Abstract
Usually, quantum mechanics is considered as the prototype of a probabilistic theory. In contrast to statistical mechanics, dice throwing, and roulette game, quantum mechanical probability statements cannot be reduced to causally determined individual events, whose explicit calculation is, however, too complicated for all practical purposes. Even hypothetically, one must not assume that quantum mechanical events were determined in principle and merely computationally intractable, since that assumption would lead to probabilistic predictions which contradict quantum mechanics. Hence, the title of this article seems somewhat surprising at first glance, and in particular it seems difficult to connect a probability free quantum mechanics with the work of John von Neumann.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Busch, P., P. Lahti and P. Mittelstaedt (1991), The Quantum Theory of Measurement, Springer, Heidelberg (2nd edition 1996 ).
DeWitt, B.S. (1971), “The Many-Universes Interpretation of Quantum Mechanics”, in: Foundations of Quantum Mechanics, IL Corso, B. d’Espagnat, ed., Academic Press, New York, pp. 167–218.
Everett, H. (1957), “Relative State Formulation of Quantum Mechanics”, Review of Modern Physics, 29, pp. 454–62.
Finkelstein, D. (1962), “The logic of quantum physics”, Trans. New York Acad. Sci. 25, pp. 621–37.
Gutmann, S. (1995), “Using Classical Probability to Guarantee Properties of Infinite Quantum Sequences”, quant-ph/ 9506016.
Hartle, J. B. (1968), “Quantum mechanics of individual systems”, Am. Journ. Phys. 36, pp. 704–12.
Mittelstaedt, P. (1976), Philosphical Problems of Modern Physics, D. Reidel, Dordrecht.
Mittelstaedt, P. (1978), Quantum Logic, D. Reidel, Dordrecht.
Mittelstaedt, P. (1990), “The objectification in the measuring process and the many worlds interpretation”, in: Symposium on the Foundations of Modern Physics 1990, World Scientific, Singapore, pp. 261–279.
Mittelstaedt, P. (1998), The Interpretation of Quantum Mechanics and the Measurement Process, Cambridge, University Press.
von Neumann, J. (1932), Mathematische Grundlagen der Quantenmechanik, Springer Verlag, Berlin.
Birkhoff, G. and Iv. Neumann, (1936), “The Logic of Quantum Mechanics”, Annals of Mathematics 37, pp. 823–43.
von Neumann, J. (1938), “On infinite direct products”, Compositio Mathematica 6, pp. 1–77.
Stachow, E.-W. (1984), “Structures of a Quantum Language for Individual Systems”, in: Recent Developments in Quantum Logic, eds. P. Mittelstaedt and E.-W.Stachow, BI-Wissenschaftsverlag, Mannheim.
Solèr, M.P. (1995), “Characterisation of Hilbert Spaces by Orthomodular Lattices”, Communications in Algebra, 23 (1), pp. 219–243.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Mittelstaedt, P. (2001). Quantum Mechanics Without Probabilities. In: Rédei, M., Stöltzner, M. (eds) John von Neumann and the Foundations of Quantum Physics. Vienna Circle Institute Yearbook [2000], vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2012-0_12
Download citation
DOI: https://doi.org/10.1007/978-94-017-2012-0_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5651-1
Online ISBN: 978-94-017-2012-0
eBook Packages: Springer Book Archive