Quantum effects in tribology

197 Pages·2017·2.678 MB·English

by  Dmitry Nikolaevich Lyubimov, Kirill Nikolaevich Dolgopolov

Quantum Effects in
Tribology

Quantum Effects in
Design, Fabrication, Properties
and ApplTicraitbioonslo ogf Symart and
Advanced Materials
Dmitry N. Lyubimov
Director for Science of Engineering Center
Lyubimov & Co. Ltd.
Shakhty, Rostov Region, Russia
Kirill N. Dolgopolov
Leading Engineer
Laboratory of NanotecEhdniotloorgy and New Materials
Rostov State Transport University
Xu Hou
Rostov-on-Don
Harvard University
Rostov Region, Russia
School of Engineering and Applied Sciences
Cambridge, MA, USA
With assistance from
L.S. Pinchuk
p,
A SCIENCE PUBLISHERS BOOK
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Preface
“...we see unexpected things: we see things that are far from what we would guess – far from what
we could have imagined. Our imagination is stretched to the utmost, not, as in fiction, to imagine
things which are not really there, but just to comprehend those things which are there.”
Richard Feynman, American physicist
Paradigm (Greek παράδειγμα “pattern, example, sample”) is defined as universally recognized
scientific achievements that, for a time, provide model problems and solutions for a community of
practitioners.
Thomas Kuhn, The Structure of Scientific Revolution
This book is a continuation of the Tribophysics cycle (published by Springer as
Micromechanism of Frictiona and Wear. Introduction to Relativistic Tribology) and
Quantum Tribophysics. These books considered the changes faced by the atomic-
molecular structure of a substance at friction and the associated micromechanisms
of forming lubricating layers. They also tried to develop a mathematical formalism
relevantly describing the stages of tribosystems evolution resulting from the ongoing
tribotransformations.
Any theoretical model of modern physics should be based on quantum mechanics
as a fundamental physical concept that describes the laws of the microworld. In this
book, we introduce the quantum mechanical formalism into the presentation of
the basics of tribology—from the revision of views on the nature of friction to the
description of its special chapters reflecting the tribomutations, the fields generation
as a result of frictional interaction of particles, ‘birth’ and ‘destruction’ of tribosystem
elements at the micro-, meso- and macrolevels of its evolution.
In the methods of quantum theory, when adapted to the concepts of friction
processes, we actively use the publications of the greatest physicists who created
the modern picture of our being—from Einstein and Bohr to Penrose and Hawking.
In order not to become like the Swift’s commentators1 in interpreting the ideas
of classics who built the modern physical worldview that formed the theoretical basis
of this book, we apply the method of a broad quotation of the scientists whose works
1 In his numerous travels, the main character of Jonathan Swift, Lemuel Gulliver, finds himself on the
island of Glubbdubdrib ruled by a magician-necromancer who is able to communicate with deceased
heroes. With his help, Gulliver meets, among others, Homer and Aristotle: “... I soon discovered that
both of them were perfect strangers to the rest of the company, and had never seen or heard of them
before; and I heard a whisper from a ghost who shall be nameless, that these commentators always kept
in the most distant quarters from their principals, in the lower world, through a consciousness of shame
and guilt, because they had so horribly misrepresented the meaning of those authors to posterity.”
Quantum Effects in Tribology
are included in the contents. Talking about quantum models, we try not to distort the
meaning put by their creators.
We accept this form of information transfer and the layout of the book’s chapters
so that the presentation of the selected topic of quantum-mechanical triboprocesses
nature is acceptable from both the classical positions of tribology and new ideas in
physics. Since quantum theory is an extensive fundamental scientific discipline, it is
impossible to include all its methods in one book. Hence, the necessary additional
information from each chapter of the scientific disciplines embedded in the book are
collected in the form of short definitions, supplements, digressions and explanations,
which facilitate a compact presentation of such vast material.
The contents of the book center around the development of Bohr’s theory on the
nature of the measurement of physical parameters with respect to friction units and
the impact of this process on the properties of the tribosystem. Very useful are the
ideas about the non-locality of quantum objects, reduction of the wave function and
the elements of secondary quantization formalism. The evolution of friction units
is depicted in the form of spatial transitions of a quantum tribosystem: the birth of
the elements of the tribosystem structure out of the physical vacuum in the friction
process, the formation of friction subsystems by those elements; the interaction
between the subsystems, through interpenetration of non-local connections, leading
to the formation and transformation of the tribosystem as a whole. Using the chosen
approach, one may obtain not only the quantum microparameters that reveal the
nature of the fundamental processes that base the frictional interaction, but also
derive the relations to evaluate the quantities traditionally accepted in tribology. Use
of the formalism of quantum theory allows reliable and logical bringing together of
mechanical and atomic-molecular friction models with the ideas of modern tribology,
such as tribonic model of frictional interaction of solids, which is given in detail for
the first time in tribological literature.
The book shows that the application of the laws of quantum mechanics allows
creation of an integrated friction model or even a unified tribological theory in general
scientific sense. We hope that the first such essay in tribology will find its supporters
and yield in both solving theoretical problems and popularization of tribology and
related scientific areas among the physics audience.
With profound respect to all who open this book.
vi
Contents
Preface v
1 Problems in Creation of the Generalized Physical Model of 1
Friction and Wear
1.1 Subject and Methods of Tribology 1
1.2 Classical Structure of Friction Science 3
1.3 Paradigms of Tribology 11
1.4 The Analogy Principle as a Step towards a New Paradigm of Friction 16
2 Quantum Algorithm for Solving the Fundamental Paradox of 22
Tribology
2.1 Continuity of the Instrument – Object Relation (Bohr’s 23
Measurement Concept)
2.2 The Einstein – Podolsky – Rosen Paradox and the Problem 32
of ‘Incompleteness’ of Quantum Equations
2.3 Information Contents of Quantum Parameters 50
2.4 Changes in Physical Parameters of Quantum Systems as a 55
Result of Measurement
3 Quantum Spaces of Tribosystems 64
3.1 The Concept of Linear Vector Spaces 64
3.2 Linear Spaces in Quantum Mechanics 69
3.3 Relation between the Quantum Values for Dimensional Subspaces 78
3.4 Spatial Transformations in Quantum Mechanics 86
3.5 Transitions between Subspaces in a Quantum Tribosystem 96
4 Quantum Dynamics of Tribosystems 107
4.1 Minkowski Space as the Observable Tribosystem World 108
4.2 Quantum Principle of Least Action (Feynman Diagrams and 119
Tribosystem Wave Function)
4.3 The Action of Force Fields on the Wave Function of a Tribosystem 131
4.4 Relativistic Corrections to the Tribosystem Wave Function 139
5 Quantum States of Manifested Tribosystem 146
5.1 Secular Equation of Manifested Tribosystem 147
5.2 Quantum Representations of Mechanical Parameters of a 152
Tribosystem
Quantum Effects in Tribology
5.3 Macrocharacteristics of a Manifested Tribosystem 158
5.4 Evaluation of the Degree of Quantum Entanglement between 162
Various Tribosystems
Epilogue 177
Bibliography 179
Index 187
viii
Chapter 1
Problems in Creation of
the Generalized Physical
Model of Friction and
*
Wear
The centuries-old history of the study of friction and wear was marked
in the second half of XX century by the formation of a specialized
discipline – tribology [1]. Unfortunately, that did not lead to the devel-
opment of a unified doctrine, which would make it possible to describe
the processes of friction, lubrication and wear. This is evidenced, first
of all, by the definitions of tribology as a science.
1.1 Subject and Methods of Tribology
For the first time the term ‘tribology’ was proposed by a group of
British experts in a report to the Parliament on lubrication problems.
Its contents ran as follows: “Tribology is a science and technology of
interacting surfaces in relative motion, as well as related phenomena
and their practical consequences” [2].
*Work carried out with the financial support (Project No. 14-29-00116) the grant
of the Russian Science Foundation, K.N. Dolgopolov (Rostov State Transport
University) participated in the project.
1