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Physical Review A

Comment on ‘‘Wave-function collapse by measurement and its simulation’’

James R. Johnston

Published Sep 1, 1993• 4 citations
Publisher

Abstract

Namiki and Pascazio [Phys. Rev. A 44, 39 (1991)] propose a model of wave-function collapse associated with the nonfiring of a detector in one of two paths for which a particle is known to be present, and argue that the collapse has the same status as the collapse associated with a measurement involving an actual detection. I question this proposal on the following grounds: (i) it is based on a shift in detection probabilities in the two paths while there is no shift in wave-function amplitudes, and (ii) Namiki and Pascazio use an insufficient measure, loss of interference, as an indicator of collapse.

DOI
10.1103/physreva.48.2497

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Wave-function collapse by measurement and its simulation

Mikio Namiki, Saverio Pascazio

The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ``yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter \ensuremath{\epsilon} that quantitatively describes the degree of decoherence. Its value ranges from \ensuremath{\epsilon}=0 (which describes the case in which the two waves are perfectly coherent) to \ensuremath{\epsilon}=1 (which describes the case in which coherence is totally lost); for this reason \ensuremath{\epsilon} is named the ``decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex \ensuremath{\delta} potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit \ensuremath{\epsilon}=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.

Physical Review A•Jul 1, 1991•84 citations
Namiki and Pascazio [Phys. Rev. A 44, 39 (1991)] propose a model of wave-function collapse associated with the nonfiring of a detector in one of two paths for which a particle is known to be present, and argue that the collapse has the same status as the collapse associated with a measurement involving an actual detection. I question this proposal on the following grounds: (i) it is based on a shift in detection probabilities in the two paths while there is no shift in wave-function amplitudes, and (ii) Namiki and Pascazio use an insufficient measure, loss of interference, as an indicator of collapse.
We discuss and clarify the concept of dephasing in the many-Hilbert-space approach to the quantum measurement problem. We argue that the phase randomization provoked by a detecting macroscopic device is responsible for the loss of quantum coherence, and that the ``collapse of the wave function'' is to be regarded as a statistical process for the accumulated distribution over many events. In stressing the fundamental differences between our approach and the Copenhagen interpretation, we counter the objections put forward by Johnston [preceding Comment, Phys. Rev. A 48, 2497 (1993)], whose standpoint is essentially similar to the Copenhagen one.
We provide a reasonable explanation for measurement where no wave function in the sense of quantum mechanics is collapsed. The wave functions of the particles in the measuring device should be considered together with the measured particle as one system. The measurement is actually a physical process which makes the wave functions of different paths orthogonal. The collapsed wave function is just an equivalent one to explain certain physical phenomena. Our understanding of measurement also provides reasonable explanations for both EPR paradox and the experiments of delayed quantum eraser.
An experiment that would measure noncommuting quantum-mechanical observables without collapsing the wave function has been recently proposed by Y. Aharonov, J. Anandan, and L. Vaidman [Phys. Rev. A 47, 4616 (1993)]. These authors argue that this ``protected measurement'' may give an indication on ``the reality of the wave function.'' We show that the proposed experiment admits a much simpler interpretation: it is an experiment in which the quantum system is (assumed to be) in an eigenstate of the observable being measured. As such, the fact that no collapse occurs is trivial and can be understood without the need of the concept of ``protective'' devices. We argue that the experiment does not provide a way for measuring noncommuting observables without a collapse, does not bear on the issue of the ``reality of the wave function,'' and does not add any particular insight into our understanding (or nonunderstanding) of quantum mechanics.
A single-particle multi-branched wave-function is studied. Usual which-path tests show that if the detector placed on one branch clicks, the detectors on the other branches remain silent. By the collapse postulate, after this click, the state of the particle is reduced to a single branch, the branch on which the detector clicked. The present article challenges the collapse postulate, claiming that when one branch of the wave-function produces a click in a detector, the other branches don't disappear. They can't produce clicks in detectors, but they are still there. An experiment different from which-path test is proposed, which shows that detectors are responsible for strongly decohering the wave-function, but not for making parts of it disappear. Moreover, one of the branches supposed to disappear may produce an interference pattern with a wave-packet of another particle.
I study the quantum mechanics of a spin interacting with an "apparatus." Although the evolution of the whole system is unitary, the spin evolution is not. The system is chosen so that the spin exhibits loss of quantum coherence, or "wave function collapse," of the sort usually associated with a quantum measurement. The system is analyzed from the point of view of the spin density matrix (or "Schmidt paths"), and also using the consistent histories approach. These two points of view are contrasted with each other. Connections between the results and the form of the Hamiltonian are discussed in detail.
The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ``yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter \ensuremath{\epsilon} that quantitatively describes the degree of decoherence. Its value ranges from \ensuremath{\epsilon}=0 (which describes the case in which the two waves are perfectly coherent) to \ensuremath{\epsilon}=1 (which describes the case in which coherence is totally lost); for this reason \ensuremath{\epsilon} is named the ``decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex \ensuremath{\delta} potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit \ensuremath{\epsilon}=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.