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arXiv:2605.23943

Spacetime Formation under Requirements: Contextual Realization and Form-Dependent Probability

Song-Ju Kim

cs.AIphysics.hist-phquant-phSubmitted May 1, 2026• Announced May 5, 2026• 0 citations
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Abstract

Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements. The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability. Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form. The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.

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19 pages, 1 figure

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Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements.
The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability.
Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form.
The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.
Human reasoning is traditionally modeled through rational-order frameworks that assume stability, separability, and coherence. Yet across judgment, valuation, perception, and social decision-making, empirical work consistently reveals patterned violations of these assumptions. These deviations intensify in real-world contexts shaped by institutional constraints, identity commitments, and collective narratives, where reasoning must navigate incompatible interpretive frames and interdependent evaluative pressures. Existing theories typically treat such phenomena as noise, bias, or bounded rationality, leaving no formal account of how rational-order rules interact with the variability inherent in social domains. This article proposes a structural framework that explains why these two regimes diverge and how their interaction produces systematic mismatches. Building on quantum probability theory, not as a physical metaphor but as a representational tool, it formalizes evaluative states that remain indeterminate until elicited, transform under contextual modulation, and become relationally coupled across agents and domains. Whereas, existing quantum-cognition models primarily address task-level effects such as conjunction errors or order dependence, this framework scales quantum principles to socially and institutionally embedded reasoning. The account identifies contradiction, interference, entanglement, and resolution as recurrent properties of real-world cognition and shows how quantum formalisms provide a coherent vocabulary for capturing these phenomena. To support cumulative progress, the article outlines a research agenda with empirically testable designs for distinguishing incompatible bases, assessing inseparability, modeling context-driven transformations, and integrating multi-level reasoning environments. This program positions quantum and classical approaches within a unified architecture and advances a broader science of reasoning.
This paper argues that the quantum measurement problem is not a single explanatory gap but a collection of distinct tasks. We separate detector representability, probability structure, single-event actuality, and outcome-conditioned refinement, and distinguish all four from causal registration, the physical criterion by which an already-instantiated event becomes a completed measurement record. These are explanatory roles within one measurement phenomenon rather than successive temporal stages. The analysis begins from the contrast between a global quantum description containing several detector-correlated components and the single entry that appears in a realized measurement history. Rather than compressing this contrast into an unexplained transition often labeled “collapse,” we ask which specific explanatory constraints must be satisfied before the relation between the two descriptions can be diagnosed precisely. A finite-resolution alternating position–momentum history is used throughout to separate questions of record formation, probability, actuality, causal registration, and outcome-conditioned refinement. A continuum analysis shows that making the registered history arbitrarily dense does not by itself recover a classical trajectory. Several parts of the architecture are exact once their inputs are specified. A detector representation induces an exact quotient; a specified acquisition channel and record family induce system-side effects; and a specified quantum instrument determines a family of subnormalized conditional branches before any one outcome is instantiated. Given a realized outcome label, the same instrument determines the corresponding normalized outcome-conditioned state. A finite-dimensional acquisition model explicitly realizes the representability chain, while a record-algebra indistinguishability result shows that removing coherence between detector-record sectors can leave all expectation values in the lifted record algebra unchanged even when that coherence remains detectable in a richer context. These results sharpen, but do not dissolve, the measurement problem. Record structure does not derive Born weights; a probability law does not itself constitute the event realized in one run; a mathematically available conditional branch family does not select one branch condition as actual; and causal onset, stabilization, registration, and conditional refinement all presuppose or follow that event rather than produce it. The resulting constraint audit tests—without assuming—the hypothesis that global quantum multiplicity and detector-record definiteness may belong to different representational levels. The main conclusion is not a new collapse dynamics but a localization of the remaining explanatory burden. Once representability, probability, causal registration, and conditional refinement are assigned their proper roles, the unresolved actuality transition can no longer be hidden inside the single label “collapse.” In the typed measurement architecture considered here, no pre-event operation has the mathematical role of producing an individual event token without additional event-producing structure. This is version 1.0 of the manuscript.
This paper formulates a hypothesis concerning the logical structure of observational, temporal, causal, and geometrical propositions in timelike quantum-causal domains. In classical relativity, timelike order is invariant once a Lorentzian geometry is fixed. In quantum theory, however, propositions associated with incompatible operational contexts need not belong to a single Boolean algebra. This paper investigates the possibility that, when observers, clocks, matter sources, or effective geometrical degrees of freedom are quantum systems, the set of observer-indexed propositions describing records, clock readings, simultaneity, temporal order, causal accessibility, and effective spacetime geometry may be locally Boolean without admitting a single observer-independent global Boolean valuation. This hypothesis shows to be compatible with the postulates of quantum mechanics, allowing context-dependent propositional structures, and with relativistic causality, causal consistency is preserved within each effective Lorentzian context. The resulting framework states that temporal and causal propositions may remain well defined within compatible operational contexts, while the total structure of facts across observers, clocks, and quantum geometrical degrees of freedom need not possess a single global Boolean representation.
We propose a simple reinterpretation of probability as a contextual notion arising from projections of a total system onto chosen decompositions. In this view, probability is not an intrinsic property of events but is defined only relative to a context (a partition of the whole). This perspective provides a unified conceptual framework in which classical probability appears as the case of compatible contexts, while quantum probability arises when contexts are incompatible and probabilities are derived from amplitude superposition. The aim is not to replace existing theories but to clarify their common structural basis.
Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.
Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much additional contextual information must a classical simulation introduce when it tries to keep a shared internal description fixed across contexts? To make this question precise, we analyze a minimal external-label simulation model in which the remaining context dependence is carried only by an auxiliary label. For this model, we define an obstruction cost as the minimum mutual information between the context and the auxiliary label required to reproduce the observed statistics. We then prove a conservative quantitative lower bound: any linear witness that separates the observed statistics from the zero-obstruction set yields a positive lower bound on this cost. We do not claim that this bound is tight, and we do not claim that the simulation model covers every possible classical architecture. Its role is narrower and more explicit: under fixed shared-state semantics, contextuality can be read as a certificate of irreducible external bookkeeping cost in a simple and well-defined simulation model.