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Five Formulations of the Quantum Measurement Problem in the Frame of the Standard Interpretation

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Abstract

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, but to a set of sub-problems.

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Notes

  1. For a definition of “scientific realism”, see for instance Hacking (1983), or van Fraassen (1989). Can Dirac’s and von Neumann’s interpretations be qualified as “realist”? This is a controversial question. For, on the one hand, some quotations can be found where the two physicists are supporting instrumentalist ideas, and on the other, they are responsible for the introduction of the notion of “state”, which has a strong realist connotation. I will leave this question aside. What matters here is the fact that most of the manuals, referring to Dirac’s and von Neumann’s work, are based on a realist approach. On this point, see Bohm and Hiley (1993, pp. 17–24).

  2. According to many manuals of QM, the apparatus has to be described by means of classical physics. This idea is generally attributed to Bohr. However, contrary to the authors of the manuals who consider the quantum/classical cut as an ontological one (e.g. Landau and Lifchitz 1958), Bohr considers it only as an epistemological one: “the description of quantum phenomena requires a distinction in principle between the objects under investigation [described quantum mechanically] and the measuring apparatus [described thanks to classical physics] by means of which the experimental conditions are defined” (1963, p. 78; I have emphasized “in principle”).

  3. Historically, the “quantum description” has first been suggested by von Neumann. But contrarily to what is sometimes written, von Neumann didn’t advocated for it. He rather tried to show that this description is equivalent to the standard description, in the sense that it doesn’t eschew the need for postulating the quantum jump hypothesis (1955, pp. 420–437).

  4. In 1970, Zeh claimed that a measurement apparatus cannot be considered as an isolated system because it is a macroscopic system (1970, p. 73). This argument has since been challenged by various experiments, those for example using superconductor devices (for a review and a discussion concerning these experiments, see Leggett 2002). Nevertheless, a measurement apparatus has the peculiarity to be a largely dissipative system, so that the effect of its interaction with the environment is always significant (cf. Omnès 1994, Chap. 7).

  5. Some years before, Daneri et al. (1962) proposed a description of the measurement process taking into account the thermo-dynamical aspects of the measurement apparatus. It can be viewed as a precursory work to decoherence theory.

  6. It is not question of finding, or reproducing, the minimal assumptions generating the measurement problem to which the “insolubility” proofs refer (see Sect. 1 and below). The aim here is to reproduce as accurately as possible the most common conception of what is the “standard” interpretation.

  7. This is the ideal case. Nevertheless, all the discussion on the measurement problem can be generalised to the non-ideal case where the correlation between S and M is not perfect. In particular, the “insolubility” proof of the measurement problem holds (cf. Bush and Shimony 1996).

  8. This quantum jump hypothesis, applied in the context of measurement, is reminiscent of Bohr’s atom model (1913) according to which an orbital electron can “jump” to a lower energy level by emitting a radiation.

  9. In the literature, the two expressions “reduction” and “quantum jump” are usually taken as synonym. But this is a conceptual confusion, since we could well imagine a reduction taking a non-zero lapse of time, being deterministic, and reversible.

  10. Expression due to Margenau (1958, p. 29).

  11. This term has been introduced by Schrödinger (1983, p. 161). Nevertheless, contrarily to what is often said, Schrödinger didn’t write that the “entanglement” concerns the systems’ physical states. For him, only the predictions of outcomes (for measurement performed on these systems) can be “entangled” (ibid.).

  12. Expression due to Putnam (1965, p. 75).

  13. In fact, these proofs are based on more general assumptions than the ones mentioned above (in particular, they do not assume the eigenvalue-eigenvector link). For a discussion of this proofs, see Dickson (2003).

  14. This is the famous experiment imagined by Einstein et al. (1935), reformulated by Bohm in terms of spins 1/2 (1951, pp. 614–619), and then carried out in the 1980s by Aspect et al. (1981, 1982) and others.

  15. The question of whether the EPR experiment is an evidence for some kind of non-locality is still controversial and the subject of a wide literature. Let us note that the answer depends on the assumed interpretative background. Indeed, as de Muynck (1986, p. 999) has shown it: “violation of the Bell inequalities in the [...] EPR-like experiments is not acceptable as experimental evidence of non-locality [...] a purely instrumentalist attitude does not give rise to any suspicion of non-locality. Only if the quantum mechanical description is supposed to refer to an objective reality does the idea of non-locality present itself”. Furthermore, it has been proven that if QM is interpreted as a non-local theory, then at least this non-locality cannot be used for supra-luminal transmission of information (cf. Eberhard 1978; Ghirardi et al. 1980; Jarerett 1984).

  16. This is Bell’s expression (1990, p. 33).

  17. It is true, the initial ignorance is irreducible, by contrast with our ignorance at the end of the measurement (concerning the notion of irreducibility, see Margenau 1963b, pp. 7–11). But this doesn’t change the point.

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Acknowledgements

This work received financial support from the European Union (Marie Curie Actions).

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Bächtold, M. Five Formulations of the Quantum Measurement Problem in the Frame of the Standard Interpretation. J Gen Philos Sci 39, 17–33 (2008). https://doi.org/10.1007/s10838-008-9054-0

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