Download Quantum Physics, Fuzzy Sets and Logic: Steps Towards a by Jaroslaw Pykacz PDF
By Jaroslaw Pykacz
This short provides steps in the direction of elaborating a brand new interpretation of quantum mechanics in keeping with a selected model of Łukasiewicz infinite-valued good judgment. It starts with a brief survey of major interpretations of quantum mechanics already proposed, in addition to quite a few versions of many-valued logics and former makes an attempt to use them for the outline of quantum phenomena. the possible many-valued interpretation of quantum mechanics is soundly in line with a theorem in regards to the isomorphic illustration of Birkhoff-von Neumann quantum common sense within the kind of a distinct Łukasiewicz infinite-valued common sense endowed with in part outlined conjunctions and disjunctions.
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2. Schrödinger, E. “Quantisierung als Eigenwertproblem”, Annalen der Physik, 79 (1926) 361– 376; 499–507; 80 (1926) 437–490; 81 (1926) 109–139. 3. , and P. Jordan, “Zur Quantenmechanik”, Zeitschrift für Physik, 34 (1925) 858–888. 4. , W. Heisenberg, and P. Jordan, “Zur Quantenmechanik II”, Zeitschrift für Physik, 35 (1926) 557–615. 5. Born, M. “Zur Quantenmechanik der Stossvorgänge”, Zeitschrift für Physik, 37 (1926) 863– 867. 6. Dirac, P. A. M. “The fundamental equations of quantum mechanics”, Proc.
However, after von Weizsäcker’s work the interest of researchers definitely shifted from three-valued or many-valued logics to the non-distributive but two-valued logic of the type proposed by Birkhoff and von Neumann as early as 1936 [22]. In the author’s opinion the attempts to found quantum mechanics on any version of three-valued logics were bound to fail also because three-valued logics are not “rich enough in truth values” and, therefore, are not “flexible” enough. One should not expect to be able to describe by these means the whole variety of quantum phenomena, especially when truth values are supposed to be connected with the numerical results of experiments, if there is only one truth value (besides the classical 0 and 1) available.
G. and G. Cassinelli, The Logic of Quantum Mechanics (Addison-Wesley, Reading, 1981). 5. Pták, P. and S. Pulmannová, Orthomodular Structures as Quantum Logics (Kluwer Academic Publishers, Dordrecht, 1991). 6. M¸aczy´nski, M. J. “The orthogonality postulate in axiomatic quantum mechanics”, International Journal of Theoretical Physics, 8 (1973) 353–360. 7. M¸aczy´nski, M. J. “Functional properties of quantum logics”, International Journal of Theoretical Physics, 11 (1974) 149–156. 8. Pykacz, J. “Quantum logics as families of fuzzy subsets of the set of physical states”, Preprints of the Second International Fuzzy Systems Association Congress, Tokyo, July 20–25, 1987, vol 2, 437–440.