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  1. Alberto C. De la Torre (2007). Observables Have No Value: A No-Go Theorem for Position and Momentum Observables. [REVIEW] Foundations of Physics 37 (8):1243-1252.
    The Bell–Kochen–Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the existence of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.
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  2. Zoltan Domotor (1972). Species of Measurement Structures. Theoria 38 (1-2):64-81.
  3. Zoltan Domotor & Vadim Batitsky (2008). The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective. Measurement Science Review 8 (6):129-146.
    In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources of mathematical analysis) are used as a unified mathematical framework for modeling (a) the time-dependent behavior of natural systems, (b) interactions between natural systems and measuring instruments, (c) error and uncertainty in measurement, and (d) the formal propositional language for describing and reasoning about measurement results. We also discuss how a celebrated theorem in analysis, known as Gelfand (...)
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  4. Theodore J. Everett (2010). Observation and Induction. Logos and Episteme 1 (2):303-324.
    This article offers a simple technical resolution to the problem of induction, which is to say that general facts are not always inferred from observations of particular facts, but are themselves sometimes defeasibly observed. The article suggests a holistic account of observation that allows for general statements in empirical theories to be interpreted as observation reports, in place of the common but arguably obsolete idea that observations are exclusively particular. Predictions and other particular statements about unobservable facts can then appear (...)
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  5. Marian Grabowski (1989). What is an Observable? Foundations of Physics 19 (7):923-930.
    The concept of generalized observable in the scheme of Hilbert quantum mechanics is discussed. We give an example of a possible ambiguity of this notion. The role of interpretation and the strong connection with concrete experimental procedures in the discussion of generalized observables are stressed to explain the above ambiguity.
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  6. S. P. Gudder & G. T. Rüttimann (1986). Observables on Hypergraphs. Foundations of Physics 16 (8):773-790.
    Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an “effect” and show that observables are related to effect-valued measures. Finally, (...)
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  7. Pekka Lahti & Juha-Pekka Pellonpää (2010). On the Complementarity of the Quadrature Observables. Foundations of Physics 40 (9-10):1419-1428.
    In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space (...)
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  8. Asher Peres (2003). What's Wrong with These Observables? Foundations of Physics 33 (10):1543-1547.
    An imprecise measurement of a dynamical variable (such as a spin component) does not, in general, give the value of another dynamical variable (such as a spin component along a slightly different direction). The result of the measurement cannot be interpreted as the value of any observable that has a classical analogue.
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  9. S. Pulmannová (1981). On the Observables on Quantum Logics. Foundations of Physics 11 (1-2):127-136.
    Two postulates concerning observables on a quantum logic are formulated. By Postulate 1 compatibility of observables is defined by the strong topology on the set of observables. Postulate 2 requires that the range of the sum of observables ought to be contained in the smallestC-closed sublogic generated by their ranges. It is shown that the Hilbert space logicL(H) satisfies the two postulates. A theorem on the connection between joint distributions of types 1 and 2 on the logic satisfying Postulate 2 (...)
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  10. H. Reiter & W. Thirring (1989). Arex Andp Incompatible Observables? Foundations of Physics 19 (8):1037-1039.
    Common eigenfunctions of nontrivial projectors of x and p are constructed.
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  11. Beloslav Riečan (2000). On the Joint Distribution of Observables. Foundations of Physics 30 (10):1679-1686.
    A general algebraic system M is considered with two binary operations. The family of all measurable functions with values in the unit interval is a motivating example. A state is a morphism from M to the unit interval, an observable is a morphism from the family of Borel sets to M. A joint distribution of two observables is constructed. It is applied for the construction of the sum of observables and for a representation of conditional probability.
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