Abstract
The purpose of this article is to bring out in as conceptually clear terms as possible what seems to be a major incompleteness in the probability theory of particles offered by classical quantum mechanics. The exact nature of this incompleteness is illustrated by consideration of some simple quantum-mechanical examples. In addition, these examples are contrasted with the fundamental assumptions of Brownian motion in classical physics on the one hand, and with a controversy of a decade ago in mathematical psychology. (The psychological example is described in detail in the appendix.) Our central claim is that classical quantum mechanics is radically incomplete in its probabilistic account of the motion of particles.
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
Preview
Unable to display preview. Download preview PDF.
References
Bartlett, M. S. and Moyal, J. E., `The Exact Transition Probabilities of Quantum-mechanical Oscillators Calculated by the Phase-Space Method’, Proceedings of the Cambridge Philosophical Society 45 (1949), 545–553.
Gnedenko, B. V.,The Theory of Probability (4th ed.), Chelsea, New York, 1968 (translated from the Russian).
Ito, K. and McKean, H. P., Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965.
Karlin, S., A First Course in Stochastic Processes, Academic Press, New York, 1966.
Nelson, E., Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, N.J., 1967.
Schiff, L. I., Quantum Mechanics (1st ed.), McGraw-Hill, New York, 1949.
Suppes, P. and Ginsberg, R., `A Fundamental Property of All-or-None Models, Binomial Distribution of Responses Prior to Conditioning, with Application to Concept Formation in Children’, Psychological Review 70 (1963), 139–161.
Suppes, P. and Donio, J., `Foundations of Stimulus-sampling Theory for Continuous-Time Processes’, Journal of Mathematical Psychology 4 (1967), 202–225.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Suppes, P., Zanotti, M. (1976). Stochastic Incompleteness of Quantum Mechanics. In: Suppes, P. (eds) Logic and Probability in Quantum Mechanics. Synthese Library, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9466-5_15
Download citation
DOI: https://doi.org/10.1007/978-94-010-9466-5_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-1200-4
Online ISBN: 978-94-010-9466-5
eBook Packages: Springer Book Archive