Search results for 'Observables' (try it on Scholar)

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  1.  41
    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 (...)
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  2.  38
    Hans Westman & Sebastiano Sonego (2008). Events and Observables in Generally Invariant Spacetime Theories. Foundations of Physics 38 (10):908-915.
    We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.
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  3.  11
    Irina Basieva & Andrei Khrennikov (2014). Complementarity of Mental Observables. Topics in Cognitive Science 6 (1):74-78.
    The aim of this note is to complete the discussion on the possibility of creation of quantum-like (QL) representation for the question order effect which was presented by Wang and Busemeyer (2013). We analyze the role of a fundamental feature of mental operators (given, e.g., by questions), namely, their complementarity.
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  4.  8
    Anatolij Dvurečenskij (2013). Smearing of Observables and Spectral Measures on Quantum Structures. Foundations of Physics 43 (2):210-224.
    An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure.
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  5. Bryan W. Roberts (2014). A General Perspective on Time Observables. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:50-54.
    I propose a general geometric framework in which to discuss the existence of time observables. This frameworks allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist subject to a restriction on the vector fields that they generate. Pauli's prohibition on quantum time observables is derived as a corollary to this result. I will then discuss how time observables can be regained in modest (...)
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  6.  86
    Claudio Garola & Sandro Sozzo (2011). Generalized Observables, Bell's Inequalities and Mixtures in the ESR Model for QM. Foundations of Physics 41 (3):424-449.
    The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of (...)
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  7. Michael Kohlhase, Capturing the Content of Physics: Systems, Observables, and Experiments.
    We present a content markup language for physics realized by extending the OMDoc format by an infrastructure for the principal concepts of physics: observables, physical systems, and experiments.
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  8.  93
    David J. Foulis (2007). Effects, Observables, States, and Symmetries in Physics. Foundations of Physics 37 (10):1421-1446.
    We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.
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  9. Giuseppe NisticÒ (1995). Empirical Relations Between Noncommuting Observables. Foundations of Physics 25 (12):1757-1767.
    A relation ≺ϕ between noncommuting 1-0 quantum observables (i.e., projections) is introduced, ϕ being the state vector of the system. This relation extends the empirical implication between commuting projections. An operational interpretation of the new relation is given, which can be expressed also in counterfactual terms. It is shown that a relation proposed some years ago by Hardegree, namely the Sasaki arrow ↪ϕ, can be interpreted in terms of the relation ≺ϕ; furthermore, this new relation turns out to be (...)
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  10.  55
    H. P. Stapp (1994). Comments on "Interpretations of Quantum Mechanics, Joint Measurement of Incompatible Observables, and Counterfactual Definiteness". Foundations of Physics 24 (12):1665-1669.
    Some seeming logical deficiencies in a recent paper are described. The author responds to the arguments of the work by de Muynck, De Baere, and Martens , who argue it is widely accepted today that some sort of nonlocal effect is needed to resolve the problems raised by the works of Einstein, Podolsky, and Rosen and John Bell. In MBM a variety of arguments are set forth that aim to invalidate the existing purported proofs of nonlocality and to provide, moreover, (...)
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  11.  91
    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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  12.  47
    Hans Halvorson & Rob Clifton (1999). Maximal Beable Subalgebras of Quantum-Mechanical Observables. International Journal of Theoretical Physics 38:2441-2484.
    The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e alone. In (...)
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  13.  50
    K. Kong Wan (1988). Local Observables, Nonlocality, and Asymptotically Separable Quantum Mechanics. Foundations of Physics 18 (9):887-911.
    Quantum mechanics is troubled by the problem of nonlocality inherent in the theory. In a series of papers we explore the possibility of an algebraic formulation of quantum mechanics based on local observables which would incorporate nonlocality when small distances are involved but would be separable at large distances. This paper reviews some of the basic ideas and theories developed recently. These include a unified localization scheme, the introduction of local comoving evolution, local comoving observables, and related conservation (...)
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  14.  50
    GianCarlo Ghirardi (2000). Local Measurements of Nonlocal Observables and the Relativistic Reduction Process. Foundations of Physics 30 (9):1337-1385.
    In this paper we reconsider the constraints which are imposed by relativistic requirements to any model of dynamical reduction. We review the debate on the subject and we call attention on the fundamental contributions by Aharonov and Albert. Having done this we present a new formulation, which is much simpler and more apt for our analysis, of the proposal put forward by these authors to perform measurements of nonlocal observables by means of local interactions and detections. We take into (...)
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  15.  13
    Paul Busch (1987). Some Realizable Joint Measurements of Complementary Observables. Foundations of Physics 17 (9):905-937.
    Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.
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  16.  15
    Dean Rickles, Time, Observables, and Structure.
    In this chapter I consider what recent work on background independent physics can do for structuralism, and what structuralism can do for background independent physics. I focus on the problems of time and observables in gravitational physics. The ‘frozen’ character of the observables of general relativity is usually considered to constitute a serious problem for the theory. I argue that by invoking correlations between physical quantities we can provide a natural explanation of the appear- ance of time and (...)
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  17.  42
    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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  18.  22
    Benjamin Feintzeig (2015). Hidden Variables and Incompatible Observables in Quantum Mechanics. British Journal for the Philosophy of Science 66 (4):905-927.
    This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell’s theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can’t serve (...)
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  19.  23
    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 (...)
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  20.  52
    Valerie Gray Hardcastle (1994). The Image of Observables. British Journal for the Philosophy of Science 45 (2):585-597.
    This paper challenges a central tenet of constructive empiricism, namely that empirical adequacy has a privileged epistemic status. I argue that perceptions of observables are theory-wrought, and theory-wrought in the same ways as the observation sentences we use to describe those perceptions, van Fraassen can draw no privileged or fundamental distinction between what we observe and interpreting those observations through theory. Since empirical adequacy depends upon accurately describing what we observe, and we have no theory-independent reason to believe that (...)
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  21.  68
    Tilman Sauer (2007). An Einstein Manuscript on the EPR Paradox for Spin Observables. Studies in History and Philosophy of Science Part B 38 (4):879-887.
    A formulation by Einstein of the Einstein-Podolsky-Rosen incompleteness argument found in his scientific manuscripts is presented and briefly commented on. It is the only known version in which Einstein discussed the argument for spin observables. The manuscript dates, in all probability, from late 1954 or early 1955 and hence also represents Einstein's latest version of the incompleteness argument and one of his last statements on quantum theory in general. A puzzling formulation raises the question of Einstein's interpretation of space (...)
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  22.  25
    E. Prugovečki (1974). Fuzzy Sets in the Theory of Measurement of Incompatible Observables. Foundations of Physics 4 (1):9-18.
    The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of (...)
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  23.  11
    Shant Shahbazian & Mansour Zahedi (2006). The Role of Observables and Non-Observables in Chemistry: A Critique of Chemical Language. [REVIEW] Foundations of Chemistry 8 (1):37-52.
    In this paper, aspects of observable and non-observable based models are discussed. A survey of recent literature was done to show how using non-observable-based language carelessly may cause disagreement, even in professional research programs and incorrect assertions, even in prestigious journals. The relation between physical measurements and observables is discussed and it is shown that, in contrast to general belief, this relation may be complicated and not always straightforward. The decomposition of the system into basic subsystems (physical or conceptual) (...)
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  24.  22
    Franklin E. Schroeck Jr (1985). Compatible Stochastic Observables That Do Not Commute. Foundations of Physics 15 (6):677-681.
    It is shown that stochastic observables defined by an instrument need not, and generally do not, commute.
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  25.  57
    Nicolaas P. Landsman, Macroscopic Observables and the Born Rule. I. Long Run Frequencies.
    We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which (...)
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  26.  4
    Gordon N. Fleming (2015). Response to Dr. Pashby: Time Operators and POVM Observables in Quantum Mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:39-43.
    I argue against a general time observable in quantum mechanics except for quantum gravity theory. Then I argue in support of case specific arrival time and dwell time observables with a cautionary note concerning the broad approach to POVM observables because of the wild proliferation available.
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  27.  20
    Teiko Heinosaari, Daniel Reitzner & Peter Stano (2008). Notes on Joint Measurability of Quantum Observables. Foundations of Physics 38 (12):1133-1147.
    For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly (...)
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  28.  16
    Paul Teller (1977). On the Problem of Hidden Variables for Quantum Mechanical Observables with Continuous Spectra. Philosophy of Science 44 (3):475-477.
    Existing "no hidden variable proofs" for quantum mechanics deal exclusively with observables with discrete spectra. This note shows that similar results hold for observables with continuous spectra.
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  29.  18
    S. Twareque Ali, Claudio Carmeli, Teiko Heinosaari & Alessandro Toigo (2009). Commutative POVMs and Fuzzy Observables. Foundations of Physics 39 (6):593-612.
    In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.
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  30.  47
    Roderich Tumulka (2007). Determinate Values for Quantum Observables. British Journal for the Philosophy of Science 58 (2):355 - 360.
    This is a comment on J. A. Barrett's article 'The Preferred-Basis Problem and the Quantum Mechanics of Everything' ([2005]), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called 'hidden') variables. I point out that it is far from clear, for most observables, what such a postulate is supposed to mean, unless the postulated additional variable is related to a clear ontology in space-time, such as particle world lines, string world sheets, or (...)
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  31.  45
    Sheldon Goldstein, Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory.
    Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...)
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  32.  13
    K. Kong Wan (1991). Local Spatial Transformations and Local Observables. Foundations of Physics 21 (9):1107-1116.
    Traditionally spatial transformations such as translations and rotations are formulated in terms of transformations of the entire spatial space. In other words, transformations are taken automatically to be of a global nature. This paper investigates a local approach to spatial transformations; local transformations lead naturally to local observables in quantum mechanics.
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  33.  3
    Alexey E. Rastegin (2015). Uncertainty Relations for General Canonically Conjugate Observables in Terms of Unified Entropies. Foundations of Physics 45 (8):923-942.
    We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, (...)
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  34.  11
    Ernst Breitenberger (1985). Uncertainty Measures and Uncertainty Relations for Angle Observables. Foundations of Physics 15 (3):353-364.
    Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and (...)
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  35.  7
    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 (...)
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  36.  7
    Alexander S. Holevo & Juha-Pekka Pellonpää (2009). Extreme Covariant Observables for Type I Symmetry Groups. Foundations of Physics 39 (6):625-641.
    The structure of covariant observables—normalized positive operator measures (POMs)—is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.
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  37.  5
    Eduard Prugovečki (1973). A Postulational Framework for Theories of Simultaneous Measurement of Several Observables. Foundations of Physics 3 (1):3-18.
    A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.
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  38.  3
    Stan Gudder (1999). Observables and Statistical Maps. Foundations of Physics 29 (6):877-897.
    This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda ,{\text{ }}\mathcal{B}} \right) (...)
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  39.  1
    W. Tomé & S. Gudder (1990). Convergence of Observables on Quantum Logics. Foundations of Physics 20 (4):417-434.
    We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are “close” if bounded functions of them are “close.” We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these types of convergence strengthen (...)
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  40.  1
    Sylvia Pulmannová (1980). Relative Compatibility and Joint Distributions of Observables. Foundations of Physics 10 (7-8):641-653.
    The notion of relative compatibility of observables is treated and its relation to the existence of joint distributions is obtained. The case of conventional quantum mechanics is studied and a generalization to the case of the quantum logic approach to quantum mechanics is given. It is shown that relative compatibility is equivalent to the existence of so-called “type 1” joint distributions.
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  41. Richard J. Connell (2000). From Observables to Unobservables in Science and Philosophy. Upa.
    From Observables to Unobservables in Science and Philosophy focuses on knowing unobservable real things or attributes by means of observing real things or attributes, a topic central to twentieth-century scientific philosophy. Engaging both current and perennial issues in metaphysics, epistemology, philosophy of nature and of science, Connell writes from a realist perspective. He adds a cogent, well written, and much needed voice to the current debate over foundationalism from the perspective of the undersubscribed quarter of empirical realism. Principal audiences (...)
     
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  42. Benjamin Feintzeig (forthcoming). Toward an Understanding of Parochial Observables. British Journal for the Philosophy of Science:axw010.
    Ruetsche claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This would signal that in addition to the abstract algebra, one must use Hilbert space representations for some purposes. I argue to the contrary that there is a way to recover all of the physically significant observables by purely algebraic methods. 1 Introduction2 Preliminaries3 Three Extremist Interpretations3.1 Algebraic imperialism3.2 Hilbert space (...)
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  43.  8
    Ruth E. Kastner (2014). ‘Einselection’ of Pointer Observables: The New H-Theorem? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48:56-58.
    In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: ‘molecular chaos.’ The program of ‘Einselection’ within Everettian approaches faces a similar ‘Loschmidt’s Paradox’: the universe, according to the Everettian picture, is a closed system obeying only unitary dynamics, and it therefore contains no distinguishable environmental subsystems with the necessary ‘phase randomness’ to effect einselection of a pointer observable. The theoretically unjustified assumption of (...)
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  44.  73
    Willem M. De Muynck (1984). A Quantum Mechanical Theory of Local Observables and Local Operations. Foundations of Physics 14 (3):199-253.
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  45.  32
    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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  46.  41
    Paul Busch & Abner Shimony (1996). Insolubility of the Quantum Measurement Problem for Unsharp Observables. Studies in History and Philosophy of Science Part B 27 (4):397-404.
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  47.  15
    W. M. De Muynck, W. De Baere & H. Martens (1994). Interpretations of Quantum Mechanics, Joint Measurement of Incompatible Observables, and Counterfactual Definiteness. Foundations of Physics 24 (12):1589-1664.
    The validity of the conclusion to the nonlocality of quantum mechanics, accepted widely today as the only reasonable solution to the EPR and Bell issues, is questioned and criticized. Arguments are presented which remove the compelling character of this conclusion and make clear that it is not the most obvious solution. Alternative solutions are developed which are free of the contradictions related with the nonlocality conclusion. Firstly, the dependence on the adopted interpretation is shown, with the conclusion that the alleged (...)
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  48.  15
    Thomas Pashby (forthcoming). Reply to Fleming: Symmetries, Observables, and the Occurrence of Events. Studies in the History and Philosophy of Modern Physics.
    In this article I reply to Fleming׳s response to my ‘Time and quantum theory: a history and a prospectus.’ I take issue with two of his claims: (i) that quantum theory concerns the (potential) properties of eternally persisting objects; (ii) that there is an underdetermination problem for Positive Operator Valued Measures (POVMs). I advocate an event-first view which regards the probabilities supplied by quantum theory as probabilities for the occurrence of physical events rather than the possession of properties by persisting (...)
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  49.  2
    Thomas Breuer (2002). A Kochen-Specker Theorem for Unsharp Spin 1 Observables. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer 195--203.
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  50.  23
    Gianpiero Cattaneo, Tiziana Marsico, Giuseppe Nisticò & Guido Bacciagaluppi (1997). A Concrete Procedure for Obtaining Sharp Reconstructions of Unsharp Observables in Finite-Dimensional Quantum Mechanics. Foundations of Physics 27 (10):1323-1343.
    We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.
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