International Journal of Theoretical Physics

, Volume 32, Issue 12, pp 2207–2220 | Cite as

Quantum structures due to fluctuations of the measurement situation

  • Diederik Aerts


We analyze the meaning of the nonclassical aspects of quantum structures. We proceed by introducing a simple mechanistic macroscopic experimental situation that gives rise to quantum-like structures. We use this situation as a guiding example for our attempts to explain the origin of the nonclassical aspects of quantum structures. We see that the quantum probabilities can be introduced as a consequence of the presence of fluctuations on the experimental apparatuses, and show that the full quantum structure can be obtained in this way. We define the classical limit as the physical situation that arises when the fluctuations on the experiment apparatuses disappear. In the limit case we come to a classical structure, but in between we find structures that are neither quantum nor classical. In this sense, our approach not only gives an explanation for the nonclassical structure of quantum theory, but also makes it possible to define and study the structure describing the intermediate new situations. By investigating how the nonlocal quantum behavior disappears during the limiting process, we can explain the“apparent”locality of the classical macroscopic world. We come to the conclusion that quantum structures are the ordinary structures of reality, and that our difficulties of becoming aware of this fact are due to prescientific prejudices, some of which we point out.


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  1. Accardi, L., and Fedullo, A. (1982).Lettere al Nuovo Cimento,34, 161.Google Scholar
  2. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics,Journal of Mathematical Physics,27, 203.Google Scholar
  3. Aerts, D. (1987). The origin of the non-classical character of the quantum probability model, inInformation, Complexity and Control in Quantum Physics, A. Blanquiereet al., eds., Springer-Verlag, New York.Google Scholar
  4. Aerts, D. (1992a). A macroscopical classical laboratory situation with only macroscopical classical entities giving rise to a quantum mechanical description, inQuantum Probabilities, Volume VI, L. Accardi, ed., World Scientific, Singapore.Google Scholar
  5. Aerts, D. (1992b). In search of the meaning of quantum structures, inProceedings of the ANPA meeting, Stanford University.Google Scholar
  6. Aerts D., and Reignier, J. (1991). On the problem of non-locality in quantum mechanics,Helvetica Physica Acta,62, 527.Google Scholar
  7. Aerts, D., and Van Bogaert, B. (1992). A mechanical classical laboratory situation with a quantum logic structure,International Journal of Theoretical Physics,31, 1839.Google Scholar
  8. Aerts, D., Durt, T., Grib, A. A., Van Bogaert, B., and Zapatrin, R. R. (1992a). Quantum structures in macroscopical reality,International Journal of Theoretical Physics.Google Scholar
  9. Aerts, D., Durt, T., and Van Bogaert, B. (1992b). A physical example of quantum fuzzy sets and the classical limit, inProceedings of the International Conference on Fuzzy Sets, Liptovsky, Tatra Mountains Mathematical Publications, Volumes 1, 5.Google Scholar
  10. Aerts, D., Durt, T., and Van Bogaert, B. (1992c). Quantum interdeterminism, the classical limit and non-locality, inProceedings of the Symposium on the Foundations of Modern Physics, Helsinki 1992, World Scientific, Singapore.Google Scholar
  11. Aerts, D., Coecke, B., Durt, T., and Van Bogaert, B. (1993). Quantum, classical and intermediate,Proceedings of the“Winter School on Measure Theory”, Liptovsky, February 1993, to appear.Google Scholar
  12. Bell, J. (1966).Rev. Mod. Phys.,38, 447.Google Scholar
  13. Gleason, A. M. (1957).J. Math. Mech.,6, 885.Google Scholar
  14. Gudder, S. P. (1968).Rev. Mod. Phys.,40, 229.Google Scholar
  15. Jauch, J. M., and Piron, C. (1963).Helvetica Physica Acta,36, 827.Google Scholar
  16. Kochen, S., and Specker, E. P. (1967).J. Math. Mech.,17, 59.Google Scholar
  17. Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, N.J.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Diederik Aerts
    • 1
  1. 1.Senior Research Associate of the Belgian National FundTENA, Free University of BrusselsBrusselsBelgium

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