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.
Notes
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).
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”).
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).
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).
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.
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.
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).
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.
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.
Expression due to Margenau (1958, p. 29).
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.).
Expression due to Putnam (1965, p. 75).
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).
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).
This is Bell’s expression (1990, p. 33).
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.
References
Albert, D., & Loewer, B. (1988). Interpreting the many worlds interpretation. Synthese, 77, 195–213.
Aspect, A., Grangier, Ph., & Roger, G. (1981). Experimental tests of realistic local theories via Bell’s theorem. Physical Review Letters, 47, 460–467.
Aspect, A., Grangier, Ph., & Roger, G. (1982). Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell’s inequalities. Physical Review Letters, 48, 91–94.
Bassi, A., & Ghirardi, G. (2003). Dynamical reduction models. Physics Reports, 379, 257–426.
Barrett, J. (1999). The quantum mechanics of minds and worlds. Oxford: Oxford University Press.
Bell, J. (1990). Against measurement. Physics World, 8, 33–40.
Bitbol, M. (1996). Mécanique quantique, une introduction philosophique. Paris: Flammarion.
Blanchard, Ph., et al. (Eds.) (2000). Decoherence: Theoretical, experimental, and conceptual problems. Berlin, Heidelberg: Springer.
Bohm, D. (1951). Quantum theory. Englewood Cliffs: Prentice-Hall.
Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ‘hidden’ variables, I and II. Physical Review, 85, 166–193.
Bohm, D., & Hiley, B. (1993). The undivided universe: An ontological interpretation of quantum theory. London: Routledge & Kegan Paul.
Bohr, N. (1913). On the constitution of atoms and molecules, Part I, II, and III. Philosophical Magazine, 26, 1–25, 476–502, and 857–875.
Bohr, N. (1963). Essays 1958–1962 on atomic physics and human knowledge. New York: Interscience.
Brown, H. (1986). The insolubility proof of the quantum measurement problem. Foundations of Physics, 16, 857–870.
Brukner, Č., & Zeilinger, A. (2003). Information and fundamental elements of the structure of quantum theory. In L. Castell & O. Ischebeck (Eds.), Time, quantum, information. Berlin, Heidelberg: Springer.
Bub, J. (1992). Quantum mechanics without the projection postulate. Foundations of Physics, 22, 737–754.
Bub, J. (1997). Interpreting the quantum world. Cambridge: Cambridge University Press.
Busch, P., Lahti, P., & Mittelstaedt, P. (1996). The quantum theory of measurement. Berlin, Heidelberg: Springer.
Bush, P., & Shimony, A. (1996). Insolubility of the quantum measurement problem for unsharp observables. Studies in History and Philosophy of Modern Physics, 27, 397–404.
Butterfield, J. (2001). Some worlds of quantum theory. In R. Russell, et al. (Eds.), Quantum mechanics: Scientific perspectives on divine action (pp. 111–140). Vatican City State: Vatican Observatory Publications & Berkeley.
Daneri, A., Loinger, A., & Prosperi, G. (1962). Quantum theory of measurement and ergodicity conditions. Nuclear Physics, 33, 297–319.
D’Espagnat, B. (1990). Towards a separable ‘empirical reality’?. Foundations of Physics, 20, 1147–1172.
D’Espagnat, B. (1995). Veiled reality: An analysis of present-day quantum mechanical concepts. Reading (Mass.): Addison-Wesley.
DeWitt, B., & Graham, N. (Eds.) (1973). The many worlds interpretation of quantum mechanics. Princeton: Princeton University Press.
Dickson, M. (2003). The measurement problem. Routledge Encyclopedia of Philosophy.
Dieks, D. (1994). Modal interpretation of quantum mechanics, measurements, and macroscopic behaviour. Physical Review A, 49, 2290–2300.
Dirac, P. (1958). The principles of quantum mechanics. Oxford: Clarendon Press (1st pub.: 1930).
De Muynck, W. (1986). On the relation between the Einstein-Podolsky-Rosen Paradox and the problem of nonlocality in quantum mechanics. Foundations of Physics, 16, 973–1002.
Eberhard, P. (1978). Bell’s theorem and the different concepts of locality. Nuevo Cimento, 46B, 392–419.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780.
Everett, H. (1957). ‘Relative State’ formulation of quantum mechanics. Reviews of Modern Physics, 29, 454–462.
Fine, A. (1970). Insolubility of the quantum measurement problem. Physical Review D, 2, 2783–2787.
Fine, A. (1973). Probability and the interpretation of quantum mechanics. British Journal for the Philosophy of Science, 24, 1–37.
Fuchs, C. (2002). Quantum mechanics as quantum information (and only a little more). arXiv e-print, quant-ph/0205039.
Gell-Mann, G., & Hartle, J. (1990). Quantum mechanics in the light of quantum cosmology. In W. Zurek (Ed.), Complexity, entropy, and the physics of information (pp. 425–458). Redwood City: Addison-Wesley.
Ghirardi, G., Rimini, A., & Weber, T. (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34, 470–491.
Ghirardi, G., Pearle, P., & Rimini, A. (1990). Markov Processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Physical Review A, 42, 78–89.
Ghirardi, G., Rimini, A., & Weber, T. (1980). A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere al Nuovo Cimento, 27, 293–298.
Giulini, D., et al. (Eds.) (1996). Decoherence and the appearance of the classical world in quantum theory. Berlin, Heidelberg: Springer.
Griffiths, R. (1984). Consistent histories and the interpretation of quantum mechanics. Journal of Statistical Physics, 36, 219–272.
Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge: Cambridge University Press.
Healey, R. (1989). The philosophy of quantum mechanics: An interactive interpretation. Cambridge: Cambridge University Press.
Jarrett, J. (1984). On the physical significance of the locality conditions in the Bell arguments. Noûs, 18, 569–589.
Joos, E. (2000). Elements of environmental decoherence. In Ph. Blanchard et al. (Eds.), Decoherence: Theoretical, experimental, and conceptual problems (pp. 1–17). Berlin, Heidelberg: Springer.
Landau, L., & Lifchitz, E. (1958). Quantum Mechanics: non-relativistic theory. London: Pergamon Press.
Leggett, A. (2002). Testing the limits of quantum mechanics: Motivation, state of play, prospects. Journal of Physics: Condensed Mater, 14, R415–R451.
Lockwood, M. (1989). Mind, brain, and the quantum. Oxford: Blackwell.
Lyre, H. (1999). Against measurement?–On the concept of information. In Ph. Blanchard & A. Jadczyk (Eds.), Quantum future: From Volta and Como to present and beyond. Berlin: Springer.
Margenau, H. (1958). Philosophical problems concerning the meaning of measurement in physics. Philosophy of Science, 25, 23–33.
Margenau, H. (1963a). Measurements and quantum in quantum mechanics. Annals of Physics, 23, 469–485.
Margenau, H. (1963b). Measurements and quantum states. Philosophy of Science, 30, 1–16, 135–157.
Mittelstaedt, P. (1998). The interpretation of quantum mechanics and the measurement process. Cambridge: Cambridge University Press.
Omnès, R. (1994). The interpretation of quantum mechanics. Princeton: Princeton University Press.
Popper, K. (1982). Quantum theory and the Schism in Physics: The postscript to the logic of scientific discovery, III. London: Hutchinson.
Popper, K. (1990). A world of propensities. Bristol: Thoemmes Press.
Putnam, H. (1965). A philosopher looks at quantum mechanics. In R. Colodny (Ed.), Beyond the edge of certainty (pp. 75–101). Prentice Hall: Englewood Cliffs.
Saunders, S. (1995). Time, quantum mechanics, and decoherence. Synthese, 102, 235–266.
Shimony, A. (1974). Approximate measurement in quantum mechanics, II. Physical Review D, 9, 2321–2323.
Shimony, A. (1986). Events and processes in the quantum world. In R. Penrose & C. Isham (Eds.), Quantum concepts in space and time (pp. 182–203). Oxford: Clarendon Press.
Schrödinger, E. (1983). The present situation in quantum mechanics. In J. Wheeler & W. Zurek (Eds.), Quantum theory and measurement (pp. 152–167). Princeton: Princeton University Press (1st pub.: “Die gegenwärtige Situation in der Quantenmechanik”, 1935).
Teller, P. (1983). The projection postulate as a fortuitous approximation. Philosophy of Science, 50, 413–431.
Van Fraassen, B. (1989). Laws and symmetry. Oxford: Clarendon Press.
Van Fraassen, B. (1991). Quantum mechanics: An empiricist View. Oxford: Clarendon Press.
Von Neumann, J. (1955). Mathematical foundations of quantum mechanics. Princeton: Princeton University Press (1st pub.: Mathematische Grundlagen der Quantenmechanik, 1932).
Wallace, D. (2002). Everett and structure. Studies in the history and philosophy of modern physics, 34, 87–105.
Wigner, E. (1963). The problem of measurement. American Journal of Physics, 29, 6–15.
Zeh, D. (1970). On the interpretation of measurement in quantum theory. Foundations of Physics, 1, 69–76.
Zurek, W. (1981). Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? Physical Review D, 24, 1516–1525.
Zurek, W. (1982). Environment-induced superselection rules. Physical Review D, 26, 1862–1880.
Zurek, W. (1991). Decoherence and the transition from quantum to classical. Physics Today, 44, 36–44.
Acknowledgements
This work received financial support from the European Union (Marie Curie Actions).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10838-008-9054-0