Discussion of the Book “The Quantum Challenge”

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).