Virtual Reality: Consequences of No-Go Theorems for the Modal Interpretation of Quantum Mechanics
The modal interpretation of quantum mechanics is a no-collapse interpretation that provides a rule for assigning properties to quantum mechanical systems, depending on their (reduced) quantum state, whether this state be pure or mixed. The modal interpretation was originally developed by Kochen (1985), Dieks (1989) and Healey (1989) (with slight differences) modifying ideas by Van Fraassen (1973, 1991), and was further developed by Vermaas and Dieks (1995) and Clifton (1995). In the original version, the rule for assigning properties is applied to all quantum systems. However, a recent series of no-go theorems by Bacciagaluppi (1995), Clifton (1996) and Vermaas (1997) has shown that this unrestricted application of the rule leads to contradictions. This has prompted some authors (Bacciagaluppi and Dickson, 1999; Dieks, 1998) to restrict application of the rule only to ‘elementary’ or ‘atomic’ systems. We call this version the atomic modal interpretation. In this paper, we shall describe the no-go results, and discuss the picture yielded by the atomic modal interpretation. We shall proceed as follows.
Unable to display preview. Download preview PDF.
- Bacciagaluppi, G.: 1999, Modal Interpretations of Quantum Mechanics. Cambridge: Cambridge University Press, forthcoming.Google Scholar
- Bacciagaluppi, G., Dickson, M.: 1999, ‘Dynamics for Modal Interpretations’, forthcoming in Foundations of Physics.Google Scholar
- Bacciagaluppi, G., Donald, M.J., Vermaas, P.E.: 1995, ‘Continuity and Discontinuity of Definite Properties in the Modal Interpretation’, Helvetica Physica Acta, 68, 679–704.Google Scholar
- Bacciagaluppi, G., Hemmo, M.: 1998, ‘State Preparation in the Modal Interpretation’, Minnesota Studies in the Philosophy of Science, 17, 95–114.Google Scholar
- Dieks, D.: 1998, ‘Preferred Factorizations and Consistent Property Attribution’, Minnesota Studies in the Philosophy of Science, 17, 144–159.Google Scholar
- Fraassen, B.: 1973, ‘Semantic Analysis of Quantum Logic’ in C.A. Hooker, ed., Contemporary Research in the Foundations and Philosophy of Quantum Theory. Dordrecht: Reidel, 180–213.Google Scholar
- Kernaghan, R.: 1994, ‘Bell-Kochen-Specker Theorem with 20 Vectors’, Journal of Physic, A 27, L829–L830.Google Scholar
- Kochen, S.: 1985, ‘A New Interpretation of Quantum Mechanics’, in P. Lahti and P. Mittelstaedt, eds, Symposium on the Foundations of Modern Physics 1985: 50 Years of the Einstein-PodolskiRosen Gedankenexperiment. Singapore: World Scientific, 151–169.Google Scholar
- Kochen, S., Specker, E.P.: 1967, ‘On the Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics, 17, 59–87.Google Scholar
- Pitowsky, I.: 1989, Quantum Probability-Quantum Logic. Berlin: Springer.Google Scholar
- Vermaas, P.E.: 1998a, ‘Expanding the Property Ascriptions in Modal Interpretations of Quantum Theory’, Minnesota Studies in the Philosophy of Science, 17, 115–143.Google Scholar
- Vermaas, P.E.: 19986, P.E.: 19986, ‘The Pros and Cons of the Kochen—Dieks and the Atomic Modal Interpretation’, in D. Dieks and P.E. Vermaas, eds, The Modal Interpretation of Quantum Mechanics. Dordrecht: Kluwer, 103–148.Google Scholar