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Two-slit experiment: quantum and classical probabilities
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2015 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 90, no 7, 074017Article in journal (Refereed) Published
Abstract [en]

Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum-classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincare disk model for the Lobachvesky plane).

Place, publisher, year, edition, pages
2015. Vol. 90, no 7, 074017
Keyword [en]
quantum probability, intereference, classical probability
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-45790DOI: 10.1088/0031-8949/90/7/074017ISI: 000357541800018OAI: oai:DiVA.org:lnu-45790DiVA: diva2:847414
Available from: 2015-08-20 Created: 2015-08-19 Last updated: 2016-05-03Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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