routing, scheduling, and hardware states need not be treated as equally relevant points within enormous combinatorial spaces. Identifying admissible low-dimensional structure before exhaustive computation offers a route toward reduced search complexity, improved orchestration, higher computational and energy efficiency, and physics-informed predictive control. In aerospace, energy, advanced manufacturing, climate systems, and data-center infrastructure, the framework similarly motivates identifying the geometry of physically participating transport before expending computational resources resolving the entire mathematically accessible domain. The work therefore proposes a common principle extending from fundamental physics to computational engineering: Mathematical possibility is larger than physical realization. Uncertainty may remain genuine at the level of an individual event without implying an absence of antecedent structure. The results presented here provide empirical evidence consistent with the proposition that physical realization is organized by relational geometry prior to probability, while identifying the further tests required to establish whether this ordering constitutes a fundamental law of quantum and classical motion. The next decisive tests include prospective Bell predictions, multipartite and contextuality experiments, Lorentz-covariant formulation, recovery of the classical limit, and extension to quantum field theory and curved spacetime. Nature need not explore everything mathematics permits. Motion is the realization of what physical structure admits. That description captures the actual architecture of the finished 130-page work: it preserves Bell's theorem rather than attempting to evade it, explicitly separates mathematical accessibility from physical participation, and treats the NIST comparison as evidence for the proposed framework while acknowledging that a distinctive prediction beyond standard quantum mechanics remains necessary for a physical replacement of collapse. Principal Implications What This Means for Bell’s Inequality Bell's theorem remains intact. The present framework does not attempt to restore Bell-local hidden variables, weaken Bell's result, or explain the observed correlations through faster-than-light signalling. Bell establishes that the correlations observed between Alice and Bob cannot be reproduced by the relevant locally factorized description. The question developed here begins after that result: if Bell-local separability fails, what physical structure carries the correlations? The proposed answer is relational geometry. Alice and Bob remain spatially separated and perform local measurements, but their outcomes arise from different interrogations of a common non-separable quantum structure. Spatial separation therefore does not imply informational or relational separability. The correlation need not be interpreted as something transmitted from Alice to Bob at the moment of measurement; it can instead be understood as a property of the joint structure to which both measurements belong. The NIST analysis gives this interpretation a quantitative form. The characterized entangled state determines the relational geometry before the subsequent detector records are used for evaluation. Alice's and Bob's measurement settings sample different regions of that geometry. The resulting Bell outcomes exhibit strongly unequal participation, while Bell violation and no-signalling are preserved. The proposed implication is therefore: Bell violation demonstrates the failure of Bell-local factorization; admissibility proposes a geometry for the non-separable physical structure that remains. This reframes the familiar intuition of "action at a distance." The deeper question may not be how information crosses the distance between Alice and Bob, but why spatial distance should require the relational information defining their joint state to become separable in the first place. What This Means for Wave-Function Collapse The framework does not discard wave-function collapse as an operational rule for updating the quantum state after an observation. It changes the proposed ontological role assigned to collapse. In the conventional collapse-centered picture, the quantum state contains multiple possible outcomes and measurement marks the transition to a definite result. This leaves a foundational question: what physically distinguishes the outcome that becomes real from those that do not? Admissibility inserts a structural stage before observation. The accessible quantum
We propose a conceptual analysis of probability within a discrete relational frameworkbased on the additive group (nZ, +). The central claim is that, under the simultaneousassumptions of exact laws, global symmetries, and strict conservation principles, probabilityis more naturally interpreted as epistemic than as the manifestation of ontological chance.In the framework considered here, events are treated as elements of a globally constrainedrelational structure, without introducing fundamental time or a physically postulated wave.We discuss the possible relevance of this perspective for the conceptual relation betweengeneral relativity and quantum mechanics.
This preprint proposes a discrete relational framework indexed by the additive group (nZ,+), in which neither fundamental time, nor primitive dynamics, nor ontological randomness, nor a physical wave ontology is assumed. The global structure is described by a relational configuration (Ψ,R)(\Psi,R)(Ψ,R) constrained by a master equation of coherence, interpreted as an atemporal global constraint (no derivatives, no evolution law). The work introduces the notion of a “relational book”: events are assumed to be fully pre-inscribed in a negative branch of the index set, while the positive branch contains virtual events that become apparent only through a relational connection to their pre-inscribed symmetric counterparts. Within this setting, quantum measurement is reformulated as constrained relational selection/activation driven by the measurement device, with no wave collapse and no underlying wave propagation. The Born rule is reinterpreted as a relational compatibility density whose observed statistical regularities emerge from partial relational access to the global structure. The preprint also discusses interference “without waves” (e.g., double-slit scenarios) as a signature of global relational constraints, and includes a structural comparison with Everett (Many-Worlds), Bohmian mechanics, Relational Quantum Mechanics, and QBism.