The Pros and Cons of the Kochen-Dieks and the Atomic Modal Interpretation

  • Pieter E. Vermaas
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 60)

Abstract

In this paper I discuss two versions of the modal interpretation of quantum mechanics: the modal interpretation as formulated by Kochen and Dieks, and the atomic modal interpretation proposed by Bacciagaluppi and Dickson. I examine whether these interpretations yield a conceptually coherent description of reality and whether they solve the measurement problem.

Modal interpretations ascribe actually possessed properties to quantum systems. I argue that the Kochen-Dieks interpretation cannot simultaneously ascribe properties to many systems, that it does not provide dynamics for the ascribed properties and that it yields an odd though tenable relation between the properties of systems and subsystems. The atomic modal interpretation violates in its turn the assumption that measurements which yield with probability 1 a positive outcome, reveal initially possessed properties.

The Kochen-Dieks and the atomic modal interpretation do not always solve the measurement problem because they do not always ascribe the required readings to the measurement device after a measurement. I define for both interpretations classes of measurements for which they do solve the measurement problem. These classes comprise error-prone measurements and measurements perturbed by environmental influences.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, D. Z and B. Loewer (1990), “Wanted Dead or Alive: Two Attemps to Solve Schrödinger’s Paradox”, in Fine, Forbes and Wessels (1990), pp. 277–285.Google Scholar
  2. Albert, D. Z and B. Loewer (1993), “Non-Ideal Measurements”, Foundations of Physics Letters 6, 297–305.CrossRefGoogle Scholar
  3. Arntzenius, F. (1990), “Kochen’s Interpretation of Quantum Mechanics”, in Fine, Forbes and Wessels (1990), pp. 241–249.Google Scholar
  4. Bacciagaluppi, G. (1995), “A Kochen-Specker Theorem in the Modal Interpretation of Quantum Mechanics”, International Journal of Theoretical Physics 34, 1205–1216.CrossRefGoogle Scholar
  5. Bacciagaluppi, G. (1996), “Delocalised Properties in the Modal Interpretation of a Continuous Model of Decoherence”, University of Cambridge Preprint.Google Scholar
  6. Bacciagaluppi, G. and W. M. Dickson (1996), “Modal Interpretations with Dynamics”, in preparation.Google Scholar
  7. Bacciagaluppi, G., M. J. Donald, and P. E. Vermaas (1995), “Continuity and Discontinuity of Definite Properties in the Modal Interpretation”, Helvetica Physica Acta 68, 679–704.Google Scholar
  8. Bacciagaluppi, G. and M. Hemmo (1996), “Modal Interpretations, Decoherence and Measurements”, Studies in History and Philosophy of Modem Physics 27, 239–277.CrossRefGoogle Scholar
  9. Bacciagaluppi, G. and P. E. Vermaas (1998), “Virtual Reality: Consequences of No-Go Theorems for the Modal Interpretation of Quantum Mechanics”, in M. Dalla Chiara, R. Giuntini, and F. Laudisa (eds.), Philosophy of Science in Florence, 1995 (Kluwer, Dordrecht), forthcoming.Google Scholar
  10. Bub, J. (1992), “Quantum Mechanics without the Projection Postulates”, Foundations of Physics 22, 737–754.CrossRefGoogle Scholar
  11. Clifton, R. K. (1995), “Independent Motivation of the Kochen-Dieks Modal Interpretation of Quantum Mechanics”, British Journal for the Philosophy of Science 46, 33–57.CrossRefGoogle Scholar
  12. Clifton, R. K. (1996), “The Properties of the Modal Interpretations of Quantum Mechanics”, British Journal for the Philosophy of Science 47, 371–398.CrossRefGoogle Scholar
  13. Dieks, D. (1988), “The Formalism of Quantum Theory: An Objective Description of Reality?”, Annalen der Physik 7, 174–190.CrossRefGoogle Scholar
  14. Dieks, D. (1994), “Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior”, Physical Review A 49, 2290–2300.CrossRefGoogle Scholar
  15. Dieks, D. (1998), “Preferred Factorizations and Consistent Property Attribution”, in Healey and Hellman (1998), forthcoming.Google Scholar
  16. Elby, A. (1993), “Why “Modal” Interpretations of Quantum Mechanics don’t Solve the Measurement Problem”, Foundations of Physics Letters 6, 5–19.CrossRefGoogle Scholar
  17. Fine, A., M. Forbes, and L. Wessels (eds.) (1990), Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, Volume 1 (Philosophy of Science Association, East Lansing, Michigan).Google Scholar
  18. Healey, R. (1989), The Philosophy of Quantum Mechanics: An Interactive Interpretation (Cambridge University Press, Cambridge).CrossRefGoogle Scholar
  19. Healey, R. and G. Hellman (eds.) (1998), Quantum Measurement: Beyond Paradox, Volume 17 of Minnesota Studies in the Philosophy of Science (University of Minnesota Press, Minneapolis), in preparation.Google Scholar
  20. Kochen, S. (1985), “A New Interpretation of Quantum Mechanics”, in P. J. Lahti and P. Mittelsteadt (eds.), Symposium on the Foundations of Modem Physics (World Scientific, Singapore), pp. 151–169.Google Scholar
  21. Rellich, F. (1969), Perturbation Theory of Eigenvalue Problems (Gordon and Breach, New York).Google Scholar
  22. Ruetsche, L. (1995), “Measurement Error and the Albert-Loewer Problem”, Foundations of Physics Letters 8, 327–344.CrossRefGoogle Scholar
  23. Svetlichny, G., M. L. G. Redhead, H. Brown, and J. Butterfield (1988), “Do the Bell Inequalities Require the Existence of Joint Probability Distributions?”, Philosophy of Science 55, 387–401.CrossRefGoogle Scholar
  24. Van Fraassen, B. C. (1991), Quantum Mechanics (Clarendon, Oxford).CrossRefGoogle Scholar
  25. Vermaas, P. E. (1996), “Unique Transition Probabilities in the Modal Interpretation”, Studies in History and Philosophy of Modern Physics 27, 133–159.CrossRefGoogle Scholar
  26. Vermaas, P. E. (1997), “A No-Go Theorem for Joint Property Ascriptions in Modal Interpretations of Quantum Mechanics”, Physical Review Letters 78, 2033–2037.CrossRefGoogle Scholar
  27. Vermaas, P. E. (1998a), “Expanding the Property Ascriptions in the Modal Interpretation of Quantum Theory”, in Healey and Hellman (1998), forthcoming.Google Scholar
  28. Vermaas, P. E. (1998b), Possibilities and Impossibilities of Modal Interpretations of Quantum Mechanics, Ph. D. thesis, Utrecht University.Google Scholar
  29. Vermaas, P. E. and D. Dieks (1995), “The Modal Interpretation of Quantum Mechanics and Its Generalization to Density Operators”, Foundations of Physics 25, 145–158.CrossRefGoogle Scholar
  30. Von Neumann, J. (1955), Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Pieter E. Vermaas
    • 1
  1. 1.Utrecht UniversityThe Netherlands

Personalised recommendations