Consistent quantum measurements

Highlights

• The quantum measurement problems are discussed using consistent histories.

• A Stern–Gerlach spin measurement illustrates the problems and their solutions.

• An appropriate framework solves the problem of definite output pointer states.

• The second problem is to relate measurement outcomes to measured properties.

• It is resolved by choosing a suitable family of consistent histories.

Abstract

In response to recent criticisms by Okon and Sudarsky, various aspects of the consistent histories (CH) resolution of the quantum measurement problem(s) are discussed using a simple Stern‐Gerlach device, and compared with the alternative approaches to the measurement problem provided by spontaneous localization (GRW), Bohmian mechanics, many worlds, and standard (textbook) quantum mechanics. Among these CH is unique in solving the second measurement problem: inferring from the measurement outcome a property of the measured system at a time before the measurement took place, as is done routinely by experimental physicists. The main respect in which CH differs from other quantum interpretations is in allowing multiple stochastic descriptions of a given measurement situation, from which one (or more) can be selected on the basis of its utility. This requires abandoning a principle (termed unicity), central to classical physics, that at any instant of time there is only a single correct description of the world.

Introduction

The immediate motivation for this paper comes from criticisms by Okon and Sudarsky (2014), recently published in this journal, of the consistent histories (CH) interpretation of quantum mechanics. These authors claim that CH does not provide a satisfactory resolution of the quantum measurement problem. Such criticism deserves to be taken seriously, for the CH approach claims to resolve all the standard problems of quantum interpretation which form the bread and butter of quantum foundations research: it is local (Griffiths, 2011), so there are no conflicts with special relativity; it is noncontextual (Griffiths, 2013b), in contrast to hidden variable interpretations; it resolves the EPR, BKS, Hardy, three boxes, etc., etc. paradoxes, see of Griffiths (2002, chaps. 19–25). And while it may be defective, its (purported) solutions to the full gamut of quantum conceptual difficulties have been published in detail and are available right now for critical inspection, not just as promissory notes for some future time. Thus the Okon and Sudarsky criticisms, while based (we believe) on an imperfect understanding of the CH approach, are dealing with important issues that need to be discussed.

Of particular significance is the fact that the CH approach does not include any reference to measurements among its basic principles for interpreting quantum mechanics. Measurements are simply treated as a particular type of physical process to which the same quantum principles apply as to any other physical process. When understood in this way quantum mechanics no longer has a measurement problem as that term is generally used in quantum foundations: a conflict between unitary time development of a combined system plus measuring device and a macroscopic outcome or “pointer position.” Not only so, in addition CH shows how the outcome of a measurement can be shown to reveal the presence of a microscopic quantum property possessed by the measured system just before the measurement took place, in accordance with the belief, common among experimental physicists, that the apparatus they have built performs the function for which it was constructed. This second measurement problem has received far too little attention in the quantum foundations literature, and resolving it is no less important than the first problem if the entire measuring process is to be understood in fully quantum-mechanical terms.

Rather than an abstract discussion, the present paper examines a particular measurement scenario, using it as an example of the application of CH principles, and also a basis for comparison with some other interpretations of quantum mechanics mentioned in Okon and Sudarsky (2014). These include the spontaneous localization approach developed by Ghirardi et al. and Pearle, see Ghirardi et al., 1985, Ghirardi et al., 1986, Pearle (1989), Frigg (2009), and Ghirardi (2011), often abbreviated as GRW (the initials of the authors of Ghirardi et al., 1985), and the pilot wave approach of de Broglie and Bohm, which we shall refer to as Bohmian mechanics (Bohm, 1952, de Broglie, 1927, Holland, 1993, Goldstein, 2012). Textbook or standard quantum mechanics and the many worlds interpretation of Everett and his successors, Everett (1957), DeWitt and Graham (1973), and Saunders, Barrett, Kent, and Wallace (2010) also enter the discussion from time to time. Since details of the CH approach are readily available in the literature, e.g., Griffiths, 2002, Griffiths, 2009, Griffiths, 2013a, Griffiths, 2014a, Griffiths, 2014b and Hartle (2011), only those aspects needed to make the discussion reasonably self-contained are included in this paper.

Our aim is to present and discuss as clearly as possible the central features of the CH approach that have given rise to the criticisms in Okon and Sudarsky (2014), and which are undoubtedly shared by other critics, e.g., Kent (1998), Bassi and Ghirardi (2000), Pearle (2005), and Mermin (2013). Of particular importance is the fact that CH abandons a principle, here called unicity, which is deeply embedded in both conventional and scientific thought, and is taken for granted in classical physics. It is the idea that at any instant of time there is precisely one exact description of the state of the world which is true. If the CH understanding is correct, quantum mechanics has made unicity obsolete in somewhat the same way as modern astronomy has replaced an unmovable earth at the center of the universe with our current understanding of the solar system, and ignoring this feature of the quantum world is what has given rise to so many conceptual difficulties.

The contents of the remainder of the paper are as follows. The measurement problem(s) of quantum foundations are discussed in general terms in Section 2, followed in Section 3 by a specific measurement model, a modernized version of the famous experiment of Stern and Gerlach (Stern, 1921, Gerlach and Stern, 1922). Its description in CH terms begins in Section 4 with a discussion of the first measurement problem, whose solution is compared with some other approaches in Section 4.2. The CH solution to the second measurement problem is the subject of Section 5, and it is compared with standard quantum mechanics, spontaneous localization, many worlds, and Bohmian mechanics in Section 6. Our response to the specific criticisms of Okon and Sudarsky occupies (Section 7). Section 8 is a brief summary of the whole paper.