Artifcial Intelligence, Measurement, and the Young Double-Slit Experiment: Interaction as Relational Emergence in a Discrete Framework Based on (nZ, +)
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.
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.
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
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.
DESCRIPTION THE MIRROR, MEMORY AND THE DOUBLE SLIT — THE RELATIONAL ARCHITECTURE OF RECOGNITION This work presents an interdisciplinary investigation into the relationship between configuration, memory, observation, and recognition. It proposes a relational framework in which the present configuration of a system is analyzed together with information about the process through which that configuration was formed. The central proposition is expressed as: FORM = CONFIGURATION + MEMORY OF THE PROCESS The manuscript develops this proposition across philosophy of consciousness, cognitive science, memory research, developmental psychology, and the interpretation of the double-slit experiment. It examines how the recognition of identity and continuity may depend not only on the system’s current state but also on the retention and integration of prior states and interactions. The study distinguishes conceptual propositions from operational definitions and computational results. It establishes a methodological framework for investigating relational patterns, process history, predictive performance, and the conditions under which the proposed model could be independently evaluated. It also distinguishes the physical mechanisms involved in quantum measurement from claims concerning consciousness, without treating the double-slit experiment as proof that consciousness directly produces quantum effects. A computational experiment compares two predictive models using a synthetic dataset of 6,000 observations. Model A uses three variables describing the current configuration, whereas Model B incorporates an additional feature representing process history. The evaluation uses a test set of 1,800 observations and reports accuracy, log loss, Brier score, ROC-AUC, confusion matrices, and paired error analysis. The results favor Model B within the simulated data-generating process. Accuracy increases from 68.39% to 71.56%, a difference of 3.17 percentage points. Log loss decreases from 0.59547 to 0.55787, Brier score decreases from 0.20461 to 0.18872, and ROC-AUC increases from 0.74523 to 0.78537. These findings indicate that the history feature provides additional predictive information under the conditions of the simulation. They do not, by themselves, establish a general theory of consciousness or demonstrate a causal relationship between consciousness and quantum phenomena. The manuscript also outlines criteria for reproducibility, independent validation, robustness analysis, and testing with empirical data. The computational findings are presented as results within a synthetic environment, while real-world validation remains a subsequent research stage. The contribution of this work lies in organizing a relational approach to recognition around the interaction between present configuration and process memory, connecting conceptual analysis with an explicit computational comparison and a framework for further empirical investigation. Keywords: relational architecture; consciousness; self-recognition; memory; process history; configuration; observation; double-slit experiment; computational modeling; predictive performance; synthetic data; interdisciplinary research. Author: Cláudio Vicente da SilvaAffiliation: Independent ResearcherLocation: Londrina, Paraná, BrazilDate: 14 October 2026
This work revisits foundational thought experiments in physics—most notably Schrödinger’s Cat and Young’s double-slit experiment—from the perspective of logic, language, and discrete reasoning, rather than probability or continuous modeling. The book begins with a close reading of Schrödinger’s original text and treats the cat experiment as a logical and linguistic test rather than a physical paradox. By following the description step by step, the analysis shows that the experiment centers on first events, non-repeatability, amplification, and restricted access to information. The uncertainty lies in description and access, not in physical superposition. The discussion then broadens to related cases, including non-repeatable experiments, multifacet descriptions, sealed systems, and the distinction between reality and observation. Familiar examples such as the blind men and the elephant are used to clarify how superposition can arise from language and partial description rather than from objects themselves. A stripped-down “cat in a box” case shows that the logical structure of Schrödinger’s Cat exists independently of radioactive devices. The book also revisits Young’s double-slit experiment, focusing on the role of the slit as a physical boundary and interaction region rather than an abstract geometric opening. Light and electrons are treated as discrete entities whose cumulative outcomes arise from individual events and in-slit interactions with solid surfaces. The interference pattern is interpreted as a historical summary of discrete trajectories and interactions, not as evidence of continuous wave behavior passing through empty space. Taken together, these analyses lead to a unified view: many celebrated “paradoxes” arise from linguistic compression, continuous idealization, and the loss of discrete structure in description. In the final chapters, Schrödinger’s Cat is reframed as a reasoning benchmark, comparable in spirit to the Turing Test. Whereas the Turing Test evaluates imitation through conversation, Schrödinger’s Test evaluates careful reading, logical inference, and consistency when language, time, and access to information are intertwined. Artificial intelligence plays a natural role in this framework. AI systems operate through finite steps, substitution, and rule-based manipulation of language. These properties align closely with the logical structure required to analyze both Schrödinger’s Cat and the double-slit experiment. The book therefore proposes Schrödinger’s Test as a reading-comprehension and logical-reasoning benchmark for both humans and artificial intelligence systems. No technical background in physics is assumed. The discussion relies on logic, language, and close reading. The goal is not to resolve paradoxes, but to show that none are required when foundational experiments are read precisely.
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.