No 4 (2021)

The philosophical and historical review of the emergence of new metaphysical and worldview provisions is made. New approaches to solving urgent problems in modern science could appear on this basis. The main provisions of as an example of a new approach and using the original mathematical apparatus are given. Methods can be fruitful in obtaining new results in modern physics are described. Some suggestions about the presence of a sunset high “collective organization” that can systematize the behavior of systems regardless of their nature origin (physical, chemical, biological, social, economic, etc.) are made.

The development of the logical and mathematical foundations of quantum physics and, first of all, quantum mechanics is the work of a large team of physicists, mathematicians and philosophers who have contributed to the solution of this problem. The title of the article lists the names of four scientists who, according to the author, paved the way for the creation of quantum logic. This must be understood in such a way that from the very beginning (Heisenberg and Schrödinger) it was established that the properties of quantum objects are described not by numbers, but by operators. In the relationships of the operators themselves, one could see an analogue of Boolean algebra of classical logic. Weizsäcker raised the question of how the physical quantity of time, in describing the motion states of quantum objects, can be represented: an operator or a state vector? The author of the article shows that the development of quantum mechanics has gone through two stages. The first stage differs in that complex numbers and functions were introduced into physics, in other words, elements of the theory of functions of a complex variable. At the second stage, spinor calculus penetrated into quantum physics. If at the first stage methods were presented for describing the external degrees of freedom (motion) of elementary particles and other quantum objects, then the second stage was marked by the description of internal degrees of elementary particles. It became possible to understand that the measured mass of an electron or any other fermion is an averaged quantity, it consists of two ingredients: a positive mass and a negative mass (two values of the corresponding operator). An important role in this discovery played the operation of dialectical negation (privation), borrowed from Heidegger's fundamental ontology.

The paper discusses possible experimental consequences of the assumption that physical realization of the Mach’s principle can be associated with some oscillatory process between gravitating masses. It is noted that in the case expected phenomenological picture turns out to be close to that obtained in the course of studies of the Earth microseismic noise spectra by V.A. Dubrovsky in 1987-1993. The article describes Dubrovsky’s experiments as well as a brief history of the laboratory in which they were performed. Possible directions for further experimental research are considered.

The following brief review considers the history of discovery and main stages of investigations of the macroscopic fluctuations phenomenon, which were the work of life of Simon E. Shnoll. The works considered in this article are the first in world literature to study the universal laws revealed in the course of studying the properties of fluctuations in processes of various nature. Brief descriptions of the main experiments and the results obtained are given.

The article summarizes ideas of A.M. Molchanov about cooperative property of the Solar system - its “maximum synchronicity”. The general scientific significance of the principle of “maximum synchronicity” is discussed on an interdisciplinary basis. It is noted that the considered theoretical ideas have received numerous observational confirmations. In recent decades, it has been shown that: solar activity are involved in general dynamic of solar system; special resonance periods were found in the dynamics of the solar system; found correlations of variations in the total magnetic field of the Sun and the dynamics of planets; the important role of synchronization in the formation of the fine structure of Saturn's rings is shown. Synchronicity is found in many phenomena in the habitat of our planet.

The article discusses the relationship between the periods of oscillation of physical systems with the problem of distribution of rational numbers on the number axis. The representation of numbers by continued fractions is also considered. Particular attention is paid to the physical consequences of the ratios of the periods of oscillations, such as the connection of the “golden section” with the law of distribution of planetary distances, the connection of the laws of information transmission processes with the sensitivity of the human eye realized in nature.

This short article is dedicated to the 200th anniversary of the outstanding Russian mathematician - P.L. Chebyshev. P.L. Chebyshev was born in May 1821 in the village of Okatovo, Borovsk district. P.L. Chebyshev is one of the founders of the St. Petersburg or, as it is called, the Chebyshev mathematical school. The mathematician made a significant contribution to the development of number theory, probability theory, mathematical analysis and is one of the founders of the constructive theory of function. This paper discusses some of the results of P.L. Chebyshev related to the problem of the distribution of prime numbers. As you know, this problem is closely related to the currently most famous mathematical problem - the Riemann hypothesis.