Abstract
Three times in my scientific life I fell in love. For the first time, in the middle of the Seventies of the XX Century the object of my love was (and still is, since real love never ends) the theory of quantum logics. Quantum logics are mathematical structures that are encountered in the very foundations of quantum mechanics. Formally, they are order-theoretic structures more general than Boolean algebras: orthomodular partially ordered sets or lattices, that are believed to represent properties of quantum objects in the same way as Boolean algebras represent properties of objects that conform to laws of classical physics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Mączyński, M.J.: The Orthogonality Postulate in Quantum Mechanics. International Journal of Theoretical Physics 8, 353–360 (1973)
Giles, R.: Łukasiewicz Logic and Fuzzy Set Theory. International Journal of Man-Machine Studies 67, 313–327 (1976)
Pykacz, J.: Quantum Logics as Families of Fuzzy Subsets of the Set of Physical States. Preprints of the Second IFSA Congress, Tokyo, July 20-25, vol. 2, pp. 437–440 (1987)
Pykacz, J.: Fuzzy Quantum Logics and Infinite-valued Łukasiewicz Logic. International Journal of Theoretical Physics 33, 1403–1416 (1994)
Peres, A.: Unperformed Experiments Have no Results. American Journal of Physics 46, 745–747 (1978)
Bell, J.S.: On the Einstein Podolsky Rosen Paradox. Physics 1, 195–200 (1964)
Pykacz, J., D’Hooghe, B.: Bell-type Inequalities in Fuzzy Probability Calculus. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9, 263–275 (2001)
Wigner, E.: On the Quantum Correction for Thermodynamic Equilibrium. Physical Review E 40, 749–759 (1932)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pykacz, J. (2013). Fuzzy Sets in Foundations of Quantum Mechanics. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-35644-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35643-8
Online ISBN: 978-3-642-35644-5
eBook Packages: EngineeringEngineering (R0)