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International Journal of Theoretical Physics

, Volume 31, Issue 10, pp 1873–1898 | Cite as

Physical content of preparation-question structures and Brouwer-Zadeh lattices

  • Gianpiero Cattaneo
  • Giuseppe Nisticó
Article

Abstract

We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given.

Keywords

Field Theory Elementary Particle Quantum Field Theory Algebraic Structure Property Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aerts, D. (1981a). The one and the many. Towards a unification of the quantum and the classical description of one and many physical entities, Doctoral thesis, Vrije Universiteit Brussel, TENA.Google Scholar
  2. Aerts, D. (1981b). Description of compound physical systems and logical interaction of physical systems, inCurrent Issues in Quantum Logic, E. G. Beltrametti and B. C. van Fraassen, eds., Plenum Press, New York.Google Scholar
  3. Aerts, D. (1982). Description of many and separated physical entities without the paradoxes encountered in quantum mechanics,Foundations of Physics,12, 1131.Google Scholar
  4. Aerts, D., and Daubechies, I. (1978a). About the structure-preserving maps of a quantum mechanical propositional system,Helvetica Physica Acta,51, 637.Google Scholar
  5. Aerts, D., and Daubechies, I. (1978b). Physical justification for using the tensor product to describe two quantum systems as one joint system,Helvetica Physica Acta,51, 661.Google Scholar
  6. Aerts, D., and Daubechies, I. (1979). A characterization of subsystems in physics,Letters on Mathematical Physics,3, 11.Google Scholar
  7. Cattaneo, G., and Nisticò, G. (1989a). Brouwer-Zadeh posets and three-valued Lukasiewicz posets,Fuzzy Sets and Systems,33, 165.Google Scholar
  8. Cattaneo, G., and Nisticò, G. (1989b). Coexistence of questions in Jauch-Piron theory, Preprint DMUC 1989, Dipartimento di Scienze dell'Informazione, Università di Milano, Milan, Italy.Google Scholar
  9. Cattaneo, G., and Nisticò, G. (1990). A note on Aerts' description of separated entities,Foundations of Physics,20, 119.Google Scholar
  10. Cattaneo, C., dalla Pozza, C., Garola, C., and Nisticò, G. (1988). On the logical foundation of the Jauch-Piron approach to quantum physics,International Journal of Theoretical Physics,27, 1313.Google Scholar
  11. Jauch, J. A. (1983).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.Google Scholar
  12. Jauch, J. M., and Piron, C. (1969). On the structure of quantal propositions systems,Helvetica Physica Acta,42, 842.Google Scholar
  13. Nash, C. G., and Joshi, G. C. (1987a). Composite systems in quaternionic quantum mechanics,Journal of Mathematical Physics,28, 2883.Google Scholar
  14. Nash, C. G., and Joshi, G. C. (1987b). Component states of a composite quaternionic system,Journal of Mathematical Physics,28, 2886.Google Scholar
  15. Piron, C. (1976).Foundations of Quantum Physics, Benjamin, Reading, Massachusetts.Google Scholar
  16. Pulmannová, S. (1985). Tensor product of quantum logics,Journal of Mathematical Physics,26, 1.Google Scholar
  17. Raggio, G. A. (1981). States and composite systems inW *-algebraic quantum mechanics, ETH Zurich, preprint No. 6824.Google Scholar
  18. Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Gianpiero Cattaneo
    • 1
  • Giuseppe Nisticó
    • 2
  1. 1.Dipartimento di Scienze dell'InformazioneUniversità di MilanoMilanItaly
  2. 2.Dipartimento di MatematicaUniversità della CalabriaRendeItaly

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