Foundations of Quantum Mechanics, an Empiricist Approach

Muynck, Willem M. de

doi:10.1007/0-306-48047-6

Cited by 146 publications

(307 citation statements)

References 290 publications

(564 reference statements)

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“…Earlier reviews on this problem were given by London and Bauer [30] and Wigner [13]. We can presently witness a renewed interest for measurement theory; among many recent contributions we may mention the book of de Muynck [31] and the review articles by Schlosshauer [32] and Zurek [33]. Extensive references are given in the pedagogical article [34] and book [35] by Laloë which review paradoxes and interpretations of quantum mechanics.…”

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

“…It is natural to wonder whether the perturbation of S has a lower bound. Much work has therefore been devoted to the ideal measurements, those which preserve at least the statistics of the observableŝ in the final state of S, also referred to as non-demolition experiments or as measurements of the first kind [31]. Such ideal measurements are often described by assuming that the apparatus A starts in a pure state 6 .…”

Section: Classical Versus Quantum Measurements: Von Neumann-wigner Thmentioning

confidence: 99%

“…While such operations are feasible for a few variables, they cannot be carried out for a macroscopic apparatus nor even for a mesoscopic apparatus involving, say, 1000 particles. What the experimentalist does in a quantum measurement is quite the opposite [10,11,3,31]: rather than purifying the initial state of A, he lets it stabilize macroscopically by controlling a few collective parameters such as the temperature of the apparatus. The adequate theoretical representation of the initial state of A, which is a mixed state, is therefore a density operator denoted asR(0).…”

Section: Truncation Versus Reduction Ashes To Ashes Dust To Dust Genmentioning

confidence: 99%

“…The expression (1.10) is the result of weak truncation, while the selection of the runs characterized by the outcome A i produces for S the weak reduction into the stater i . The latter process constitutes a preparation of S. As already noted in § 1.1.2, the fact that simply tracing out A may lead to a (weakly) truncated or a reduced state for S solves in no way the physics of the measurement process, a well known weakness of some models [10,11,31,68,69]. …”

Section: Quantum Measurements In the Language Of Statistical Physicsmentioning

confidence: 99%

“…It is currently realized that the violation of Bell's inequalities [27,29,31,34] should be attributed to the non-commutative nature of the distribution D rather than to non-locality; quantum mechanics does not involve ordinary probabilities nor ordinary correlations. The violation of the classical inequality, observed experimentally [144,145,146,147,148,149] arises when one puts together outcomes of measurements performed in different experimental contexts, and this may itself be a problem [150,151,152,153,154].…”

Section: Measurements In Underlying Classical Theorymentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

Section: Classical Versus Quantum Measurements: Von Neumann-wigner Thmentioning

confidence: 99%

Section: Truncation Versus Reduction Ashes To Ashes Dust To Dust Genmentioning

confidence: 99%

Section: Quantum Measurements In the Language Of Statistical Physicsmentioning

confidence: 99%

Section: Measurements In Underlying Classical Theorymentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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After Bell

Khrennikov

2016

Fortschritte der Physik

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We analyze foundational consequences of recently reported loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. The conventional one is “Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality.” However, in line with discussions in literature during last decade, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will call the attention of experts in quantum foundations and convince them that the case is not closed, so that they should come with their own comments on the status of the final Bell test.

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Introduction to Soliton Theory: Applications to Mechanics

Munteanu

Donescu

2005

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Foundations of Quantum Mechanics, an Empiricist Approach

Cited by 146 publications

References 290 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

After Bell

Introduction to Soliton Theory: Applications to Mechanics

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