Quantum mechanics of Hyperion

Wiebe, Nathan; Ballentine, L. E.

doi:10.1103/physreva.72.022109

Cited by 42 publications

(45 citation statements)

References 23 publications

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“…As convincingly argued by Wiebe and Ballentine [133] and Ballentine [207], realistic macroscopic Hamiltonian systems can -and sometimes even should -achieve the classical limit without invoking any decoherence effect. This concerns both chaotic and regular Hamiltonian systems, although the concrete scenarios of approaching the classical limit differ for the two cases.…”

Section: Decoherence Theorymentioning

confidence: 95%

“…For any subensemble E sub , coherences might exist near the end of the process, but according to section 11, they would rapidly disappear, owing to the large size of M and to suitable weak interactions within the apparatus ( § 11.2.4 and § 11.2.5). The 132 Avoiding lengths, I become obscure 133 Every time he told the story, the caught fish became bigger correlations between the signs of s z and of m produced during the registration, and the uniqueness property ( § § 11.3.1 and 11.3.2), then separate the two sectors. The large size of the pointer is therefore essential for a complete solution of the ideal measurement problem.…”

Section: Dutch Expressionmentioning

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: Decoherence Theorymentioning

confidence: 95%

Section: Dutch Expressionmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…Schlosshauer objects that in [4] we showed a classical limit for only one component of the angular momentum. However, that component (J z ) was chosen only as typical.…”

Section: Classicality Of Hyperionmentioning

confidence: 99%

“…Indeed, Schlosshauer suggests that different assumptions-an ensemble vs an individual interpretationmay be at the root of the disagreement between Wiebe and myself [4] and Zurek [5] regarding the origin of classical behavior in macroscopic objects. Let us consider these two interpretations, Ensemble interpretation: A state vector describes the statistical properties of an ensemble of similarly prepared systems.…”

Section: Ensemble Vs Individual Interpretations Of the State Vectormentioning

confidence: 99%

Classicality without Decoherence: A Reply to Schlosshauer

Ballentine

2008

Found Phys

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Schlosshauer has criticized the conclusion of Wiebe and Ballentine (Phys. Rev. A 72:022109, 2005) that decoherence is not essential for the emergence of classicality from quantum mechanics. I reply to the issues raised in his critique, which range from the interpretation of quantum mechanics to the criterion for classicality, and conclude that the role of decoherence in these issues is much more restricted than is often claimed.

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“…In their study [13], Wiebe and Ballentine define proper quantum-classical correspondence for Hyperion via the condition…”

Section: What Classicality? An Analysis Of Different Paradigmsmentioning

confidence: 99%

Classicality, the Ensemble Interpretation, and Decoherence: Resolving the Hyperion Dispute

Schlosshauer

2008

Found Phys

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We analyze seemingly contradictory claims in the literature about the role played by decoherence in ensuring classical behavior for the chaotically tumbling satellite Hyperion. We show that the controversy is resolved once the very different assumptions underlying these claims are recognized. In doing so, we emphasize the distinct notions of the problem of classicality in the ensemble interpretation of quantum mechanics and in decoherence-based approaches that are aimed at addressing the measurement problem.

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Quantum mechanics of Hyperion

Cited by 42 publications

References 23 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Classicality without Decoherence: A Reply to Schlosshauer

Classicality, the Ensemble Interpretation, and Decoherence: Resolving the Hyperion Dispute

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