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.