Abstract
The double slit experiment for a massive scalar particle is described using intuitionistic logic with quantum real numbers as the numerical values of the particle’s position and momentum. The model assigns physical reality to single quantum particles. Its truth values are given open subsets of state space interpreted as the ontological conditions of a particle. Each condition determines quantum real number values for all the particle’s attributes. Questions, unanswerable in the standard theories, concerning the behaviour of single particles in the experiment are answered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adelman, M., and J.V. Corbett, ‘Quantum Mechanics as an Intuitionistic form of Classical Mechanics’, Proceedings of the Centre Mathematics and its Applications, ANU, Canberra 2001, pp. 15–29.
Bozic, M., D. Arsenovic, and L. Vuskovic, ‘On the (non)existence of quantum particle’s trajectories behind an interferometric grating’, Concepts of Physics, Vol. II, No. 3-4, 2005.
Corbett, J.V., and T. Durt, ‘Quantum Mechanics interpreted in Quantum Real Numbers’, quant-ph/0211180, 1–26, 2002.
Corbett J.V., Durt T.: ‘Collimation processes in quantum mechanics interpreted in quantum real numbers’. Studies in History and Philosophy of Modern Physics 40, 68–83 (2009)
Corbett, J.V., and T. Durt, ‘Quantum Mechanics as a Space-Time Theory’, quantph/ 051220, 1–27, 2005.
Corbett J.V.: ‘The Pauli Problem, state reconstruction and quantum real numbers’. Reports on Mathematical Physics 57, 53–68 (2006)
Corbett, J.V., The mathematical structure of quantum-real numbers, preprint, arXiv:math-ph/0905.0944 v1, 7 May 2009.
Cushing J.T.: Foundational Problems in and Methodological Lessons from Quantum Field Theory. In: Brown, H.R., Harré, R. (eds) Philosophical Foundations of Quantum Field Theory, pp. 29. Oxford University Press, Oxford (1990)
Feynman, R. P., R.B. Leighton, and M. Sands, Feynman Lectures on Physics, vol. 3, Addison-Wesley, Reading, MA, 1964, chap. 9.1.
Home, D., Conceptual Foundations of Quantum Physics, Chapter 2.3, Plenum Press, New York and London, 1997, pp. 78–83.
Johnstone P.T.: Topos Theory. Academic Press, New York (1977)
Leggett, A. J., in J. de Boer, E. Dal and O. Ulfbeck (eds.), The Lesson of Quantum Theory, Elsevier Science Publishers B.V., Amsterdam, 1986 pp. 35–57.
MacLane S., Moerdijk I.: Sheaves in Geometry and Logic. Springer–Verlag, New York (1994)
Merli P.G., Missiroli G.F., Pozzi G.: ‘On the statistical aspect of electron interference phenomena’. American Journal of Physics 44, 306–7 (1976)
Editorial, ‘The double-slit experiment’, Physics World, September 2002, extended article May 2003 on physicsweb.
Reed W., Simon B.: Methods of Mathematical Physics I: Functional Analysis. Academic Press, NewYork (1972)
Schmudgen, K., Unbounded Operator Algebras and Representation Theory Operator Theory: Vol. 37, Birkhauser Verlag, 1990.
Stout, L.N., Cahiers Top. et Geom. Diff. XVII, 295, 1976; C. Mulvey, ‘Intuitionistic Algebra and Representation of Rings’ in Memoirs of the AMS 148, 1974; W. Lawvere, ‘Quantifiers as Sheaves’, Actes Congres Intern. Math. 1, 1970.
Swan, R.G., The Theory of Sheaves, University of Chicago Press, Chicago and London, 1964, §3.2, pp. 29–31.
Tonomura A., Endo J., Matsuda T., Kawasaki T., Ezawa H.: ‘Demonstration of single-electron build-up of an interference pattern’. American Journal of Physics 57, 117–120 (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Corbett, J.V., Durt, T. An Intuitionistic Model of Single Electron Interference. Stud Logica 95, 81–100 (2010). https://doi.org/10.1007/s11225-010-9246-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-010-9246-6