Any quantum particle at rest has a probability amplitude that characterizes the possibility to find this system in any point of phase multidimensional space. This chapter establishes the dependencies between the energies of various states of a manifested tribosystem, which, in turn, is a product of reduction of a quantum non-local ‘properly tribosystem’. Quantum mechanism of frictional interaction is based on the assumption that the friction force may be represented as an exchange of special quasiparticles, tribons, the quanta of frictional interaction, between the surfaces. There are two approaches to the notation of the motion equation in quantum mechanics. They are called Schrodinger and Heisenberg pictures. The diagonal elements of the density matrix describe the basic state of a quantum system and the off-diagonal elements characterize the correlations inside a tribosystem. The points on the Bloch sphere surface corresponding to the pure state are localized near the poles of the system; the other points correspond to mixed quantum states.
Any quantum particle at rest has a probability amplitude that characterizes the possibility to find this system in any point of phase multidimensional space. This chapter establishes the dependencies between the energies of various states of a manifested tribosystem, which, in turn, is a product of reduction of a quantum non-local ‘properly tribosystem’. Quantum mechanism of frictional interaction is based on the assumption that the friction force may be represented as an exchange of special quasiparticles, tribons, the quanta of frictional interaction, between the surfaces. There are two approaches to the notation of the motion equation in quantum mechanics. They are called Schrodinger and Heisenberg pictures. The diagonal elements of the density matrix describe the basic state of a quantum system and the off-diagonal elements characterize the correlations inside a tribosystem. The points on the Bloch sphere surface corresponding to the pure state are localized near the poles of the system; the other points correspond to mixed quantum states.
A concrete realization of a tribosystem, the ‘manifested tribosystem’, is observed in terms of quantum theory, in full accordance with the meaning given to fundamental concept by P. Dirac. A manifested tribosystem is a result of the information field perturbation is properly tribosystem being in the initial nonlocal quantum state. Under the quantum approach, a tribosystem is born by perturbations of the primary information field at the measurement, like splashes from a liquid surface when various items fall there and like those splashes break up into separate drops, individual visible tribosystems arise. The use of formalism and the views of perturbation theory as the basis for quantum system dynamics are based on the definition of motion as energy exchange of a physical system with the environment or neighboring physical systems. The physical consideration of the impact of physical fields on the kinetics of tribophysical processes, based on applying continuum electrodynamics, is a complicated task from the mathematical point of view.
Section 5.4 in its contents resembles the educational articles in modern physics. From the authors’ point of view, it is unknown whether it is bad or good. We aimed to show the general picture of changes in a tribosystem structure, using full sets of visual representations found in scientific and educational literature by L. Cooper, R. Feynman, K. Thorne, S. Hawking et al. We hope that the final chapter fully com- pletes the general picture of fundamental quantum-relativistic mecha- nism of tribosystem evolution while preserving the elements of rigor. Thinking about the graphical forms which could represent the nuances of the quantum world to a small extent, we suddenly discovered the ‘implicit graphicity’ of the matrix notation of quantum quantities. In presenting the material, the transposition of matrices ( 3.69 ) was pre- sented a sequence of two rotations of coordinate axes by 45 ∘ ( 3.72 ), and Fig. 3.4, where the ‘chess’ structure of matrix ( 3.59 ) reflects not only the degenerate nature of the quantum system showing that its phase space contains three more subspaces representing Minkowski contin- uum, but also that the structure of matrix ( 3.59 ) contains the basic elements a 22 and a 33 that are common for two subspaces cells at once. The latter is very similar to the transitions between the phase subspaces as shown graphically in Fig. 5.4.
The present work deals with the changes which evolve in the tribosystem from the viewpoint of the quantum theory of measurement. It is shown that measurement both enables to determine some parameters of the friction unit and affects the tribosystem structure and properties. The theoretical argumentation in the article is based on the most fundamental concepts: the non-force quantum fields, nonlocal correlations, quantum entanglement, and model of H. Everett. The tribosystem evolution is viewed as the set of spatial transitions from non-local original state to tribosystem material state registrable by measurement. Some conclusions from the evolution quantum model are confirmed experimentally by studying triboplasma matter as a quantum object.
Abstract This chapter presents the basic elements of quantum theory, including the Dirac bra and ket notation for quantum states, Hermitian operators and their eigenstates, commutators and the Schrödinger and Heisenberg equations of motion. Simple model atoms are described as an effective spin and their properties related to the familiar Pauli spin-half operators. The density matrix is introduced to describe incoherent processes. The electric-dipole coupling between and atom and the electromagnetic field is treated leading to coupled equations for the probability amplitudes. Finally, quantized field modes are introduced and their elementary properties described leading to the fundamental Jaynes–Cummings model of a single two-state atom interacting with a quantized field mode.
Abstract The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the fundamental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that represents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.
When comparing the findings of quantum mechanics with the experimental data, the states would act as two ‘manifestations’ in terms of their observation and in term of their ‘preparing’. It should be emphasized that a physical description using vectors must be perfectly symmetric, which can be interpreted as the isotropy of time, which is expressed in the requirement of a Hermitian character of a quantum space metric. In a number of problems that quantum physics faces, it is very convenient to convert the operators in quantum-mechanical equations into the matrix form. A quantum system generally refers to any physical system described in terms of states with the use of concepts, such as wave function, state vector, and density matrix. Further development of the axioms of quantum mechanics requires the extension of the definition of the ‘state’ concept with the use of space time concepts.