International Journal of Theoretical Physics

, Volume 23, Issue 12, pp 1171–1196 | Cite as

Modalities and quantum mechanics

  • F. J. Burghardt


Three approaches concerning the usage of modalities in the language of quantum mechanics were considered; Mittelstaedt and I built up a dialog semantics for modalities on a metalinguistic level, and a calculus of quantum modal logic is known that is complete and sound with respect to this dialogic semantics. Van Fraassen replaced the usual interpretation of quantum mechanics (with the projection postulate) by his “modal interpretation” based on a modal object language. Dalla Chiara translated a nonmodal object language for quantum mechanics and the appropriate quantum logic into a modal language. Specifically we are interested in the similarities and the differences of these three approaches.


Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Modal Logic 
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  1. Burghardt, F. J. (1979).Modale Quantenmetalogik mit dialogischer Begründung. Dissertation, Cologne.Google Scholar
  2. Burghardt, F. J. (1980). Modal quantum logic and its dialogic foundation,Inter. J. Theor. Phys.,19, 843–866.Google Scholar
  3. Carnap, R. (1934).Logische Syntax der Sprache. Springer, Vienna.Google Scholar
  4. Dalla Chiara, M. L. (1977). Quantum logic and physical modalities,J. Phil. Log.,6, 391–404.Google Scholar
  5. Dalla Chiara, M. L. (1979). Some metalogical pathologies of quantum logic, inCurrent Issues in Quantum Logic, E. Beltrametti and B. C. van Fraassen, eds., Plenum Press, New York.Google Scholar
  6. van Fraassen, B. C. (1972). A formal approach to the philosophy of science, in pp. 303–368.Paradigms and Paradoxes, R. Colodny, ed. University of Pittsburgh Press, Pittsburgh.Google Scholar
  7. van Fraassen, B. C. (1973). Semantic analysis of quantum logic, in C. A. Hooker, ed., pp. 80–113.Contemporary Research in the Foundations and Philosophy of Quantum Theory. D. Reidel, Dordrecht.Google Scholar
  8. van Fraassen, B. C. (1976). The Einstein-Podolski-Rosen Paradox, inLogic and Probability in Quantum Mechanics, P. Suppes, ed., pp. 283–301. (Synthese Library, Vol. 78) D. Reidel, Dordrecht.Google Scholar
  9. van Fraassen, B. C. (1979). A modal interpretation of quantum mechanics, inCurrent Issues in Quantum Logic, E. Beltrametti and B. C. Van Fraassen, eds. Plenum Press, New York.Google Scholar
  10. Goldblatt, R. I. (1974). Semantical analysis of orthologic,J. Phil. Log.,3, pp. 19–35.Google Scholar
  11. Hughes, G. E., and Cresswell, M. J. (1968).An Introduction to Modal Logic. Methuen, London.Google Scholar
  12. Lorenzen, P. (1954). Zur Begründung der Modallogik,Archiv für mathematische Logik und Grundlagenforschung,2, 15–28 (Archiv für Philosophie,5, pp. 95–108).Google Scholar
  13. Mittelstaedt, P. (1976).Philosophical Problems of Modern Physics. Reidel, Dordrecht.Google Scholar
  14. Mittelstaedt, P. (1978).Quantum Logic. Reidel, Dordrecht.Google Scholar
  15. Mittelstaedt, P. (1979a). The Modal Logic of Quantum Logic,J. Phil. Log. 8, 479–504.Google Scholar
  16. Mittelstaedt, P. (1979b). The dialogic approach to modalities in the language of quantum physics, inCurrent Issues in Quantum Logic. E. Beltrametti and B. C. van Fraassen, eds. Plenum Press, New York.Google Scholar
  17. Mittelstaedt, P. (1980). Wahrheit, Wirklichkeit und Logik in der Sprache der Physik, to be published.Google Scholar
  18. Rautenberg, W. (1979).Klassische und nichtklassische Aussagenlogik. F. Vieweg & Sohn, Braunschweig-Wiesbaden.Google Scholar
  19. Stachow, E.-W. (1981). Der quantenmechanische Wahrscheinlichkeitsbegriff, in J. Nitsch, J. Pfarr, and E.-W. Stachow, eds.,Grundlagenprobleme der modernen Physik-Festschrift für Peter Mittelstaedt zum 50.Geburtstag. Bibliographisches Institut, Mannheim.Google Scholar
  20. Ochs, W. (1979).Some comments on the concept of State in Quantum Mechanics. unpublished.Google Scholar
  21. Gödel, K. (1932). “Eine Interpretation des intuitionistischen Aussagenkalküls,”Ergebnisse eines mathematischen Kolloquiums,4, 39–40.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • F. J. Burghardt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität zu KölnKölnWest Germany

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