The new physics concepts of the material world structure - quantum theory and theory of relativity - are compared with the concepts of the theory of nonlinear oscillations operating in classical and Newton’s methods.
On a number of physical problems, a comparison is made of the effectiveness of the methods of cognition of quantum theory and the classical methods of Newton. The well-known statements of physicists about their excellent knowledge of classical methods turned out to be untrue. The theory of nonlinear oscillations, operating with Newton's classical methods, has shown how to solve physical problems that do not lend themselves to the methods of new physics - quantum theory and the theory of relativity.
Due to the idea of atomism, there were discovered atoms, nucleons, and electrons. The atomic theory incorporated seeds of the idea of infinite divisibility of matter aimed at perceiving the structure of the entire material world. The next step in that perceiving should have been the recognition of ether discovered in Fizeau’s experiment. However, physicists did not recognize the discovery. The neglect of ether in physical theories resulted in physicists’ failure to use the methods of “classic”, Newtonian physics to gain a detailed understanding of atomic structure, and to build a “classic” microworld theory. As consequence, there emerged the quantum hypothesis that became a basis for the quantum physics of microworld. As the quantum hypothesis appeared to be in irreconcilable contradiction with the idea of infinite divisibility of matter, because of the neglect of ether, the quantum physics failed to understand the real structure of electrons and nucleons, even though all the necessary and ample experimental facts there had been obtained on microobject accelerators. Instead of objective ideas of the structure of electrons and nucleons or further development of knowledge regarding the structure of matter, there appeared fake concepts of quarks, myons, pions, bosons, etc., that do not exist in the real material world Experimental evidence as to the lack of indivisible quanta in nature [1] seemed to have fixed the intolerable situation but quantum physicists did not “notice” that.
Failures in solving a number of physical problems associated with the structure of the microworld began due to two fundamental mistakes made in the old classical physics, when interpreting the results of the experiments of Oersted (1821) and Fizeau (1851). Because of them, it was not possible to develop a detailed understanding of the true structure of the atom; this was due to the inability of physicists to eliminate the indicated fundamental errors. Blaming the “classical” Newtonian methods for this failure, physicists proceeded to build a “new” physics - quantum theory and theories of relativity. Without realizing this, they brought into the new physics old fundamental errors that entered the paradigms of the new physics and made them inadequate. This is illustrated with specific examples.
The subject of my talk is the relations between the mathematical theory of extremal problems and the physical theory of quanta.1 The theory of quanta, or quantum mechanics, studies phenomena in the world of bodies of atomic scale. It turned out that the usual notions of motion and the usual methods of description of a mechanical system were inapplicable for such bodies. One needed to find another formulation of the basic laws of nature instead of the old one based on observations of bodies containing a very large number of atoms. The drastic revision of all usual notions of mathematics and physics was required. As a result of this revision and due to the efforts of several scientists such formulation has been found and the theory, which is as elegant and complete as the Newton mechanics is, has been created. This new theory — the new quantum mechanics — contains the Newton mechanics as a limiting case. Although some particular questions and problems remain open, the basic principles and the mathematical technique of the new theory can be considered to be completely established.
This introductory chapter outlines the differences between classical physics and quantum physics by positing three imaginary worlds. World 1 is governed by the laws of classical Newtonian mechanics, World 2 by classical field physics, and World 3 by quantum physics. The point is that classical physics deals with well-defined, continuously-existing physical quantities, including trajectories, while quantum physics is fundamentally about physical quantities defined in terms of probability functions.
The purpose of the article is to show that quantum mechanics is a synthesis of the old classical concepts and the new non-classical concepts (physics and mathematics). To illustrate the relationship of continuity between classical physics and quantum mechanics, the materials of Planck, Broglie, Schrodinger, Bohr and Dirac are considered. The author begins with a comparative study of the fundamental principles of classical and quantum physics, and concludes that, despite their opposition and irreducibility, scientists tried to adopt the principles of classical physics for constructing quantum mechanics. Survey of Planck's papers showed that Planck's formula for the blackbody spectrum containing the quantum of action is obtained as a synthesis of classical concepts and quantum concepts. Survey of Broglie's papers showed that the quantum-mechanical concept of Broglie emerged as a synthesis of the provisions of the classical (variation principles) and quantum physics (Planck's constant). Survey of Schrodinger's papers showed great generality of quantum theory in comparison with classical mechanics. Survey of Bohr's papers showed that Bohr was able to prove the basic concepts of quantum physics with the help of methodological principles. Survey of Dirac's papers showed that Dirac discovered the equivalence of Schrodinger's and Heisenberg's theories, showed that they go back to the same physical and algebraic principles, and that they can be formulated as variants of the quantum-mechanical system. The author considers the methodological features of quantum mechanics and fixes a number of methodological principles by which quantum mechanics is significantly different from classical physics. The category of quantum mechanics, on which an attempt to reconstruct the physical picture of the world based on quantum theory, is briefly discussed. On the basis of this reconstruction, there are the world picture broad categories: mass-field and space-time. The categories are related by the formula: wave-like particle moves in the classical space-time background. The first association the particles and interactions is from quantum mechanics, the second space and time from the special theory of relativity. In conclusion, a list of basic relations of quantum mechanics with classical physics is made. The development of quantum ideas resulted from direct influence of classical physics, so the main heuristic techniques to construct quantum theory are two ideas, namely, the idea of continuity and the idea of conformity which Bohr's methodological principles express. At the same time, quantum theory requires the use of classical concepts for support and verification. This is due to the restrictions imposed by the experimental technique. Thus, the author claims that quantum mechanics is a synthesis of the old classical concepts and the new non-classical concepts (physics and mathematics).