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.
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.
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.
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.
We propose a relational reinterpretation of the concept of wave within a discreteframework based on the additive group (nZ, +). Instead of postulating the waveas a fundamental entity, we explore the possibility that a wave may be understoodas an efective, coherent manifestation of a distributed relational quantity. Twocomplementary representations are introduced. In the additive representation, a waveis modeled as a succession or superposition of local quantities. In the multiplicativerepresentation, the global wave-like manifestation is modeled as a product of localrelational factors. In this second case, the natural logarithm transforms the globalproduct into a sum of local contributions, thereby revealing the internal structure ofthe manifestation. This approach connects the wave concept with relational scenes,graph Laplacians, coherence functionals, efective localization, and emergent physicaldescriptors. The work is presented as a mathematical and conceptual exploration,not as a replacement of standard wave theory
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
Abstract This paper develops a metaphysical interpretation of quantum probability under the title Distributed Presence (DP). The central claim is that quantum probabilities should not be understood as measures of ignorance, nor merely as formal devices for predicting measurement outcomes, but as expressions of an objective mode of being: a system’s structured distribution of presence across mutually available channels of realization. On this view, a quantum system prior to measurement is neither fully actual in one determinate outcome nor reducible to a set of hidden definite properties. Rather, it exists in a non-binary mode, articulated by normalized presence fractions associated with the possible outcomes defined by a given interaction context. The Born rule is accordingly not replaced, but reinterpreted: the standard probability assignment is read as the operational expression of an underlying ontological distribution. The paper argues that this framework provides a unified reading of several familiar quantum features. Superposition is understood as a real distribution of presence rather than as epistemic indeterminacy; measurement is interpreted as single-channel actualization rather than as the physical destruction of alternatives; wave-particle duality is recast as the relation between distributed structure and localized realization; and quantum randomness is treated as intrinsic yet structurally constrained. The proposal remains fully compatible with the standard Hilbert-space formalism and introduces no hidden variables, additional collapse dynamics, or many-world branching. Its aim is interpretive rather than revisionary. Beyond its relevance to the foundations of quantum theory, DP is advanced as a contribution to the ontology of probability more broadly. It seeks to show how probability may be objective, physically meaningful, and ontologically basic without collapsing into determinism on the one hand or epistemicism on the other. In that sense, the paper offers a realist, single-world, structurally articulated account of quantum chance.
Abstract Despite its empirical success, quantum mechanics continues to provoke foundational debates concerning the nature of probability, the ontological status of the quantum state, and the mechanism of measurement. [1] This work introduces Distributed Presence (DP) as a structural ontological framework that addresses these issues by reinterpreting quantum phenomena in terms of a system’s distributed mode of existence across its state space. Crucially, this distribution is modal rather than spatial: it concerns how a system is present across possible states, not how it is extended in physical space. Within the DP framework, a quantum system is not assumed to occupy a definite state prior to interaction. Instead, its fundamental mode of existence is an ontologically distributed presence, understood as a structural feature of reality rather than a reflection of epistemic uncertainty. From this standpoint, probability is not introduced as a primitive postulate but emerges operationally from the geometry of presence, yielding a structural derivation of the Born rule. Core quantum phenomena (including superposition, wave–particle duality, state reduction, and entanglement) are recast as different manifestations of a single underlying principle: the modal distribution, reconfiguration, and non‑separability of presence. Entanglement corresponds to the non‑factorizability of presence fractions over a composite state space, while non‑local correlations are interpreted as consequences of shared modal structure rather than dynamical signal transmission, fully consistent with relativistic causality. The framework is developed within a Euclidean geometric setting chosen to prioritize ontological clarity, without altering the predictive formalism of standard quantum mechanics or its Hilbert‑space representation. By grounding randomness, probability, and quantum behavior in the notion of modal distributed presence, DP offers a coherent foundational program that bridges the conceptual gap between unitary evolution and definite outcomes, providing an alternative to both epistemic interpretations and wave‑function realism.