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

Boris Khots; Dmitriy Khots

doi:10.1117/12.891344

28 September 2011 Two-slit interference and wave-particle duality for single photons from Observer's Mathematics point of view

Boris Khots, Dmitriy Khots

Author Affiliations +

Proceedings Volume 8121, The Nature of Light: What are Photons? IV; 81211H (2011) https://doi.org/10.1117/12.891344
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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 www.mathrelativity.com). 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.

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Boris Khots and Dmitriy Khots "Two-slit interference and wave-particle duality for single photons from Observer's Mathematics point of view", Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 81211H (28 September 2011); https://doi.org/10.1117/12.891344

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KEYWORDS

Mathematics

Particles

Single photon

Mathematical modeling

Chemical species

Instrument modeling

Logic

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