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AIP conference proceedings

Nature of Reality According to Einstein’s Statistical-Thermodynamic and Geometric Ideas Today

Alexander D. Sukhanov, O. N. Golubjeva

Published Jan 1, 2006• 0 citations
Publisher

Abstract

It is shown that among the manifold scientific legacy of Einstein, his statistical‐thermodynamic and geometric ideas take on a special significance today. A special attention is paid to his role as a founder of holistic understanding of Nature . His geometric thinking allowed creating not only special and general relativity but complete classical physics as a holistic classical version of the physical picture of the world. His statistical‐thermodynamic thinking allowed creating not only outstanding statistical and quantum theories but opened a way to unification of these theories and to becoming a nonclassical version of physical picture of the world. At last, it is demonstrated that Einstein’s discoveries proved the funadamental status of Boltzmann’s constant and allowed distinguishing micro‐ and macrolevels of Nature describing.The influence of Einstein’s geometrical approach on the modem theoretical physics methods is discussed. It is analyzed some different forms of uncertainties relations, including Shroedinger’s uncertainties relations, as some geometrical restrictions on mutual relations between quantities or their fluctuations in the nonclassical theories. By this means an opportunity of mutual transitions of thermal and quantum fluctuations at high and low temperatures is considered.Admitting the existence of two versions of the physical picture of the world and two levels of Nature describing, a physics structure in the form of planar table is proposed. Each group of theories in the table cell responds to the corresponding version of PPW and level of Nature describing. As a result each of the group uniquely corresponds to one of four fundamental constants c, GN, ℏ, kB. As another image of this structure is offered a tetrahedron jointing four groups of theories.

DOI
10.1063/1.2399714

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It is shown that among the manifold scientific legacy of Einstein, his statistical‐thermodynamic and geometric ideas take on a special significance today. A special attention is paid to his role as a founder of holistic understanding of Nature . His geometric thinking allowed creating not only special and general relativity but complete classical physics as a holistic classical version of the physical picture of the world. His statistical‐thermodynamic thinking allowed creating not only outstanding statistical and quantum theories but opened a way to unification of these theories and to becoming a nonclassical version of physical picture of the world. At last, it is demonstrated that Einstein’s discoveries proved the funadamental status of Boltzmann’s constant and allowed distinguishing micro‐ and macrolevels of Nature describing.The influence of Einstein’s geometrical approach on the modem theoretical physics methods is discussed. It is analyzed some different forms of uncertainties relations, including Shroedinger’s uncertainties relations, as some geometrical restrictions on mutual relations between quantities or their fluctuations in the nonclassical theories. By this means an opportunity of mutual transitions of thermal and quantum fluctuations at high and low temperatures is considered.Admitting the existence of two versions of the physical picture of the world and two levels of Nature describing, a physics structure in the form of planar table is proposed. Each group of theories in the table cell responds to the corresponding version of PPW and level of Nature describing. As a result each of the group uniquely corresponds to one of four fundamental constants c, GN, ℏ, kB. As another image of this structure is offered a tetrahedron jointing four groups of theories.
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Classical thermodynamics is a theory based on coarse-graining, meaning that the thermodynamic variables arise from discarding information related to the microscopic features of the system at hand. In quantum mechanics, however, where one has a high degree of control over microscopic systems, information theory plays an important role in describing the thermal properties of quantum systems. Recently, a new approach has been proposed in the form of a quantum thermodynamic gauge theory, where the notion of redundant information arises from a group of physically motivated gauge transformations called the thermodynamic group. In this work, we explore the geometrical structure of quantum thermodynamics. Particularly, we do so by explicitly constructing the relevant principal fibre bundle. We then show that there are two distinct (albeit related) geometric structures associated with the gauge theory of quantum thermodynamics. In this way, we express thermodynamics in the same mathematical (geometric) language as the fundamental theories of physics. Finally, we discuss how the geometric and topological properties of these structures may help explain fundamental properties of thermodynamics.
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The article discusses approaches to understanding the nature of probability in mathematics and physics with the consequences of these approaches, as well as the difficulties that arise. The ontological status of probability is discussed. It is shown that probability theory, contrary to R. Mises, should be classified as a mathematical science, using the definition formulated by A.N. Kolmogorov. The application of this definition in practice is provided within the framework of the classical approach, provided that the connection with physical reality is defined through the concept of equal opportunity. To do this, the concepts of simple and complex events are introduced, and the method of decomposing complex events into simple ones is explained. The point of view is substantiated, according to which a mathematical probability determined and related to physical reality in this way can be considered an objective probability, that is, existing independently of any tests. Various interpretations of quantum mechanics and approaches to understanding probability are also revealed. It is shown that in physics today the existing approaches to understanding the nature of probability contradict each other. In the Bohm interpretation, probability is an analogue of the classical approach – statistical objective probability, which has a mathematical formalization, and in quantum Bayesianism, probability quantifies the degree of reliability and depends on the subject conducting the experiment. The Copenhagen interpretation of quantum mechanics tries to eliminate the difficulties associated with combining the wave and corpuscular properties of light and electron beams into a single picture by giving the ontological status of probability, which leads to the problem of understanding physical reality. The article argues for the need for a new connection between the mathematical description of probability and physical reality. The empirical (frequency) approach of R. Mises is analyzed, which causes a lot of criticism, as it does not have a clear consistent formalization. The article argues that this approach is inconsistent with quantum mechanics. The probability given by M. Born in the Copenhagen interpretation of quantum mechanics is also considered, which formulates a new definition of probability, which does not exclude the difficulties associated with the physical interpretation of probability. Born’s approach is based on the classical approach and is reduced to a formal axiomatic definition, which assumes the interpretation of probability as a mathematical construct. The connection of probability with physical reality and the consistency of the statistical method of finding probability values remain unresolved problems, which creates a dualism of understanding probability: in mathematics – one thing, in physics – another. If in the mathematical approach, the solution of these problems is carried out through the connection of probability with physical properties, then in quantum mechanics, in the Copenhagen interpretation, problems persist, which is caused by giving the wave function an ontological status.
Extended version / Monograph-length manuscript This work proposes a unified conceptual reconstruction of physical phenomena by examining the recurring structural patterns that connect classical and quantum systems across scales. Oscillatory behavior, potential landscapes, and binding principles form a common mathematical template that appears in mechanical oscillators, molecular vibrations, atomic orbitals, and quantized field modes. By reframing quantum phenomena as refinements of classical oscillatory structures rather than conceptual discontinuities, this work highlights the deep continuity that underlies modern physics. The framework also clarifies energy minimization, mass defect, statistical behavior, and vacuum fluctuations as manifestations of shared principles. Implications for pedagogy, theory building, and cross‑disciplinary coherence are discussed. The innovative hypotheses, which depart from classical norms, will be explicitly marked with the heading HYPOTHESIS. As such, they are excluded by default from use as references in current academic or educational frameworks. They may instead be considered “revolutionary attempts to be monitored”, that is, the very “targets” mentioned by Weinberg. Albert Einstein introduced, on the one hand, a special relativity that he wished to be perfectly reversible, and on the other hand, general relativity which, when applied to cosmology, imposed on our Universe a spherical and static state—thus of constant radius—resisting gravitational collapse through the repulsion of the cosmological constant. Here, the associated relativities will instead give priority to irreversible systems evolving in accordance with the second law of thermodynamics, within their local space-time domain of one-way time flow. quantum physics, classical physics, grand unification, field theory, atomic stability, Albert Briffoz, physique quantique, unification, théorie des champs