Properties of Symmetry of Space and Time, Hamilton’s Principle and the Invariants
Abstract
This research investigates the fundamental role of symmetry properties in space and time in justifying the use of the principle of least action (PLA) to describe the creation and evolution of nanomaterials. By examining the kinetics of structural transformations in metals, we demonstrate that the PLA is a universal principle applicable to diverse physicochemical and biological processes. We explore the principle's ability to establish invariants at various structural -scale levels of metal deformation, including nano-, submicro-, micro-, meso-, and macroscale levels. Our findings highlight the significance of symmetry properties in understanding and predicting the behavior of nanomaterials.
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Introduction
Structure determines the properties of materials under external influences. Establishing the causes, mechanisms and regularit ies of destruction of materials and, first of all, metals depends on the development of methods and technologies of their processing to increase reliable and safe operation. The complexity of the study of metal interface surface under external impacts and triboloading is determined by the lack of scientifically sound fundamental principles that can be applied at the junction of diffe rent sciences (physics, chemistry, mechanics, materials science, etc.) [1]. In addition, the complexity of the study of the metal interface surface is explained by the simultaneous occurrence of diverse processes (heat conduction, diffusion, mass transfer, hardening, fracture, amorphization, etc.) and the correct choice of the scale factor of external influence (load -velocity parameters, etc.). The latter makes it possible to divide a complex process into simpler constituent parts and to establish t he course of the dominant process in their diversity [2]. The analysis of the dominant process makes it possible to identify and establish the main fundamental regularities describing this process [3].
All physicochemical [4] and biological processes [5] take place in a space-time continuum, the properties of which should be reflected in these processes as well. If this is so, then there must also exist a fundamental and universal principle of least action (PLA) to describe these processes. The existence of invariants is a direct proof of the existence of the PLA. Invariance in physics is a fundamental concept that means independence of physical regularities from specific situations in which they are established and from the way of description of these situations [6].
Conclusion
The article convincingly shows that the symmetry of the properties of the continuum of space and time determines the use of the principle of least action to find and establish the invariants or the basic fundamental laws of the evolution of the stru cture of materials, regardless of the method by which they are obtained (rolling, tribo-loading, ultrasound, etc.). The establishment of invariants confirms the universality of using the scientifically sound fundamental principle of the least action for the c reation, evolution, and destruction of materials, including nanomaterials of various functional purposes. The application of this principle, which describes various kinetic processes at the junction of different sciences: physics, chemistry, biology, mesomechanics, nonequilibrium thermodynamics, etc. determines not only the kinetics of evolution, but also the search and establishment of new fundamental, invariant laws for processes occurring in space-time continuum.