We propose a framework, referred to as the Intrinsic Observability Framework (IOF), in which the probabilistic structure of quantum mechanics arises from an intrinsic decomposition of the Hilbert space into observable and hidden degrees of freedom. The total system is described by a pure state evolving unitarily, while observable states are obtained by restricting the description to the observable sector via a partial trace over the hidden sector. A key assumption of the present approach is that this decomposition is a fundamental and non-contextual feature of the system, rather than a modeling choice or a consequence of environmental interactions. The hidden degrees of freedom introduced here are not interpreted as unmeasured physical variables, but as components that are fundamentally excluded from the space of observable quantities. Within the IOF, mixed states and probabilistic outcomes emerge from incomplete access to the full state, without invoking intrinsic randomness, external environments, or branching worlds. This distinguishes the present formulation from decoherence-based approaches, hidden-variable theories, and many-worlds interpretations. The proposed framework provides an alternative structural perspective on the origin of quantum probabilities while preserving the standard unitary formalism. We discuss its conceptual implications and outline directions for future work.
We propose a framework, referred to as the Intrinsic Observability Framework (IOF), in which the probabilistic structure of quantum mechanics arises from an intrinsic decomposition of the Hilbert space into observable and hidden degrees of freedom. The total system is described by a pure state evolving unitarily, while observable states are obtained by restricting the description to the observable sector via a partial trace over the hidden sector. A key assumption of the present approach is that this decomposition is a fundamental and non-contextual feature of the system, rather than a modeling choice or a consequence of environmental interactions. The hidden degrees of freedom introduced here are not interpreted as unmeasured physical variables, but as components that are fundamentally excluded from the space of observable quantities. Within the IOF, mixed states and probabilistic outcomes emerge from incomplete access to the full state, without invoking intrinsic randomness, external environments, or branching worlds. This distinguishes the present formulation from decoherence-based approaches, hidden-variable theories, and many-worlds interpretations. The proposed framework provides an alternative structural perspective on the origin of quantum probabilities while preserving the standard unitary formalism. We discuss its conceptual implications and outline directions for future work.
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.
We investigate the conceptual relationship between decoherence and the origin of probabilistic outcomes in quantum mechanics. While decoherence theory successfully explains the suppression of interference and the emergence of classical behavior through interactions with environmental degrees of freedom, its role in providing a complete account of the probabilistic nature of quantum measurement remains limited. In this work, we argue that the suppression of interference and the origin of probabilistic outcomes constitute distinct problems that should be conceptually distinguished. By “probabilistic outcomes,” we refer to the appearance of statistical distributions in measurement results as described by the Born rule. To clarify this distinction, we analyze limiting scenarios, including isolated quantum systems and the universe treated as a closed system, where the standard decoherence mechanism becomes ineffective or inapplicable, yet probabilistic outcomes persist. These considerations are not intended as a formal proof, but rather as a means to isolate conceptual dependencies. We then revisit the Intrinsic Observability Framework (IOF), in which the Hilbert space is intrinsically decomposed into observable and hidden degrees of freedom. Within this framework, probabilistic descriptions arise from restricted access to the full quantum state, rather than from environmental interactions or dynamical processes. By contrasting decoherence with the IOF perspective, we argue that decoherence provides an account of the emergence of classicality, but does not directly address the origin of quantum probabilities. The IOF, on the other hand, offers a structural perspective at the level of pure states. This suggests that a complete understanding of quantum measurement requires recognizing the distinct roles played by these two elements.
We extend the Intrinsic Observability Framework (IOF) by introducing a symmetry structure underlying observer-dependent descriptions of quantum systems. In previous works, probabilistic outcomes were formulated as a consequence of restricted access to the full quantum state, and observable predictions were shown to be invariant under admissible transformations of a fixed decomposition. In the present work, we relax the assumption of a fixed decomposition and allow the partition of the Hilbert space into observable and hidden sectors to depend on the observer. To relate such descriptions, we introduce Access-Transformation Symmetry (ATS), which characterizes invariance under transformations between observer-dependent decompositions. We show that, although the assignment of observable and hidden degrees of freedom may vary between observers, all observable predictions—such as probability distributions and expectation values—remain invariant. This establishes a consistent framework in which observer-dependent representations coexist with observer-independent empirical content. The present formulation reveals that observation is inherently asymmetric, while the underlying access structure exhibits a symmetry under transformations between observers. In this way, the IOF is extended from a structural framework to one that incorporates relational aspects of observability, while preserving its empirical consistency.
We investigate the invariance structure of observable predictions in the Intrinsic Observability Framework (IOF), building on the Access-Induced Reduction Principle (ARP) introduced in Ref. [1]. While IOF allows for non-unique decompositions of a quantum system into observable and hidden degrees of freedom, physical predictions must remain invariant under admissible transformations of such decompositions. We formalize admissible transformations as those that preserve observable probability distributions derived from reduced states. Furthermore, we clarify the distinction between invariant statistical structures and non-invariant configurations of individual measurement outcomes. This establishes a consistent framework in which structural freedom coexists with empirical determinacy.
TitleStructural Observability: A Framework for Quantum Measurement and Probability This paper proposes the Structural Observability (SO) framework for interpreting quantum measurement and probability. The framework distinguishes between a Complete Relational Configuration (CRC), representing the full relational structure of reality, and the Limited Observational Reference Frame (L-ORF), representing the restricted observational perspective available to observers embedded within spacetime. Within this structure, definite outcomes arise when components of a system’s state become associated with distinguishable physical records in spacetime, a condition termed Structural Observability. Quantum probabilities then arise from the structural limitations imposed by the L-ORF description rather than from fundamental randomness in the underlying configuration. The framework preserves the standard mathematical formalism of quantum mechanics—Hilbert space, unitary evolution, and the Born rule—while providing a structural account of why these elements appear in the observational description. Version 2 — What's new: This version represents a substantial development of the framework presented in Version 1. Major additions include: a formal mathematical structure section with five axioms for the accessibility map Λ, a causal context space (Σ, ≤) making the temporal structure of the framework explicit, and a three-part Structural Observability condition stated as a formal definition with a proof that decoherence is necessary but not sufficient for SO. Six worked examples are included, replacing the purely conceptual treatment of Version 1. Two novel experimental predictions are introduced: a first prediction concerning a critical stability threshold τ below which raw unpost-selected interference is directly observable, and a second prediction concerning a retrievability timescale τR* identified with the quantum information scrambling time, above which interference may again become observable. Together, these define a three-regime non-monotonic structure of interference visibility with no analogue in standard quantum mechanics. A full Statement on AI Assistance has been added, documenting the role of AI language models in the development of the work.* Keywords Quantum foundationsQuantum measurementBorn ruleDecoherenceRelational physics Structural observabilityQuantum interpretation
Abstract We propose that quantum mechanics emerges as the effective description of a deterministic physical reality from the perspective of an internal observer that constitutes a subsystem of a finite closed world. Because such an observer cannot access the complete ontological state of the world to which it belongs, its description is intrinsically incomplete. We refer to this fundamental limitation as subjective incompleteness . It naturally induces a factorization of the ontological state space with respect to gauge degrees of freedom that are indistinguishable to the observer. Within the proposed framework, the projective geometry of quantum state space is understood as a direct consequence of subjective incompleteness. This provides a common geometric origin for characteristic quantum phenomena, including nonlocality, contextuality, and intrinsic randomness.