No 4 (2022)

In quantum theory, there are both point and integral objects. In this case, the computational technique is based exclusively on set-theoretic structures associated with the point model of the continuum. The transition to integral dynamic structures makes it possible to develop new methods that allow us to obtain useful results, in particular, to derive the formula for the spectrum of a certain class of particles: m = me ( l + k /2 m )( ĺ + s /2 t ). This formula is a generalization of the formula obtained by V.V. Varlamov in 2017. In general, such an approach is consonant with the concept of the so-called. “non-standard analysis”, in which “number-monads” play a key role.

The article contributes to the development of an a priori methodology adequate to the legitimate claims of fundamental physics as a mathematical philosophy of nature. Husserl’s phenomenological method of variations - the most important part of this methodology - is seen as a means of bringing to clarity and achieving apodictic evidence, highly relevant in the current conditions of erosion of the empirical criterion of truth, when the invention of hypotheses for the needs of deductive theorization has become the norm of so-called fundamental research. As an example for express testing of the method, a problematic principle is taken that needs to be clarified: the “Mach principle” formulated in many ways since the time of A. Einstein. The result of a clarifying reflection of one of the transitions between versions of the principle is the conclusion that the conceptual development of the general theory of relativity on methodologically clarified grounds, one of which would be a correctly formulated Mach principle, should proceed from a relational understanding of space-time consistent with this principle. Mach’s principle, since it determines the structure of the equations of the theory themselves, the solutions of which are conceived in the modus of the possible, is in no way affected in its truth value by the fact of the existence of vacuum solutions of these equations. In conclusion, the article examines the question of the influence of the Mach theory of thought experiment on the genesis of the phenomenological method of variations.

A new type of optical imaging is described, which has undoubted advantages in certain applications in comparison with traditional optical methods. The use of nonlinear optical quantum processes makes it possible to obtain entangled photon pairs rigidly correlated in space and time in the course of spontaneous parametric three-photon scattering and counter-propagating four-photon mixing. This correlation can be used to construct ghost images. A fiber-optic version of the formation of phantom images is also described, which is suitable for the study of hard-to-reach cavities and organs of the human body, which allow the introduction of a thin fiber-optic bundle.

The structure of artificial intelligence as a multilevel symmetry is built by association with natural intelligence, being its digitized analogue. The principle of reduction of multivalent truth values is formulated. A metaphysical clock with two hands describing two levels of genesis, which consists of orthogonal phases of the rhythm of becoming, is constructed. There is an easy way to directly comprehend the truth. These are two level coordinates based on a Cartesian square.

Abstracts of the report “Relational Foundations of Nonsingular Cosmology”, presented at the conference “Foundations of Fundamental Physics and Mathematics” (OFFM-2020) (ed. by Yu. S. Vladimirov, V. A. Panchelyuga. Moscow: PFUR, 2020), are being developed. The universality of the application of the relational paradigm for various areas of fundamental physics and the fallacy of considering singularities as models of real phenomena are emphasized. The role of singularities is pointed out only as a means of covering up the mysterious properties of the universe.

This article by M. Sinclair is devoted to the problem of modality in the philosophical works of M. Heidegger his study of being-possible as one of the modes of being. The author analyzes in detail the evolution of the concept of “possibility”, starting from the 1920s and ending with the later works of Heidegger, as this philosophical category undergoes certain changes. The author also analyzes the role played by Aristotle’s ontological philosophy and Husserl’s phenomenology in the formation of Heidegger as a thinker. Finally, the article presents the interpretations of the Heidegger category of possibility by modern researchers such as I. Thomson, W. McNeil, J. Wolfe and many others. It is concluded that the category of the possible was key for Heidegger in his construction of the structure of being, and the disclosure of various aspects of this category occurred throughout the entire philosophical path of M. Heidegger.