Quantum tunnelling provides an empirically successful description of discrete transitions that are classically forbidden, particularly in radioactive decay and related quantum processes. While the mathematical formalism accurately predicts decay rates and barrier dependence, its physical interpretation remains a subject of ongoing discussion. In this paper, we adopt a structure-first interpretive framework in which tunnelling is understood not as literal traversal of forbidden regions, but as a statistical description of discrete resolution when continuous temporal evolution is inadmissible. We introduce the concept of structural non-admissibility, referring to configurations in which no continuous reconfiguration pathway exists under existing constraints. In such cases, systems persist metastably until discrete reconfiguration becomes unavoidable, accompanied by emission. Probability and exponential decay laws are interpreted as ensemble-level signatures of under-resolved structural dynamics rather than intrinsic randomness. This work does not modify quantum mechanics or its equations, but clarifies the ordering of explanation by distinguishing between structural conditions that necessitate discrete transitions and the probabilistic formalisms that describe them.
Quantum tunnelling provides an empirically successful description of discrete transitions that are classically forbidden, particularly in radioactive decay and related quantum processes. While the mathematical formalism accurately predicts decay rates and barrier dependence, its physical interpretation remains a subject of ongoing discussion. In this paper, we adopt a structure-first interpretive framework in which tunnelling is understood not as literal traversal of forbidden regions, but as a statistical description of discrete resolution when continuous temporal evolution is inadmissible. We introduce the concept of structural non-admissibility, referring to configurations in which no continuous reconfiguration pathway exists under existing constraints. In such cases, systems persist metastably until discrete reconfiguration becomes unavoidable, accompanied by emission. Probability and exponential decay laws are interpreted as ensemble-level signatures of under-resolved structural dynamics rather than intrinsic randomness. This work does not modify quantum mechanics or its equations, but clarifies the ordering of explanation by distinguishing between structural conditions that necessitate discrete transitions and the probabilistic formalisms that describe them.
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.
Classical, quantum, and relativistic formalisms successfully describe physical behavior across a wide range of regimes, yet they are typically treated as conceptually distinct frameworks. Despite this separation, each exhibits well-known limiting features, including finite response to applied influence, discrete outcome structure, and geometry-dependent admissibility of motion. Inthis work, we argue that these features are not independent, but instead reflect the presence of a shared admissibility constraint governing when physical evolution is permitted.We show that the coexistence of finite propagation, finite resolution, and finite response implies the existence of a bounded configuration region within which continuous evolution may occur, and beyond which evolution is forbidden. A generic constraint formulation is introduced to characterize this admissible region without modification of existing dynamical equations. Within this framework, classical inertial behavior corresponds to sustained evolution near the constraint boundary, quantum discreteness arises from boundary intersection during interior evolution, and relativistic effects follow from geometry-induced deformation of the admissible region.The purpose of the present analysis is not to replace established theories, but to identify a structural condition implicitly shared by them. By making this condition explicit, the relationship between classical, quantum, and relativistic limits may be understood as complementary projections of a common constraint, rather than as fundamentally separate descriptions.
Physical theories constrain systems through equations of motion, symmetries, boundary conditions, and variational principles. In many cases these constraints do not uniquely specify a single trajectory or configuration, but instead permit a family of admissible histories consistent with the same governing structure. This multiplicity is often treated implicitly, absorbed into formalism, or deferred to probabilistic interpretation. In this work, I introduce allowity as a diagnostic concept that characterizes the effective extent of admissible histories implied by a set of constraints, prior to any statistical weighting, measurement, or interpretation. Allowity is not randomness, uncertainty, freedom, or ignorance; it is a structural property of constraint-based descriptions. By making admissibility explicit, this framework clarifies how physical descriptions may remain stable despite non-uniqueness, or become brittle despite apparent determinism. The analysis is conservative and framework-neutral: it introduces no new dynamics and modifies no existing formalism.
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.
This paper clarifies the structural role of the Schrödinger equation within the Paton System. Rather than introducing new physical laws or modifying quantum mechanics, the equation is interpreted as governing admissible evolution of system states prior to observational selection. The wavefunction is treated as a representation of recursively evolving admissible structure within Tier-5 (continuation), while observation occurs at Tier-4 as a constrained projection of that structure. This distinction resolves common interpretational ambiguity by separating continuous evolution from discrete observation without altering established quantum formalism.
This paper proposes a structural framework in which physical laws and quantum probability emerge from a common admissibility principle, rather than from the unification of dynamical equations.No new forces, fields, particles, or dynamical laws are introduced.Instead, a universal structural constraint governing which states are admissible as physically realizable is identified. Building on results established in Admissibility Frameworks I and II, the existence of a universal frame constant limiting allowable transitions is taken as a starting point.From this principle, an equation of existence is formulated, which does not describe time evolution but instead delineates the boundary between admissible and non-admissible states.Different physical interactions are shown to correspond to distinct structural interpretations of the same admissibility condition. Within this framework, quantum states are interpreted not as probability amplitudes but as admissibility distributions.Measurement is described as structural filtering at the admissibility boundary, rather than as a dynamical collapse process.Under minimal and physically natural assumptions—phase invariance, orthogonal additivity, and locality—the admissibility measure is shown to be uniquely quadratic, yielding the Born rule as a structural consequence rather than a postulate. The resulting theory reframes unification as the closure of existence conditions shared by all physical theories.Dynamics remain domain-specific, but admissibility is universal.In this sense, unification is achieved not by combining forces, but by identifying the single structural condition under which any physical state may exist. AI Usage Declaration: The core concepts and mathematical intuitions of this paper were conceived by the author (Byeong-Young Oh). The technical formalization of the mathematical framework and the English drafting process were performed in collaboration with Artificial Intelligence (AI) models. The author takes full responsibility for the contents and logical integrity of this work. This work is part of an ongoing independent research program. Official research index :https://jingyu-papa.github.io/publications/