Abstract
In the years 1925–1926 the development of quantum physics itself experienced a “quantum jump”: Under the influential works of Heisenberg, Schrödinger, Born, Jordan and Dirac [1–6] physicists abandoned the so-called “older quantum theory”, which was merely an amalgamate of ideas and models taken from classical physics with the addition of ad hoc “quantum conditions”, and developed quantum mechanics as an internally consistent, although mathematically highly sophisticated theory which, at least in its non-relativistic part, persists without drastic changes to the present. However, some implications of the new theory were so bizarre that there were scientists who claimed that quantum theory could not be comprehended on the grounds of classical two-valued logic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Even in Poland: When in 1991 in the Polish National Library in Warsaw I had in my hands a copy of Zawirski’s paper [9] it turned out that the pages of a booklet were still not cut apart, i.e. most probably no one had read this copy during the whole 60 years! A tribute should be paid to Max Jammer, who mentions Zawirski’s papers in his famous book [11] on the philosophy of quantum mechanics. The interested reader will find in Chap. 8 of this book a more detailed historical survey of the applications of many-valued logics in the foundations of quantum mechanics up to the early seventies of the XX century.
References
Heisenberg, W. “Über quantentheotetische Umdeutung kinematischer und mechanischer Beziehungen”, Zeitschrift für Physik. 33 879–893.
Schrödinger, E. “Quantisierung als Eigenwertproblem”, Annalen der Physik, 79 (1926) 361–376; 499–507; 80 (1926) 437–490; 81 (1926) 109–139.
Born, M., and P. Jordan, “Zur Quantenmechanik”, Zeitschrift für Physik, 34 (1925) 858–888.
Born, M., W. Heisenberg, and P. Jordan, “Zur Quantenmechanik II”, Zeitschrift für Physik, 35 (1926) 557–615.
Born, M. “Zur Quantenmechanik der Stossvorgänge”, Zeitschrift für Physik, 37 (1926) 863–867.
Dirac, P. A. M. “The fundamental equations of quantum mechanics”, Proc. Royal Society of London (A), 109 (1925) 642–653.
Zawirski, Z. “Jan Łukasiewicz 3-valued logic. On the logic of L. E. J. Brouwer. Attempts at applications of many-valued logic to contemporary natural science”, Sprawozdania Poznańskiego Towarzystwa Przyjaciół Nauk, 2–4 (1931) 1–8 (in Polish).
Zawirski, Z. “Les logiques nouvelles et le champ de leur application”, Revue de Métaphisique et de Morale, 39 (1932) 503–519.
Zawirski, Z. “Relationship between many-valued logic and the calculus of probability”, Prace Komisji Filozoficznej Poznańskiego Towarzystwa Przyjaciół Nauk, 4 (1934) 155–240 (in Polish).
Zwicky, F. “On a new type of reasoning and some of its possible consequences”, Physical Review, 43 (1933) 1031–1033.
Jammer, M. The Philosophy of Quantum Mechanics (Wiley-Interscience, New York, 1974).
Février, P. “Les relations d’incertitude de Heisenberg et la logique”, Comptes rendus Acad. Sci. Paris, 204 (1937) 481–483.
Destouches-Février, P. “Logiques et theories physiques”, Congrès International de Philosophie des Sciences, Paris 1949 (Herman, Paris, 1951) pp. 45–54.
Reichenbach, H. Philosophic Foundations of Quantum Mechanics (University of California Press, Berkeley, 1944).
Reichenbach, H. “The principle of anomaly in quantum mechanics”, Dialectica, 2 (1948) 337–350.
Reichenbach, H. “Über die erkenntnistheoretische Problemlage und den Gebrauch einer dreiwertigen Logik in der Quantenmechanik”, Zeitschrift für Naturforschung, 6a (1951) 569–575.
Reichenbach, H. “Les fondements logiques de la mécanique des quanta”, Annales de l’Institut Henri Poincaré, 13 (1952–1953) 109–158.
Feynman, R. P., R. B. Leighton, and M. Sands, The Feynmann Lectures on Physics (Addison-Wesley, Reading, MA, 1965) Vol III, p. 1–1.
Putnam, H. “Three-valued logic”, Philosophical Studies, 8 (1957) 73–80.
von Weizsäcker, C. F. “Die Quantentheorie der einfachen Alternative”, Zeitschrift für Naturforschung, 13a (1958) 245–253.
Pavičić, M. “Bibliography on quantum logics and related structures”, International Journal of Theoretical Physics, 31 (1992) 373–461.
Birkhoff, G. and J. von Neumann, “The logic of quantum mechanics”, Annals of Mathematics, 37 (1936) 823–843.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 The Author(s)
About this chapter
Cite this chapter
Pykacz, J. (2015). Many-Valued Logics in Quantum Mechanics. In: Quantum Physics, Fuzzy Sets and Logic. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-19384-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-19384-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19383-0
Online ISBN: 978-3-319-19384-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)