An observable on a quantum structure is any $σ$ -homomorphism of quantum structures from the Borel $σ$ -algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form $(-\infty,t)$ is sufficient to determine uniquely the whole observable defined on quantum structures like $σ$ -MV-algebras, $σ$ -effect algebras, Boolean $σ$ -algebras, monotone $σ$ -complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and a system of functions, and an effect-tribe.An observable on a quantum structure is any $σ$-homomorphism of quantum structures from the Borel $σ$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form $(-\infty,t)$ is sufficient to determine uniquely the whole observable defined on quantum structures like $σ$-MV-algebras, $σ$-effect algebras, Boolean $σ$-algebras, monotone $σ$-complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and a system of functions, and an effect-tribe.

arXiv:1204.6460Apr 29, 20121 citation

Further Aspects of Quantum Observables

Kevin Costello, Owen Gwilliam

Cambridge University Press eBooksSep 10, 20210 citations

Structural Observability I: A Framework for Outcome Formation in Quantum Measurement

Mark Dukes

RECORD 1 — Structural Observability I Description Structural Observability I: A Framework for Outcome Formation in Quantum Measurement This paper introduces the Structural Observability (SO) framework, which specifies the physical conditions under which definite outcomes arise in quantum measurement. The framework distinguishes between the Complete Relational Configuration (CRC) and the Limited Observational Reference Frame (L-ORF), and defines a three-condition requirement for outcome formation: stability, distinguishability, and accessibility. The SO framework does not modify the predictive formalism of quantum mechanics. Instead, it provides a structural account of why that formalism takes the form it does, identifying the conditions under which probability assignments and definite outcomes become well-defined. A companion paper, Structural Observability II, develops the experimentally testable consequences of this framework, including a threshold condition for outcome formation and multiple falsifiable predictions. Keywords quantum measurement, decoherence, measurement problem, quantum foundations, information theory, entanglement, Born ruleRECORD 1 — Structural Observability I Description Structural Observability I: A Framework for Outcome Formation in Quantum Measurement This paper introduces the Structural Observability (SO) framework, which specifies the physical conditions under which definite outcomes arise in quantum measurement. The framework distinguishes between the Complete Relational Configuration (CRC) and the Limited Observational Reference Frame (L-ORF), and defines a three-condition requirement for outcome formation: stability, distinguishability, and accessibility. The SO framework does not modify the predictive formalism of quantum mechanics. Instead, it provides a structural account of why that formalism takes the form it does, identifying the conditions under which probability assignments and definite outcomes become well-defined. A companion paper, Structural Observability II, develops the experimentally testable consequences of this framework, including a threshold condition for outcome formation and multiple falsifiable predictions. Keywords quantum measurement, decoherence, measurement problem, quantum foundations, information theory, entanglement, Born rule

Mar 21, 20260 citations

Measures on Quantum Structures

Anatolij Dvureĕenskij

Elsevier eBooksJan 1, 200210 citations

Structural Observability: A Framework for Quantum Measurement and Probability

Mark Dukes

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 interpretationTitleStructural 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

Mar 15, 20260 citations

REPRESENTATION OF QUANTUM OBSERVABLES

Karolinum Press eBooksNov 1, 20250 citations

An observable on a quantum structure is any

σ

-homomorphism of quantum structures from the Borel

σ

-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form

(-\infty,t)

is sufficient to determine uniquely the whole observable defined on quantum structures like

σ

-MV-algebras,

σ

-effect algebras, Boolean

σ

-algebras, monotone

σ

-complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and a system of functions, and an effect-tribe.