This paper argues that physical quantities should be reconstructed not as non-contextual intrinsic attributes with measurement-independent determinate values, but as equivalence classes of measurement procedures. Bell–CHSH violations first motivate the problem: they show that Bell-type local causality/factorizability, measurement independence, and the relevant form of outcome determinism or value-definiteness cannot be jointly maintained, without by themselves refuting realism as such. Kochen–Specker contextuality supplies the stronger premise for the sharp-observable case: no global, non-contextual, dispersion-free value assignment to projection-valued observables can preserve the functional relations among compatible observables in Hilbert spaces of dimension at least three. The positive proposal uses algebraic quantum theory to identify physical quantities with classes of measuring procedures that yield the same outcome statistics over a full or tomographically complete state domain. This reconstruction preserves the classical deterministic limit while rejecting the stronger claim that measured quantities are context-independent values possessed independently of measurement. The analysis is restricted to sharp observables and projection-valued measurements; POVMs and unsharp measurements are noted as extensions. The resulting view is realist about an observer-independent world but non-intrinsic about empirical quantities, and it situates Wheeler's "It from Bit" as an interpretive corollary rather than as a foundational premise.
This paper argues that physical quantities should be reconstructed not as non-contextual intrinsic attributes with measurement-independent determinate values, but as equivalence classes of measurement procedures. Bell–CHSH violations first motivate the problem: they show that Bell-type local causality/factorizability, measurement independence, and the relevant form of outcome determinism or value-definiteness cannot be jointly maintained, without by themselves refuting realism as such. Kochen–Specker contextuality supplies the stronger premise for the sharp-observable case: no global, non-contextual, dispersion-free value assignment to projection-valued observables can preserve the functional relations among compatible observables in Hilbert spaces of dimension at least three. The positive proposal uses algebraic quantum theory to identify physical quantities with classes of measuring procedures that yield the same outcome statistics over a full or tomographically complete state domain. This reconstruction preserves the classical deterministic limit while rejecting the stronger claim that measured quantities are context-independent values possessed independently of measurement. The analysis is restricted to sharp observables and projection-valued measurements; POVMs and unsharp measurements are noted as extensions. The resulting view is realist about an observer-independent world but non-intrinsic about empirical quantities, and it situates Wheeler's "It from Bit" as an interpretive corollary rather than as a foundational premise.
This dissertation investigates statistical constraints on measurement outcomes in quantum mechanics, addressing two fundamental features that distinguish quantum theory from classical physics: non-reality and uncertainty.We examine these features through two perspectives: observable-dependent statistical constraints on quantum correlations and estimationbased measurement uncertainty in infinite-dimensional quantum systems.In the first part, we study realizability problems in both local realism and quantum theory, focusing on observable-dependent constraints.While previous studies have mainly characterized quantum correlations independently of observables, we derive a necessary and sufficient condition for quantum realizability of correlations in the Clauser-Horne-Shimony-Holt (CHSH) scenario when observables are fixed in advance.Our main result provides an explicit inequality that imposes stronger constraints than previously known observable-independent bounds.We demonstrate that the maximum CHSH inequality violation depends on observable choice and apply our results to Bell's original scenario, revealing that whether Bell's original inequality is violated depends sensitively on observable selection.These findings demonstrate that non-reality does not manifest equally in all measurement configurations.In the second part, we extend the estimation-based formulation of measurement uncertainty by Watanabe, Sagawa, and Ueda to infinite-dimensional quantum systems.The original formulation provided clear physical interpretation but excluded fundamental observables such as position and momentum.Using pseudo-inverse forms of positive-semidefinite sesquilinear forms, we develop classical and quantum estimation theory for statistical models whose parameter space is the set of full-rank quantum states on infinite-dimensional Hilbert spaces.We derive classical and quantum Cramér-Rao inequalities and define estimationbased measurement errors for both bounded and unbounded operators.For each error type, we establish error-error uncertainty relation inequalities stronger than the original Watanabe-Sagawa-Ueda bound due to an improved derivation utilizing the full Cauchy-Schwarz inequality.Our work provides a universal definition of measurement errors with a clear physical interpretation while maintaining mathematical rigor.Our results contribute to quantum foundations by deepening the understanding of how measurement outcome constraints arise from quantum structure and observable properties.The methodological tools introduced-including characteristic functions, quasi-joint probability distributions, symmetry-based reduction techniques, and pseudo-inverse forms-may prove useful for future investigations in quantum foundations and quantum information theory.
The standard measurement postulate of quantum mechanics stipulates an instantaneous, non-local update of the global wavefunction upon measurement of an entangled subsystem. This postulate has been a persistent source of foundational tension, both with the locality structure of relativistic physics and with the dynamical character of the decoherence program. We separate the measurement postulate into three logically independent claims: definite outcome realization, Born-rule probability assignment, and instantaneous projection for the global wavefunction. We argue that the third claim can be eliminated at the axiomatic level and propose a modified measurement postulate, Postulate M, that replaces it. Under Postulate M, a single pointer outcome is realized locally when environmental decoherence has einselected a pointer basis at the measurement site; the corresponding selection acts on the global wavefunction as a conditional restriction to a branch rather than as a physical operation on spacelike-separated regions. We show that Postulate M recovers the standard measurement postulate as a limiting idealization for vanishing decoherence time, derives Lüders’ rule for sequential measurements, and yields no-signaling as an automatic structural consequence — not only at the level of measurement statistics but at the level of physical states themselves. Two explicit illustrations in the EPR scenario — with one and with both particles coupled to local spin environments — demonstrate the framework concretely and exhibit its frame-independent, manifestly local character. The framework is built on standard decoherence theory, compatible with multiple candidate mechanisms for single-outcome realization including gravitationally-induced collapse proposals, and naturally situated within a ψ-ontic reading of the quantum state. It represents, we argue, a reformulation of quantum mechanics as a local, state-realist theory — preserving Einstein’s aspiration for an objective physical world in the only form consistent with the empirical content of quantum mechanics, namely realism about the wavefunction rather than about pre-measurement observable values.
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.
Quantum mechanics represents physical states through complex amplitudes, state vectors, and density operators, yet the ontological status of these objects remains interpretation-dependent. This paper develops a closure-based formulation in which a quantum state is interpreted as a representation of contextually partial relational closure: the state possesses definite mathematical and relational structure while remaining unresolved relative to one or more observational contexts. Within this language, decoherence differentiates closure channels and redistributes locally accessible coherence into relational structure; environmental redundancy stabilizes records; and classical facts emerge as approximately fixed, effectively commuting, redundantly recorded structures. Measurement is separated into three problems—context, weight, and outcome—so that decoherence, Born weighting, and unique outcome selection are not conflated. The paper then distinguishes two stronger research programs from the exact reformulation. First, it asks whether Hilbert-space quantum mechanics can be reconstructed from primitive closure, incompatibility, composition, and consistency principles. Second, it formulates a falsifiable closure-history extension in which physically relevant information might exist beyond the present density operator. Quantum Partial Closure Theory is therefore presented as a relational interpretation and information calculus, a reconstruction program, and a prospective experimental framework rather than as an established replacement for quantum mechanics. Keywords: quantum foundations; closure; wavefunction ontology; coherence; entanglement; decoherence; measurement; classical emergence; quantum information; Hilbert-space reconstruction The wavefunction question Quantum theory is operationally clear about what a wavefunction does. For a normalized pure-state vector ψ∈H and a projective measurement with alternatives {Π_i}, the Born weights are p_i=Tr(ρ_ψ Π_i ), ρ_ψ=ψψ^†. For a rank-one outcome Π_i=e_i e_i^†, this reduces to p_i=|e_i^† ψ|^2. Yet the mathematical clarity of the formalism does not by itself settle what the state vector is ontologically. Interpretations of quantum theory differ over whether the state should be regarded as physical, epistemic, relational, branch-relative, dispositional, or otherwise. The present paper proposes a specific interpretive and reconstructive language: partial relational closure. The central claim is not that the wavefunction is literally a new material substance called closure. Rather, ▭(ψ "is interpreted as a Hilbert-space representation of coherent partial relational closure" .) The word partial is crucial. It does not mean that a state is a scalar fraction of being real or complete. It means that information and constraint are distributed across local, coherent, and relational sectors, and that closure is always specified relative to a context. A Bell state, for example, can be locally indefinite while being relationally exact. A decohered state can be closed with respect to one effective macroscopic context while retaining a larger quantum embedding. A selective outcome can be locally definite without implying that every larger-scale relation in the universe is globally closed. This formulation is motivated by three observations. First, projective dephasing is naturally closure-like because it is idempotent. Second, modern quantum information already supplies exact measures for local coherence, correlations, and record redundancy. Third, the quantum-to-classical transition is naturally relational: local coherence can disappear from a subsystem while information migrates into system-environment correlations. The paper has three epistemic layers. Layer A uses established quantum mathematics. Layer B derives exact information identities and interprets them in closure language. Layer C states reconstruction conjectures and an explicitly speculative beyond-QM closure-history hypothesis. These layers are kept separate throughout. A quantum system is not structureless before measurement. Its amplitudes, phases, conservation relations, and correlations are tightly organized. What remains unresolved is how that structure will become locally definite relative to a chosen measurement context. The partial-closure view therefore distinguishes three broad regimes: Coherent partial closure. Alternatives remain phase-related and can interfere. Contextual differentiation. Interaction or dephasing suppresses coherence between alternatives relative to a context without necessarily choosing one. Selective local closure. A particular outcome is conditioned or realized relative to the measurement relation. In this language, wave-like behavior corresponds to spatially or otherwise contextually unresolved coherent closure, while particle-like detection corresponds to localized closure. Entanglement is closure stored in relations rather than in isolated subsystems. Decoherence is not simply destruction: in a globally pure description it can be a transfer of local coherence into relational entanglement. Classical objectivity appears when relevant records become stable and redundantly accessible. The framework does not assign consciousness a privileged dynamical role. An observer is a partial closure process for constraining possibilities. Explainer video Watch on YouTube (Roots of Reality): https://www.youtube.com/watch?v=UYx_omk3h3A The video, its thumbnail and description are included in this record.
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical view that measuring an observable does not mean ascertaining the value that it has, but producing the outcome, having only a personal meaning. However, precise analysis supporting this view is unknown. Here, we show that a quantum mechanical analysis turns down this view. Supposing that two observers simultaneously measure the same observable, we can well pose the question as to whether they always obtain the same outcome, or whether the probability distributions are the same, but the outcomes are uncorrelated. Contrary to the widespread view in favor of the second, we shall show that quantum mechanics predicts that only the first case occurs. We further show that any measurement establishes a time-like entanglement between the observable to be measured and the meter after the measurement, which causes the space-like entanglement between the meters of different observers. We also show that our conclusion cannot be extended to measurements of so-called 'generalized' or 'unsharp' observables, suggesting a demand for reconsidering the notion of observables in foundations of quantum mechanics.
Superdeterminism has received recent attention as a possible path toward a locally causal explanation of the entanglement correlations that appear in experimental tests of Bell's theorem. While the term `superdeterminism' was coined by Bell to refer to restrictions on the free will of experimenters, it was not rigorously defined until recently. It has now been defined as a property of any physical theory that produces systematic violations of statistical independence. Here we focus on formalizing the requirements that being nonsuperdeterministic places on a physical theory, and setting a standard that must be met before we can conclude that a given theory is not superdeterministic. We begin by carefully examining how a physical theory determines what outcomes we observe when performing measurements in terms of ontic states and response functions, and how this differs between superdeterministic and nonsuperdeterministic theories, in terms of the behavior of the types of vetted random sampling procedures that we use in experiments. The core result is that individual samples and measurement outcomes must be representative of the observed distributions, which is explained in detail. This also has a bearing on how measurement settings are chosen by agents, whether freely or randomly, and we argue that this standard ultimately defines what freedom/independence actually mean. We then discuss contextuality, and show that in most cases, superdeterminism is contextual. Finally, we discuss how different physical theories, with different notions of ontic states and response functions, can give rise to the same empirical data, and how the same operational contextuality may appear in different forms.