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Proceedings Paper

Two-slit interference and wave-particle duality for single photons from Observer's Mathematics point of view
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Paper Abstract

When we consider and analyze physical events with the purpose of creating corresponding mathematical models we often assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We proved the following theorems: 1) Theorem A (Two-slit interference). Let Ψ1 be a wave from slit 1, Ψ2 - from slit 2, and Ψ = Ψ1 + Ψ2. Then the probability of that Ψ is a wave equals to 0.5; and 2) Theorem B (Wave-particle duality for single photons). If v is small enough, then λ is a random variable.

Paper Details

Date Published: 28 September 2011
PDF: 6 pages
Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 81211H (28 September 2011); doi: 10.1117/12.891344
Show Author Affiliations
Boris Khots, Compressor Controls Corp. (United States)
Dmitriy Khots, Compressor Controls Corp. (United States)

Published in SPIE Proceedings Vol. 8121:
The Nature of Light: What are Photons? IV
Chandrasekhar Roychoudhuri; Andrei Yu. Khrennikov; Al F. Kracklauer, Editor(s)

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