Abstract
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).
Highlights
The authors of the books describing the foundations of quantum mechanics usually try to avoid the difficulties and to make no mention of the unsolved problems of this area of science
Book [1] allowed a new insight into the problems of quantum physics and pave the way for a new alternative to the particle-wave dualism, which may be formulated as the geometric interpretation of micro-world on the basis of differences in the metric of infinitesimal [5,6,7,8]
Theoretical considerations substantiating the application of Weierstrass and Fourier transforms to the description of light interference will be presented below
Summary
The authors of the books describing the foundations of quantum mechanics usually try to avoid the difficulties and to make no mention of the unsolved problems of this area of science. Born made the idea more exact by stating that the squared wave function describes the density of the probability to detect a particle in a given place The latter assumption is generally accepted at present. The author has always been interested in the philosophical problems of science, its history and development [2,3,4] In this connection, book [1] allowed a new insight into the problems of quantum physics and pave the way for a new alternative to the particle-wave dualism, which may be formulated as the geometric interpretation of micro-world on the basis of differences in the metric of infinitesimal [5,6,7,8]. Some of them may be used to describe the phenomena of microworld [9, 10]
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