Ensemble interpretations of quantum mechanics. A modern perspective

Home, Dipankar; Whitaker, M. A. B.

doi:10.1016/0370-1573(92)90088-h

Cited by 87 publications

(80 citation statements)

References 224 publications

(251 reference statements)

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“…Both Einstein [23] and de Broglie [24] spent much time on such questions after their first discovery; the issue of quantum measurements was formulated by Heisenberg [2,3] and put in a mathematically precise form by von Neumann [4]; the foundations of quantum mechanics were reconsidered in this light by people like Bohm [18,19] or Everett [25,26] in the fifties; hidden variables were discussed by Bell in the sixties [27]; the use of a statistical interpretation to analyze quantum measurements was then advocated by Park [28], Blokhintsev [10,11] and Ballentine [9] (subtleties of the statistical interpretation are underlined by Home and Whitaker [29]); the most relevant papers were collected by Wheeler and Zurek in 1983 [8]. Earlier reviews on this problem were given by London and Bauer [30] and Wigner [13].…”

Section: General Features Of Quantum Measurementsmentioning

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%

“…Under the influence of the system to be measured this conservation is broken, and there is a possibility to correlate different values of the measured observable with the pointer values. Daneri, Loinger and Prosperi invoke the basic assumption of ergodic theory and treat the overall density matrix via 28 Who cares about every little feather should not make the bed 29 When I come, come again time-averaging [21]. The time-averaged density matrix satisfies the necessary requirements for an ideal measurement.…”

Section: Ergodic Theory Approachmentioning

confidence: 99%

“…The statistical interpretation highlights the fact that quantum mechanics provides us only with probabilities [9,10,11,28,29,31,52,58]. Although a probabilistic theory may produce some predictions with certainty, most quantities that we deal with at the microscopic scale are subject to statistical fluctuations: expectation values, correlations at a given time, or autocorrelations at different times when we observe for instance the successive transitions of a trapped ion [307,308].…”

Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

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: Measurements In Underlying Classical Theorymentioning

confidence: 99%

Section: Ergodic Theory Approachmentioning

confidence: 99%

Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…In the 1960s this difference in the approach to measurement gave rise to what has been called the ''Princeton school''. This term refers in particular to Eugene Wigner's view of measurement (see Home & Whitaker, 1992;Freire, 2007 Lakatos, 28 Jan 1968, in Lakatos & Feyerabend, 1999 points in common. All of them endorsed both indeterminism and the assumption of the corpuscular and discrete nature of atomic phenomena.…”

Section: Article In Pressmentioning

confidence: 99%

The origin of the Everettian heresy

Osnaghi

Freitas

Freire

2009

Studies in History and Philosophy of Science Part B: Studies in

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Foundations of Thermodynamics

Hardy¹,

Binek²

2014

Thermodynamics and Statistical Mechanics

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Abstract. On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local (hydrodynamic) and microlocal (kinetic) equilibrium.The present, self-contained treatment needs very little formal machinery and stays very close to the formulas as they are applied by the practicing physicist, chemist, or engineer. From a few basic assumptions, the full structure of phenomenological thermodynamics and of classical and quantum statistical mechanics is recovered.Care has been taken to keep the foundations free of subjective aspects (which traditionally creep in through information or probability). One might describe the paper as a uniform treatment of the nondynamical part of classical and quantum statistical mechanics "without statistics" (i.e., suitable for the definite descriptions of single objects) and "without mechanics" (i.e., independent of microscopic assumptions). When enriched by the traditional examples and applications, this paper may serve as the basis for a course on thermal physics.

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Ensemble interpretations of quantum mechanics. A modern perspective

Cited by 87 publications

References 224 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

The origin of the Everettian heresy

Foundations of Thermodynamics

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