Abstract
What is called “orthodox” quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions—the projection postulate and the eigenvalue-eigenvector link—that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements (all of which are standard in contemporary physics) and that the eigenvalue-eigenvector link implies that virtually all interesting properties are maximally indefinite pretty much always. I present an alternative way of conceptualising quantum mechanics that does a better job of representing quantum mechanics as it is actually used, and in particular that eliminates use of either the projection postulate or the eigenvalue-eigenvector link, and I reformulate the measurement problem within this new presentation of orthodoxy.
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Notes
- 1.
- 2.
Of course, plenty of people working on black hole decay are fairly explicit advocates of the Everett interpretation, and I have argued elsewhere that quantum cosmology generally is tacitly committed to the Everett interpretation, but it’s clear that the majority of the community embrace Mermin’s “shut up and calculate” approach (Mermin 2004).
- 3.
For more detail on the physics of this section, see, e.g., Busch et al. (1996).
- 4.
And, like most ‘standard results of quantum mechanics’, there are some tacit additional mathematical assumptions required. See Ruetsche (2011, ch.3) for details.
- 5.
See, e.g., Rudin (1991, pp. 196–202).
- 6.
The line of argument here has some resemblance to that used by Albert and Loewer (1996) to argue that the E-E link should be rejected in the GRW theory in place of a “fuzzy link”. But Albert and Loewer attributed the problem to the Gaussian collapse function used in the GRW theory, whereas as we have seen, the problem arises even in the absence of any collapse event, as a consequence of ordinary Schrödinger dynamics.
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In fact, it suffices for \({\widehat {{{\Pi }}}}\) to be a positive operator.
- 8.
See Halvorson and Clifton (2002) for discussion of its significance in this context.
- 9.
This is an instance of Quine’s classic objection to logical positivism (Quine 1951)—the empirical predictions of particular applications of quantum mechanics cannot be isolated from the influence of myriad other parts of our scientific world-view.
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- 11.
Appreciating that this is the task being performed by decoherence in contemporary physical practice also goes some way to explaining why the physics community has regarded decoherence as a major step towards understanding the interpretation of QM, something not generally shared by philosophers (Barrett (1999, p. 230) is typical: “That decoherence destroys simple interference effects does not solve the measurement problem since it does not explain the determinateness of our measurement records …In order to observe a single determinate record there must somewhere be a single determinate record.).”
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Acknowledgements
This paper has benefitted greatly from conversations with Simon Saunders and Chris Timpson, and from feedback when it was presented at the 2016 Michigan Foundations of Modern Physics workshop, especially from Jeff Barrett, Gordon Belot, and Antony Leggett.
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Wallace, D. (2019). What is Orthodox Quantum Mechanics?. In: Cordero, A. (eds) Philosophers Look at Quantum Mechanics. Synthese Library, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-030-15659-6_17
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