Overview This work presents a structural reinterpretation of fast internal degrees of freedom that remain unresolved under finite observational resolution. Rather than contributing additively to observable mass–energy, such unresolved dynamics are shown to function as constraints that determine which states are dynamically and observationally admissible. When internal dynamics evolve on timescales or length scales below observational resolution, their detailed trajectories cannot be directly accessed. Nevertheless, they impose consistency conditions that effectively project the full dynamical state space onto a reduced subset of allowed configurations. Within this framework, quantization, stability, and probabilistic descriptions arise as unified consequences of constraint-based state selection rather than from fundamental indeterminism. Probability is interpreted not as an intrinsic randomness of nature, but as a measure over ensembles of microscopic trajectories that are compatible with the same effective observable state under resolution-limited observation. This study introduces no new particles, forces, or interaction terms. Instead, it reassigns the structural role of unresolved degrees of freedom within existing dynamical frameworks, clarifying how quantization and probability emerge from deterministic dynamics subject to finite observational resolution. Supplementary Information (Dataset) A snapshot of the dataset used in this study is provided as Supplementary Information in CSV format for convenience.The authoritative and continuously revised version of the dataset is archived on Zenodo with a persistent DOI. The data used in this paper correspond exactly to the version associated with the following DOI:DOI: 10.5281/zenodo.18097066
Overview This work presents a structural reinterpretation of fast internal degrees of freedom that remain unresolved under finite observational resolution. Rather than contributing additively to observable mass–energy, such unresolved dynamics are shown to function as constraints that determine which states are dynamically and observationally admissible. When internal dynamics evolve on timescales or length scales below observational resolution, their detailed trajectories cannot be directly accessed. Nevertheless, they impose consistency conditions that effectively project the full dynamical state space onto a reduced subset of allowed configurations. Within this framework, quantization, stability, and probabilistic descriptions arise as unified consequences of constraint-based state selection rather than from fundamental indeterminism. Probability is interpreted not as an intrinsic randomness of nature, but as a measure over ensembles of microscopic trajectories that are compatible with the same effective observable state under resolution-limited observation. This study introduces no new particles, forces, or interaction terms. Instead, it reassigns the structural role of unresolved degrees of freedom within existing dynamical frameworks, clarifying how quantization and probability emerge from deterministic dynamics subject to finite observational resolution. Supplementary Information (Dataset) A snapshot of the dataset used in this study is provided as Supplementary Information in CSV format for convenience.The authoritative and continuously revised version of the dataset is archived on Zenodo with a persistent DOI. The data used in this paper correspond exactly to the version associated with the following DOI:DOI: 10.5281/zenodo.18097066
Quantum mechanics employs probabilistic formalisms that are often interpreted as reflecting intrinsic indeterminacy of physical reality. Despite its empirical success, this interpretation leaves unresolved why deterministic behavior re-emerges at macroscopic scales. This paper argues that quantum probability arises instead from finite observational resolution imposed by spacetime granularity. When physical processes are subdivided beyond the Planck-scale limits of temporal and spatial resolution, individual micro-events become unobservable in principle. In this regime, observation collapses continuous deterministic dynamics into ensemble-averaged and probabilistic descriptions. The infinite subdivision principle is introduced to formalize this transition: subdivision beyond observational bandwidth irreversibly removes phase information at the observer level while leaving underlying dynamics intact. Probability amplitudes are shown to encode compressed residual phase relationships among unresolved micro-configurations, while expectation values represent structurally stable quantities accessible above the resolution threshold. Within this framework, quantum mechanics is reinterpreted as a resolution-limited projection of deterministic structure rather than as a fundamentally indeterminate theory. This perspective aligns naturally with Existence-Quantized Geometric Theory (EQGT), in which existence and observability are governed by threshold conditions and event-biased observation.
Physical systems often exhibit stable, repeatable regimes despite being described by equations that allow many possible trajectories. This tension is typically addressed using probabilistic language, with probability treated as a fundamental feature of evolution or as a reflection of stochastic dynamics. In this paper, we argue that probabilistic descriptions instead arise from structural underdetermination in the presence of recurrence and finite resolution. We introduce a coherence-first account in which repeated traversal of structurally admissible pathways reinforces regime stability, leading to effective regime selection without invoking randomness, agency, or additional dynamical mechanisms. Within this framework, probability collapse is not a physical event but a resolution of indistinguishability as recurrence deepens constraint. This perspective completes a structural notion of determinism: outcomes need not be fixed, but admissible regimes are finite, and repeated evolution naturally sharpens their dominance. The resulting picture reconciles deterministic dynamics with probabilistic description while preserving consistency with existing physical formalisms.
We investigate the origin of probabilistic descriptions in quantum theory within the Intrinsic Observability Framework (IOF). In this framework, the Hilbert space of a system is intrinsically decomposed into observable and hidden degrees of freedom, and effective observable descriptions are obtained by restricting the full description to the observable sector. We propose that any access to a quantum system necessarily involves a restriction of the full state. This principle implies that reduced descriptions are not contingent on environmental interactions or incomplete knowledge, but arise as a structural consequence of the act of access itself. As a result, mixed states and probabilistic outcomes emerge naturally from the intrinsic limitation on observable degrees of freedom. Within this perspective, quantum probabilities are interpreted not as manifestations of intrinsic randomness or hidden deterministic variables, but as features of accessible representations of the full state. The appearance of stochastic behavior is thus tied to the structure of observability. We further argue that, while the decomposition into observable and hidden sectors is not strictly unique, all physically observable predictions must remain invariant under admissible transformations. This establishes a consistent framework in which structural freedom coexists with empirical determinacy. The present formulation clarifies the role of access in the emergence of probabilistic descriptions and provides a structural basis for understanding quantum probabilities independently of decoherence.
This record provides a preprint version of a manuscript submitted for publication. The origin of the Born rule remains a central open problem in the foundations of quantum theory. While previous approaches derive the quadratic probability rule from structural, decision-theoretic, or measure-theoretic assumptions, the physical origin of these assumptions is not always transparent. In this work, we propose that observational resolution provides a fundamental constraint on distinguishability, which in turn restricts admissible probability measures. We introduce a resolution-based observational framework in which finite resolution induces coarse-graining and suppresses phase information below a characteristic scale. We show that consistency under resolution-limited coarse-graining selects a quadratic probability structure. In particular, only the quadratic form remains stable under phase averaging while reproducing additive behavior in the classical limit. We further demonstrate that this structure is naturally connected to the quadratic mapping from complex state space to observable quantities, as realized in spinorial representations of three-dimensional geometry. These results suggest that the Born rule can be understood as a structural consequence of resolution-limited observation. This version corresponds to a manuscript submitted to Physical Review X. Version 2: Major revision focusing on the emergence of the Born rule under resolution-limited observation. The manuscript has been restructured for journal submission.
(This version has been superceeded, see v.3) Contemporary approaches to physical unification typically emphasize dynamical laws, interpretive frameworks, or information-theoretic reconstructions. Less attention is given to the structural constraints that determine which physical descriptions can remain coherent and stable under interaction, scale transition, and aggregation. This paper develops a constraint-first analysis of coherence, arguing that persistence and unification require restrictions on admissible physical continuations that are not reducible to dynamics alone. Within the framework referred to here as Quantum Coherence Theory (QCT), coherence is treated not as a fragile quantum resource but as a structural property governed by interaction geometry and constraint density. On this view, classical behavior emerges when accumulated constraints sufficiently narrow admissible evolution, while quantum behavior re-emerges when constraints are relaxed. The account does not introduce new dynamics, collapse mechanisms, or modifications of quantum formalism, but instead clarifies the conditions under which existing formalisms yield stable, unified descriptions. The resulting constraints distinguish QCT from observer-centric, intrinsic-collapse, and purely descriptive decoherence accounts, while remaining compatible with globally unitary dynamics. Formal analysis in later sections develops operational redundancy conditions, admissibility constraints on joint states, and rigidity-style arguments linking redundant record structure to the stability of classical descriptions. These results do not constitute a complete theory of unification, but they narrow the space of physically admissible descriptions and clarify the structural role of coherence in bridging quantum and classical regimes.
This work proposes a minimal informational perspective on physical observability. Instead of treating spacetime and physical states as fundamentally given, the model suggests that what we observe emerges through a structural constraint that filters possible configurations into physically accessible ones. In this view, physical reality is not defined by dynamics alone, but by limits on what information can consistently appear as an observable state. The model introduces the idea that unobserved or excluded configurations are not lost arbitrarily, but contribute indirectly by shaping the structure within which observable states emerge. The framework does not introduce new forces or speculative entities. Rather, it provides a conceptual basis for interpreting physical constraints as consequences of informational selection. The approach is deliberately minimal and compatible with existing physical theories, serving as a foundational step toward more detailed theoretical and empirical developments.