Time Symmetry in the Quantum Process of Measurement

Aharonov, Yakir; Bergmann, Peter G.; Lebowitz, Joel L.

doi:10.1103/physrev.134.b1410

Cited by 870 publications

(874 citation statements)

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“…The consistent histories approach negates the fundamental need of measurements for understanding quantum measurements (quantum mechanics without measurements). It was proposed by Griffiths [229] based on earlier ideas of Aharonov, Bergmann and Lebowitz [230]. The approach is reviewed, e.g., by Griffiths [231], Gell-Mann [232], Hohenberg [233], and Omnès [234].…”

Section: Seeking the Solution Outside Quantum Mechanicsmentioning

confidence: 99%

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: Seeking the Solution Outside Quantum Mechanicsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…The two-state vector formalism (TVSF) [4,1] alters the traditional formalism of QM by assigning an additional state vector Φ| to a system, as well as the usual state vector, |Ψ . The latter state vector |Ψ(t 0 ) unitarily evolves according to the Schrödinger equation, under U .…”

Section: What Is the Two-state Vector Formalism?mentioning

confidence: 99%

“…In section 3, I outline the key tenets of the TTI as well as its proposed solution to the measurement problem. 1 The two papers cited explicitly expound the TTI, but other papers such as [3] and [4] hint at it, since -as will become apparent shortly -the TTI naturally arises out of a wider research programme. 2 As usual, we model a measurement by a composite unitary operator U that takes the measuring device to one of several distinguishable (orthogonal) states depending on the system's state.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, I will evaluate a new interpretation proposed by Aharonov, Gruss [2], Cohen and Landsberger [9] called the Two-Time Interpretation (TTI) 1 , which claims to be local, deterministic and to predict and explain novel phenomena. I will concentrate on whether this interpretation solves the measurement problem: since a prerequisite for joining the panoply of interpretations of quantum mechanics (QM) is to solve the measurement problem.…”

Section: Introductionmentioning

confidence: 99%

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Can the two-time interpretation of quantum mechanics solve the measurement problem?

Robertson

2017

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

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Over many years, Aharonov and co-authors have proposed a new interpretation of quantum mechanics: the two-time interpretation. This interpretation assigns two wavefunctions to a system, one of which propagates forwards in time and the other backwards. In this paper, I argue that this interpretation does not solve the measurement problem. In addition, I argue that it is neither necessary nor sufficient to attribute causal power to the backwards-evolving wavefunction Φ| and thus its existence should be denied, contra the two-time interpretation. Finally, I follow Vaidman in giving an epistemological reading of Φ|.

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“…In particular, the two-state vector describes the influence on a measuring device coupled with the system at time t. An ideal measurement of a variable O yields an eigenvalue o n with probability given by the Aharonov, Bergman, Lebowitz (ABL) rule [5]:…”

Section: The Two-state Vector Formalismmentioning

confidence: 99%