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arXiv:hep-th/9304126

On the Aharonov-Anandan Experiment

Carlo Rovelli C

Published Apr 26, 1993• 0 citations
arXivHTMLPDF

Abstract

An experiment that would measure non--commuting quantum mechanical observables without collapsing the wave function has been recently proposed by Y Aharonov and J Anandan. These authors argue that this "protected measurement" may give indication on "the reality of the wave function". We argue that, depending of the precise version of the experiment considered, either the author's prediction is incorrect and the wave function does collapse, or the measurement is not a measurement on a quantum system. In either case, the experiment does not provide a way for measuring non--commuting observables without collapse, and it does not bear on the issue of the "reality of the wave function".

DOI
10.48550/arxiv.hep-th/9304126

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An experiment that would measure non--commuting quantum mechanical observables without collapsing the wave function has been recently proposed by Y Aharonov and J Anandan. These authors argue that this "protected measurement" may give indication on "the reality of the wave function". We argue that, depending of the precise version of the experiment considered, either the author's prediction is incorrect and the wave function does collapse, or the measurement is not a measurement on a quantum system. In either case, the experiment does not provide a way for measuring non--commuting observables without collapse, and it does not bear on the issue of the "reality of the wave function".
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 new type of procedures, called protective measurements, was proposed by Aharonov, Anandan, and Vaidman [Phys. Rev. A 97, 4616 (1993); Found. Phys. 26, 117 (1996)]. These authors argued that a protective measurement allows the determination of arbitrary observables of a single quantum system, and claimed that this favors a realistic interpretation of the quantum state. This paper proves that only observables that commute with the system's Hamiltonian can be measured protectively. It is argued that this restriction saves the coherence of alternative interpretations.
Recently the first protective measurement has been realized in experiment [Nature Phys. 13, 1191 (2017)], which can measure the expectation value of an observable from a single quantum system. This raises an important and pressing issue of whether protective measurement implies the reality of the wave function. If the answer is yes, this will improve the influential PBR theorem [Nature Phys. 8, 475 (2012)] by removing auxiliary assumptions, and help settle the issue about the nature of the wave function. In this paper, we demonstrate that this is indeed the case. It is shown that a psi-epistemic model and quantum mechanics have different predictions about the variance of the result of a Zeno-type protective measurement with finite N.
My view on the meaning of the quantum wave function and its connection to protective measurements is described. The wave function and only the wave function is the ontology of the quantum theory. Protective measurements support this view although they do not provide a decisive proof. A brief review of the discovery and the criticism of protective measurement is presented. Protective measurements with postselection are discussed. Introduction In the first graduate course of quantum mechanics I remember asking the question: “Can we consider the wave function as a description of a single quantum system?” I got no answer. Twelve years later, in South Carolina, after I completed my Ph.D. studies at Tel Aviv University under the supervision of Yakir Aharonov in which we developed the theory of weak measurements [1], I asked Aharonov: Can we use weak measurement to observe the wave function of a single particle? At that time I had already become a strong believer in the many-worlds interpretation (MWI) of quantum mechanics [2] and had no doubt that a single system is described by the wave function. Yakir Aharonov never shared with me the belief in the MWI. When we realized that using what is called now protective measurement , we can, under certain conditions, observe the wave function of a single quantum system, he was really excited by the result. At 1992 I was invited to a conference on the Foundations of Quantum Mechanics in Japan where I presented this result: “The Schrödinger wave is observable after all!”[3]. Then I went home to Tel Aviv where I finished writing a letter which received mixed reviews in Phys. Rev. Lett. , while Jeeva Anandan, working on the topic with Aharonov in South Carolina, wrote a paper accepted in Phys. Rev. A [4]. After acceptance of the PRA paper it was hard to fight the referees in PRL, but PLA accepted it immediately [5].
Protective measurement is a new measuring method introduced by Aharonov, Anandan and Vaidman (1993). By a protective measurement, one can measure the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. This remarkable feature of protective measurements was challenged by Uffink (1999, 2012). He argued that only observables that commute with the system's Hamiltonian can be protectively measured, and a protective measurement of an observable that does not commute with the system's Hamiltonian does not actually measure the observable, but measure another related observable that commutes with the system's Hamiltonian. In this paper, we show that there are several errors in Uffink's arguments, and his alternative interpretation of protective measurements is untenable.
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