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Landsberg, G.S. (1976) Optics. Moscow, 759 p. (In Russian)

has been cited by the following article:

  • TITLE: A New Geometric Approach to Explain the Features of the Micro World

    AUTHORS: Pavel A. Stabnikov

    KEYWORDS: Wave-Particle Duality, Geometry Postulates, Integral Transformations, Interference

    JOURNAL NAME: Natural Science, Vol.11 No.7, July 23, 2019

    ABSTRACT: A novel geometric approach is proposed for the development of the wave-particle notions. This approach is based on a comparison of the two geometries with different sizes of an infinitesimal point. It is assumed that the smaller is object mass, the larger is the size of the infinitesimal point in comparison with the point of the geometry of macro world. Within this approach, the smaller is object mass, the larger is the uncertainty of its position from the viewpoint of macro objects (macro geometry). This approach provides a natural ex-planation of Heisenberg’s indeterminancy principle. Formally, this approach appears as an unusual operation with an infinitesimal value (point). However, it should be noted that unusual operations (though with infinitely large values) are already known in physics. These are unattainability of the absolute zero of temperature and unattainability of the maximal velocity of movement. Interconnection of the two geometries with different sizes of infinitesimal values is possible with the help of the direct and inverse Weierstrass transformation. At present, diffraction effects are described using the wave notions about the light and Fourier transform. The diffraction of light is usually registered at a distance not less than 1 - 3 metres between the screens in one of which there is a slit or several slits. This distance is about 106 times longer than the wavelength of the radiation. In the present work, an approach is proposed that allows one to describe the light fluxes at short distances between the screens with the help of Fourier and Weierstrass transforms.