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Natural Science

A New Geometric Approach to Explain the Features of the Micro World

Pavel A. Stabnikov

Published Jan 1, 2019• 2 citations
Publisher

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.

DOI
10.4236/ns.2019.117024

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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.
The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitations. A geometric approach is proposed as an alternative to the wave-particle duality to explain the anomalous motion of micro objects. The basis of the geometric approach is a comparison between two geometries differing from each other in the metric of infinitesimal. The interconnection of these geometries is possible through the direct and inverse Weierstrass transformation. The application of this transformation allows one to explain diffraction effects.
General relativity is logically unsatisfactory because it bases measurement on infinitesimals, and absolute infinitesimals do not exist. A standard of comparison being a logical necessity, we propose to provide it by the new fundamental hypothesis; "The physical world is composed of elementary events of identical and definite non-zero four-dimensional extent." The photon is a possibility of absorption-event initiated by an emission event; it is exhibited as a set of superposed moving volumes or three-dimensional sections of the four-dimensional possibility. The electron is a possibility transmitted with smaller velocities. Mass or energy is proportional to the time-duration of the event-possibilities, and obeys thence, the relativity rules. A wave function is postulated for the possibility being realized, and from Doppler's principle the quantum rule necessarily follows: mass proportional to frequency, and groupvelocity equal to particle velocity. The "particle" exists only when the transmission is parallel the time-edge of the possibility; in atomic orbits presumably the condition does not apply, and the parallel-displacement tracks of relativity which are shown to to be required outside, do not apply within the atom. The finite extent of the events which exhibit the particle necessitates an indeterminacy in the situation of the particle.
Diffraction and interference fringes are stable and reproducible objective phenomena in optical experiments. Mainstream quantum mechanics puts forward the ontological interpretation of wave particle duality. It holds that the material ontology of micro particles such as photons inherently possesses both particle and wave properties, and attributes diffraction and interference phenomena directly to the intrinsic matter wave behavior of particles. This interpretation stays at the level of observational appearance and avoids underlying ontological dynamic mechanisms. It represents a research approach that deduces the intrinsic properties of material ontology merely from external observations. Within the framework of the light ontology theory, a photon is an energy state object. Energy and motion at the speed of light form an inseparable whole and are permanently bound together and cannot be separated. In the real universe, no photon with energy that does not travel at the speed of light has ever been observed. Nor has any object moving at the speed of light without energy been detected. The two cannot exist independently from one another. A photon has no physical volume but possesses inherent fixed transverse trembling property. At the moment a photon is generated, it acquires a definite trembling angle within a 360 degree spatial plane perpendicular to its propagation direction. This transverse trembling orientation remains unchanged without physical collision interaction. When the transverse trembling of a photon can reach the slit wall, absorption and reradiation secondary scattering will occur. Massive secondary photons superpose statistically to form bright and dark diffraction and interference fringes. Slit walls are stacked by large numbers of atoms. Their spatial scale is hundreds of thousands to tens of millions times larger than the scale of photon transverse trembling. For photons, slit walls constitute huge physical barriers and can produce significant interactions with trembling photons. The wave function is only a mathematical tool for fitting experimental data. Good fitting performance of a mathematical model does not mean its corresponding physical interpretation equals objective physical reality. This paper proposes a new set of comparative decisionmaking experiments. The key innovation is to place a linear polarizer in front of the slit. Before photons contact the slit, the transverse trembling orientation of photons is pre screened. The transverse trembling direction of transmitted photons is made parallel to the orientation of vertical slit walls to suppress oscillation components perpendicular to slit walls and make it difficult for photons to hit slit walls. Polarizers with different grating line widths can be replaced to observe the influence of the grating scale of polarizers on experimental results. According to the physical mechanism of slit wall scattering, characteristic diffraction and interference fringes will be greatly attenuated and only the central direct light spot will remain. Non ideal device characteristics will bring a small amount of stray scattering background, but complete bright and dark diffraction and interference structures will not appear. According to the traditional ontological interpretation of wave particle duality, the geometric parameters of slits remain completely unchanged. Only polarization orientation screening is conducted and the intrinsic matter wave of particle ontology is not affected. Therefore diffraction and interference fringes should be fully preserved. The two theories produce mutually exclusive observable predictions. This experiment can test whether the ontological interpretation of wave particle duality holds true. This paper does not deny objective diffraction and interference phenomena, nor does it deny the practical value of wave function as an engineering calculation tool.
The work addresses the solution of the problems of light diffraction at one and two narrow slits in an opaque screen. The diffraction patterns were analyzed. It was established that their appearance depends on the ratio of the characteristic size of the obstacle to the wavelength of the photon. When this ratio is less than unity, we have a smoothly changing illumination with a maximum at the center of symmetry of the system. If it one is greater than unity, then the pattern has the appearance of light and dark stripes. The numerical value of the specified ratio determines the number of maxima. The obtained results allow us to assume that the reason for the well-known paradox in the interpretation of experiments on the diffraction of light at one and two narrow slits is thе next. The experiments at one slit was carried out for the case when the wavelength was greater than the width of the slit, and at two slits - for the case, when the wavelength is much smaller than the distance between slits.
With the deep research of measurement for microscopic or nanometer level scale at present the concept of Critical Dimension(CD) is pointed out in many papers[1,4,], they always include some analyses of measuring uncertainty for current technology of measurement, but our new idea or definition for geometrical action scale (GAS) is the limited scale or uncertainty of measurement in microscope that we can approach to for the most advanced method, technology, set-up or instrument, for example: The modern interferometer, SPM[5] and other various scattering experiments using the beam of microscopic particles. It would be found that the research included fundamentals for microscopic particle geometric scale is not easy to explore, some reasons perhaps are affected by which the classical quantum mechanics study of matter usually start from energy or energy level not from geometrical scale and by the Heisenberg relation of measuring uncertainty. Our work just wants to research on these fundamentals in physics for microscopic particles geometric scale. At first, a new physical quantity relative to microscopic particle geometric scale is directly suggested in this paper, it also may be deduced from the completeness of units system or dimension system refer to optics principles or quantum optics principles. We find that the wavelength of Louis de Broglie matter wave is either the length dimension or relative to the geometric scale of microscopic particles, and we define it as the geometrical action scale (GAS) of microscopic particles. The significance of the geometrical scale of microscopic particles or GAS in physics is discussed.