International Journal of Theoretical Physics

, Volume 39, Issue 3, pp 483–496 | Cite as

The Description of Joint Quantum Entities and the Formulation of a Paradox

  • Diederik Aerts


We formulate a paradox in relation to the description of a joint entity consistingof two subentities by standard quantum mechanics. We put forward a proposalfor a possible solution, entailing the interpretation of 'density states' as 'purestates.' We explain where the inspiration for this proposal comes from and howits validity can be tested experimentally. We discuss the consequences of theproposal for quantum axiomatics.


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  1. Aerts, D. (1982). Description of many physical entities without the paradoxes encountered in quantum mechanics, Found. Phys. 12, 1131-1170.Google Scholar
  2. Aerts, D. (1984a). Construction of the tensor product for lattices of properties of physical entities, J. Math. Phys. 25, 1434-1441.Google Scholar
  3. Aerts, D. (1984b). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation, Helv. Phys. Acta 57, 421-428.Google Scholar
  4. Aerts, D. (1984c). How do we have to change quantum mechanics in order to describe separated systems, in TheWave-Particle Dualism, eds. S. Diner et al., Reidel, Dordrecht pp. 419-431.Google Scholar
  5. Aerts, D. (1985a). The physical origin of the Einstein Podolsky Rosen paradox, in Open Questions in Quantum Physics, eds. G. Tarozzi and A. van der Merwe, Reidel, Dordrecht, pp 33-50.Google Scholar
  6. Aerts, D. (1985b). The physical origin of the EPR paradox and how to violate Bell inequalities by macroscopic systems, in On the Foundations of Modern Physics, eds. P. Lathi and P. Mittelstaedt, World Scientific, Singapore, pp. 305-320.Google Scholar
  7. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics, J. Math. Phys. 27, 202-210.Google Scholar
  8. Aerts, D. (1987). The origin of the nonclassical character of the quantum probability model, in Information, Complexity, and Control in Quantum Physics, eds. A. Blanquiere, S. Diner, and G. Lochak, Springer-Verlag, New York, pp. 77-100.Google Scholar
  9. Aerts, D. (1991a). A mechanistic classical laboratory situation violating the Bell inequalities with ?2, exactly 'in the same way' as its violations by the EPR experiments, Helv. Phys. Acta 64, 1-24.Google Scholar
  10. Aerts, D. (1991b). A macroscopic classical laboratory situation with only macroscopic classical entities giving rise to a quantum mechanical probability model, in Quantum Probability and Related Topics, Volume VI, ed. L. Accardi, World Scientific, Singapore, pp. 75-85.Google Scholar
  11. Aerts, D. (1993). Quantum structures due to fluctuations of the measurement situations, Int. J. Theor. Phys. 32, 2207-2220.Google Scholar
  12. Aerts, D. (1995). Quantum structures: An attempt to explain their appearance in nature, Int. J. Theor. Phys. 34, 1165-1186.Google Scholar
  13. Aerts, D. (1999a). Foundations of quantum physics:Ageneral realistic and operational approach, Int. J. Theor. Phys. 38, 289-358.Google Scholar
  14. Aerts, D. (1999b). The stuff the world is made of: Physics and reality, in Einstein Meets Magritte: An Interdisciplinary Reflection, eds. D. Aerts, J. Broekaert, and E. Mathijs, Kluwer Academic, Dordrecht.Google Scholar
  15. Aerts, D., and Valckenborgh, F. (n.d.). Lattice extensions and the description of compound entities, in preparation.Google Scholar
  16. Aerts, D., and Van Steirteghem, B. (2000). Quantum axiomatics and a theorem of M.P. Sole`r, Int. J. Theor. Phys., this issue.Google Scholar
  17. Aerts, D., Coecke, B., D'Hooghe, B., Durt, T., and Valckenborgh, F. (1996). A model with varying fluctuations in the measurement context, in Fundamental Problems in Quantum Physics II, eds. M. Ferrero and A. van der Merwe, Plenum, New York, pp. 7-9.Google Scholar
  18. Aerts, D., Colebunders, E., Van der Voorde, A., and Van Steirteghem, B. (1999a). State property systems and closure spaces: A study of categorical equivalence, Int. J. Theor. Phys. 38, 359-385.Google Scholar
  19. Aerts, D., Broekaert, J., and Smets, S. (1999b). Inconsistencies in constituent theories of world views: Quantum mechanical examples, Found. Sci. 3, 313-340.Google Scholar
  20. Bell, J. (1964). On the Einstein Podolsky Rosen paradox, Physics 1(3), 195.Google Scholar
  21. Coecke, B. (1995a). Representation for pure and mixed states of quantum physics in Euclidean space, Int. J. Theor. Phys. 34, 1165.Google Scholar
  22. Coecke, B. (1995b). Representation of a spin-1 entity as a joint system of two spin-1/2 entities on which we introduce correlations of the second kind, Helv. Phys. Acta 68, 396.Google Scholar
  23. Coecke, B. (1996). Superposition states through correlations of the second kind, Int. J. Theor. Phys. 35, 1217.Google Scholar
  24. Einstein, A., Podolsky, B., and Rosen, N. (1935). Can quantum mechanical reality considered to be complete? Phys. Rev. 47, 777.Google Scholar
  25. Piron, C. (1964). Axiomatique quantique, Helv. Phys. Acta 37, 439.Google Scholar
  26. Piron, C. (1976). Foundations of Quantum Physics, Benjamin, New York.Google Scholar
  27. Pulmannova`, S. (1983). Coupling of quantum logics, Int. J. Theor. Phys. 22, 837.Google Scholar
  28. Pulmannova`, S. (1985). Tensor product of quantum logics, J. Math. Phys. 26, 1.Google Scholar
  29. Randall, C. and Foulis, D. (1981). Operational statistics and tensor products, in Interpretations and Foundations of Quantum Theory, ed. H. Neumann, B.I. Wissenschaftsverslag, Bibliographisches Institut, Mannheim, p. 21.Google Scholar
  30. Sole`r M.P. (1995). Characterization of Hilbert spaces by orthomodular spaces, Comm. Algebra 23, 219-243.Google Scholar
  31. Valckenborgh, F. (n.d.). Structures for the description of compound physical systems, Int. J. Theor. Phys., submitted.Google Scholar
  32. Van der Voorde, A. (2000). A categorial approach to T1 separation and the product of state property systems, Int. J. Theor. Phys., this issue.Google Scholar
  33. Van Fraassen, B. C. (1991). Quantum Mechanics: An Empiricist View, Oxford University Press, Oxford.Google Scholar
  34. Van Steirteghem, B. (2000). T0 separation in axiomatic quantum mechanics, Int. J. Theor. Phys., this issue.Google Scholar
  35. von Neumann, J., (1932). Mathematische Grundlagen der Quantenmechanik, Springer-Verlag, Berlin.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Diederik Aerts
    • 1
  1. 1.FUND and CLEABrussels Free UniversityBrusselsBelgium

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