Foundations of Quantum Mechanics I

Ludwig, Günther

doi:10.1007/978-3-642-86751-4

Cited by 430 publications

(409 citation statements)

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“…In Geneva, the school of Josef Maria Jauch was developing an axiomatic formulation of quantum mechanics [20], and Constantin Piron gave the proof of a fundamental representation theorem for the axiomatic structure [21]. Gunther Ludwig's group in Marburg [22] developed the convex ensemble theory, and in Amherst, Massachusetts, the group of Charles Randall and David Foulis [23,24] was elaborating an operational approach. Peter Mittelstaedt and his group in Cologne studied the logical aspects of the quantum formalism [25], while other workers (Jordan, Segal, Mackey, Varadarajan, Emch) [26,27] focused their attention on the algebraic structures, and Richard Feynman developed the path integral formulation [28].…”

Section: Magic With Neutronsmentioning

confidence: 99%

The Stuff the World is Made of: Physics and Reality

Aerts¹

1999

Einstein Meets Magritte: An Interdisciplinary Reflection

137

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Taking into account the results that we have been obtained during the last decade in the foundations of quantum mechanic we put forward a view on reality that we call the 'creation discovery view'. In this view it is made explicit that a measurement is an act of a macroscopic physical entity on a microphysical entity that entails the creation of new elements of reality as well as the detection of existing elements of reality. Within this view most of the quantum mechanical paradoxes are due to structural shortcomings of the standard quantum theory, which means that our analysis agrees with the claim made in the Einstein Podolsky Rosen paper, namely that standards quantum mechanics is an incomplete theory. This incompleteness is however not due to the absence of hidden variables but to the impossibility for standard quantum mechanics to describe separated quantum entities. Nonlocality appears as a genuine property of nature in our view and makes it necessary to reconsider the role of space in reality. Our proposal for a new interpretation for space makes it possible to put forward an new hypothesis for why it has not been possible to unify quantum mechanics and relativity theory.Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true, and mathematical time, of itself, and from its own nature, flows equally without relation to anything external.Isaac Newton, 1642 -1726. * Published as: Aerts, D., 1999, "The stuff the world is made of: physics and reality", in Einstein meets Magritte: an interdisciplinary reflection, eds. Aerts, D., Broekaert, J. and Mathijs, E., Kluwer Academic, Dordrecht.

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Section: Magic With Neutronsmentioning

confidence: 99%

The Stuff the World is Made of: Physics and Reality

Aerts¹

1999

Einstein Meets Magritte: An Interdisciplinary Reflection

137

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“…Equation (3.8) is the typical probability rule of modern quantum mechanics in which the notion of an "effect valued measure" F ( σ) on some σ-algebra of subsets generalizes the customary concept of a projection valued measure, or equivalently of a self-adjoint operator, associated to an observable; these observables present an idealisation that is very useful to understand the basic structure of quantum mechanics, but is too strong for representing real measuring devices (Ludwig, 1983;Kraus, 1983;Holevo, 1982;Davies, 1976). A similar situation is met if one considers the statistical operator…”

Section: Physical Discussion and Conclusive Remarksmentioning

confidence: 99%

Dynamical semigroup description of coherent and incoherent particle—Matter interaction

Lanz

Vacchini

1997

Int J Theor Phys

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The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent interaction of a single microsystem with matter.Compactly developing the calculations with superoperators, it is shown that the introduction of a time scale, linked to irreversibility of the reduced dynamics, directly leads to a dynamical semigroup expressed in terms of quantities typical of scattering theory. Its generator consists of two terms, the first linked to a coherent wavelike behaviour, the second related to an interaction having a measuring character, possibly connected to events the microsystem produces propagating inside matter. In case these events breed a measurement, an explicit realization of some concepts of modern quantum mechanics ("effects" and "operations") arises. The relevance of this description to a recent debate questioning the validity of ordinary quantum mechanics to account for such experimental situations as, e.g., neutron-interferometry, is briefly discussed.

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“…The standpoint according to which quantum mechanics actually is a probability theory is by now well understood, and even though it is still not in the spirit of typical textbook presentations, it has been developed and thoroughly investigated in various books and monographes (see e.g. [3][4][5][6][7][8][9][10]), to which we refer the reader for more rigorous and detailed presentations. A more concise account of similar ideas has also been given in [11].…”

Section: Quantum Mechanics As Quantum Probabilitymentioning

confidence: 99%

“…The reproducible quantity to be compared with the theory is the relative frequency according to which the preparation apparatus triggers the registration apparatus in a high enough number of repetitions of the experiment under identical circumstances. A most simple sketch of such a setup can be given by the so-called Ludwig's Kisten [3,12] preparation apparatus directed interaction −→ registration apparatus .…”

Section: Statistics Of An Experimentsmentioning

confidence: 99%

Theoretical Foundations of Quantum Information Processing and Communication

Brüning¹,

Petruccione²

2010

Lecture Notes in Physics

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Summary. The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in view of the related symmetry group, recalling the general structure of mappings covariant under the same group. This is done for damped harmonic oscillator, two-level system and quantum Brownian motion. Special attention is devoted to the general structure of translation-covariant master equations. Within this framework a recently obtained quantum counterpart of the classical linear Boltzmann equation is considered, as well as a general theoretical framework for the description of different decoherence experiments, pointing to a connection between different possible behaviours in the description of decoherence and the characteristic functions of classical Lévy processes.

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Foundations of Quantum Mechanics I

Cited by 430 publications

References 0 publications

The Stuff the World is Made of: Physics and Reality

The Stuff the World is Made of: Physics and Reality

Dynamical semigroup description of coherent and incoherent particle—Matter interaction

Theoretical Foundations of Quantum Information Processing and Communication

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