Autumn semester of 1995

Topic of the semester: **RESEARCH PROGRAMS OF TIME STUDIES: FROM EINSTEIN TO PRIGOGINE.**

**R. F. POLISHCHUK.** ** “PHYSICS AND METAPHYSICS OF SPACE-TIME”. **With the development of physics, the status of physical being is changing as well. The quantum-mechanical uncertainty principle makes one assume that the dimension of quantum space-time is smaller than four. One can construct physical four-dimensional space-time from light times. The macroscopic space-time emerges as an effect of dynamical quantum space-time of smaller dimension. Using dimensionless Planckian units, it is possible to connect the space-time characteristics with topology of large numbers and to reduce the metric to discrete topology (R.F. Polishchuk, "Physics and Metaphysics of Space-Time". In: Proceedings of the International Conference "Geometrization of Physics", Kazan, 1994, p. 255-258).

**Yu. S. VLADIMIROV. “GEOMETROPHYSICS AS A PROGRAM OF BUILDING A THEORY OF SPACE-TIME AND PHYSICAL INTERACTIONS” .** The program rests on the Fokker-Feynman theory of direct interparticle interactions, Kaluza-Klein multidimensional geometric models and the physical structures theory (Yu.S. Vladimirov and A.Yu. Turygin, "Theory of Direct Interparticle Interaction", Moscow, Energoatomizdat, 1986; Yu.S. Vladimirov, "Dimension of Physical Space-Time and Unification of Interactions", Moscow University Press, 1987; Yu.S. Vladimirov, "Space-Time: Evident and Hidden Dimensions, Moscow, Nauka, 1989; Yu.I. Kulakov, Yu.S. Vladimirov and A.V. Karnaukhov, "Introduction to Physical Structures Theory and Binary Geometrophysics", Moscow, Archimedes, 1992).

**I. V. VOLOVICH. “PHYSICS ON THE PLANCK SCALE AND NON-ARCHIMEDEAN GEOMETRY”.** In modern natural science, the space-time coordinates are represented by real numbers. Such a representation corresponds to Archimedean geometry. However, on small (Planck) scale metric fluctuations take place and the space-time geometry becomes non-Archimedean. An analytic description of such a geometry is realised with the aid of p-adic numbers. In the recent years, p-adic analysis has acquired wide application in quantum string theory, in quantum gravity, in spin glass theory and in models of memory. The theory of p-adic numbers especially strongly affects the structure of time at Planck and cosmological distances. The lecture presents an introduction to the theory of p-adic numbers and its applications (V.S. Vladimirov, I.V. Volovich and E.I. Zelenov, "P-adic Analysis and Mathematical Physics", Moscow, Fizmatlit, 1994).

**A. V. KOGANOV**. ** “INDUCTOR SPACES AS A GENERALIZING MODEL OF TIME”**. The lecture presents information on the evolution of time models in modern science. The notion of an inductor space occupies a logical niche between the notions of a directed graph and that of a topological space. It enables one to build models of time for processes of different nature and to generalise the notions of an automaton and a differential equation. It has been proved that an arbitrary group of transformations can be interpreted as a group of automorphisms of a certain inductor space and therewith the group topology will be preserved. This enables one to build space-time models corresponding to processes in physics, biology and engineering (A.V. Koganov, "Inductor Spaces and Processes", Dokl. Akad. Nauk, 1992, v.324, No.5, p.953-958; A.V. Koganov, "Representation of Groups by Automorphisms of Inductor Spaces", in: Abstracts Int. Conf. "Algebra and Analysis", Kazan, 1994; A.V. Koganov, The Truth Splitting Method in Paradox Protection of Logic", in: Abstracts Int. Conf. "Logic, Methodology and Philosophy of Science", Moscow-Obninsk, 1995).

**V. V. ARISTOV.** ** “MODERN PROBLEMS OF SPACE-TIME IN PHYSICAL THEORIES AND THE MODEL APPROACH”.** The program of Relativity Theory. Two branches of physical theory (special and general relativity versus statistical and quantum theory) which should have led to a synthesis in a unified field theory. Solved and unsolved problems. Geometrization of physics. The creative essence of mathematics in physics and the neo-Pythagorean ideas (Einstein, Eddington, Dirac). The meaning of the model approach. Geometrization of time. The notion of a time instant defined in terms of the configuration space of a system of particles. Metrization and a mathematical model of a clock, leading to dynamic equations. The problem of reducing the number of independent physical dimensions by building models of clocks and rulers. The possibility of dimensionless equations in physics. Development of a model for the effects of general relativity and quantum mechanics. Particle theory as an alternative to field theory. The notion of a time instant, compatible with thermodynamic quantities depending on system state. Introduction of irreversible model time connected with a distinction between two states of a system (V.V. Aristov. "Mach's Principle and a Statistical Model of Space-Time". In: Abstracts of the 8th Russian Gravitational Conference, Moscow, 1993; V.V. Aristov, "A Statistical Model of Clocks in Physical Theory", Dokl. AN, 1994, v.334, p. 161-164).

**A. V. MOSKOVSKY . “THE EINSTEIN-PODOLSKY-ROSEN PARADOX 60 YEARS AFTER”.** The history and modern status of the EPR paradox are considered: the experimental, theoretical and metaphysical effects. (See the history of the problem in: B.I. Spassky and A.V. Moskovsky, "On Non-Locality in Quantum Physics", Uspekhi Fiz. Nauk, v.142, 4th issue, 1984, p. 599-617.)

**Yu. L. KLIMONTOVICH.** ** “PHYSICS OF OPEN SYSTEMS”.** Owing to matter, energy and information exchange with ambient bodies, open systems exhibit, along with degradation, self-organisation processes. Statistical criteria of self-organisation are considered. For both passive and active macroscopic system, a possibility of a unified description of kinetic, hydrodynamical and diffusion processes is demonstrated. Suggested is a statistical description of quantum macroscopic open systems, making it possible to obtain answers to the "eternal" questions: is the quantum-mechanical description full? Are there hidden parameters in quantum theory? (Yu.L. Klimontovich, "Statistical Theory of Open Systems", Moscow, Yanus, 1995.)

**V. P. MAIKOV.** ** “TIME, ORDER, MACROQUANTA AND EINSTEIN'S PROGRAM OF THE DEVELOPMENT OF PHYSICS”.** The report considers the results of generalising the well-known phenomenon of macroquantum effects to an independent extended version of classical equilibrium thermodynamics. The methodological and physical bases of the generalisation are: the macroscopic (but not statistical) phenomenology of equilibrium thermodynamics; macroquantization; nonlocality; the relativism of general relativity; usage of only first principles of physics. A formal base for describing macroscopically elementary phenomena is the use of physically extremely small quantities instead of differential operators. For this purpose the well-known uncertainty relations are used. They make it possible to introduce the characteristic space and time scales to the description of a thermodynamical equilibrium without addressing to the quantum-mechanical procedures. The above scales determine the properties of the space-time metric in the Einstein understanding. In the equilibrium theory under consideration, unlike the non-equilibrium one (I. Prigogine), the time irreversibility phenomenon is connected with the order (entropy reduction) and the macroquanta of the space-time metric (V.P. Maikov, "Phenomenological theory of an equilibrium isotropic material medium (the quantum-thermodynamic approach)", in: Reports of Internat. Research and Engineering Conference "Urgent Problems of Basic Research", v.3: Section of Theoretical and Experimental Physics, Moscow, MGTU, 1991, p. 106-109).

(1) **Yu. A. DANILOV.** ** “THE "ARROW OF TIME" AFTER THE PUBLICATION OF THE BOOK "TIME, CHAOS, QUANTA" BY I. PRIGOGINE AND I. STENGERS”.** The irreversibility emerges on a fundamental level rather than due to averaging the reversible equations of motion.

(2) Discussion of the book "Time, Chaos, Quanta" by I. Prigogine and I. Stengers (Moscow, Progress, 1994).