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.
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 explanation 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 10 6 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.
Known models of the Universe development are discussed in the present work. At present it is not possible to state what model is true among the suggested ones because all models are based on the assumptions a validity of which is scarcely determined. There are plenty of reasons, and the most important ones are impossibility of experiments performance on a global scale, very short time of nature study and low accuracy of determination of fundamental phy- sical constants to check their possible drift. In the most of models the intellect is an unnecessary attribute. Mankind is only an inner insignificant observer in the Universe. Small changes which Humanity can produce on the Earth don’t modify our planet on a global scale. However besides changes in the material world Mankind can create intellectual valuables. Large information content can be stored, integrate and process using computers. We have no any principle restrictions in advance of the com- puter engineering. Therefore we propose a new model of the Universe development which is based on the increasing facilities of our Mankind. In this model the Earth is considered as an analogue of supercomputer. Under certain circumstances Mankind is ready to carry out information processing for other civilizations, but such civilizations have not yet been found. The Creators of the Universe could be other customers. Computer-like model of the Universe suggests a communication with the Creators in future for execution of their calculation orders. However this model is not complete because of lack of high rate of information transfer for long distances
Modern but not entirely coordinated foundations of quantum physics are described in the book "The Quantum Challenge". The difficulties and philosophical problems of this area of science are discussed. Discussions of many great scientists who paved the foundations of the physics of micro-world are described. These discussions are still urgent. The diversity of interpretations of the wave function, light interference, uncertainty principle, complementarity and completeness of micro-world description are stressed in this book. Difficulties and problems of quantum mechanics described in this book allowed the author of the present communication to propose a new approach based on the infinitely small metrics The difference of infinitesimals in two geometries allows one to explain W. Heisenberg's uncertainty principle. Interconnection of the images in these geometries is possible with the help of Weierstrass integral transform. This approach allows one to describe the interference of light behind the screen with slits as a sum of the corpuscular component (Weierstrass transform) and the wave component (Fourier transform).Open Access
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