This concluding chapter of the book presents some key concepts discussed in the book. Scale Relativity Theory (SRT) is a necessary theory of interpretation. With the advent of wave mechanics, the interpretation has been established as a necessity within the core of physics itself. Even if it is possible to eliminate the wave mechanics from our knowledge, the interpretation still cannot be eliminated. The fundamental feature of the concept of interpretation turns out to be the idea of freedom of particles: the wave function is referring to an ensemble of free particles. The approach of the interpretation concept, whereby the wave function is interpreted by ensembles of Hertz free particles, and the potential of forces describes implicitly these forces, is a natural situation according to the very idea of quantization of the wave mechanics. In hindsight, this interpretation warrants the Laurent Nottale’s approach of SRT by geodesic motions description of a fractal fluid.
This concluding chapter of the book presents some key concepts discussed in the book. Scale Relativity Theory (SRT) is a necessary theory of interpretation. With the advent of wave mechanics, the interpretation has been established as a necessity within the core of physics itself. Even if it is possible to eliminate the wave mechanics from our knowledge, the interpretation still cannot be eliminated. The fundamental feature of the concept of interpretation turns out to be the idea of freedom of particles: the wave function is referring to an ensemble of free particles. The approach of the interpretation concept, whereby the wave function is interpreted by ensembles of Hertz free particles, and the potential of forces describes implicitly these forces, is a natural situation according to the very idea of quantization of the wave mechanics. In hindsight, this interpretation warrants the Laurent Nottale’s approach of SRT by geodesic motions description of a fractal fluid.
One of the main results of scale relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The scale relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamental two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schrödinger equation can be derived.
Two types of ontologies about the universe arise: the materialist ontologies that describe the universe (and everything in it) as composed of fluids and atoms that move through space and time, and the conventional materialist ontologies that look at nature as contained in intact particles. Even though Whitehead perceives incompatibilities with the interpretations of some physicists, this section provides discussions on Abner Shimony's five points implicitly supplied by the quantum theory, Bohr's utilization of interconnected information as nature's most basic element, the benefits of the Jamesian ontological accommodation from the Interpretation of Copenhagen, and the idea of a “closed system.” Also given in this chapter are equations and sample situations to support the propositions of Murray Gell-Mann and John Bell, Werner Heisenberg's uncertainty relations, and ontological conclusions from the quantum formalism specializing in the elaboration of potential facts.
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).
The concept of a Madelung fluid makes us accept that the matter per se admits at least a description, if not even a physical structure, by ensembles of free Hertz material particles. This chapter elucidates the idea of physical freedom, according to the nonstationary Schrödinger equation. Louis de Broglie observed that either the standard deviation in the case of Gaussian, or the period ‘t’ in the case of Airy function, should be taken as ‘uncertainty parameters’ rather than geometrical quantities. According to Michael Berry and Nandor Balazs, the argument of Airy function actually represents a caustic, but in the phase space: it is the envelope of the ensemble of straight lines representing the corresponding uniform motions. The Berry-Klein theory of scaling the forces, in case it can be applied to a Wien-Lummer enclosure, acts as a universal gauging procedure which, in an undertaking of Georgescu-Roegen type, should be able to make us decide what is infrafinite, finite or transfinite.
The conceptuality interpretation, proposed by Diederik Aerts in 2009, is presented here as a possible theoretical perspective for achieving a unified understanding of many fundamental aspects of quantum mechanics and relativity. After discussing the notion of reality and the role of choice and possibility in the construction of the real, we note how the interpretation emerges from the successes of quantum cognition, and show how it allows us to reinterpret phenomena and experiments such as the double-slit experiment, quantum erasure, entanglement, Bose–Einstein condensation, and the measurement problem by assigning a central role to dynamics governed by meaning, within a pancognitivist perspective. It is further suggested that the metric of relativistic spacetime can also be coherently understood using the same interpretive key. Quantum mechanics and relativity would thus find, in the conceptuality interpretation, an ontological and foundational framework capable of making them not only more intelligible but, in some respects, even intuitive. The price to be paid for this explanatory advantage, however, is that we must relinquish the idea that we live in a world populated primarily by spatiotemporal entities, and instead conceive of reality as a fundamentally cognitive-conceptual structure, in which every interaction ultimately takes the form of a communication.
Concepts of QUANTUM MECHANICS is one of the most fundamental and intellectually profound branches of modern physics. It provides the theoretical framework for understanding the behavior of matter and energy at atomic and subatomic scales and forms the basis for numerous advancements in science and technology, including semiconductor devices, lasers, nanotechnology, quantum computing, and quantum communication. Despite its abstract nature, concepts of QUANTUM MECHANICS remains indispensable for explaining physical phenomena that cannot be addressed by classical physics. This book, Concepts of QUANTUM MECHANICS, has been written with the primary objective of presenting the subject in a clear, logical, and student-friendly manner, while maintaining the necessary mathematical rigor and conceptual depth. The text is designed to bridge the gap between classical physics and quantum theory, guiding readers through the evolution of ideas that led to the development of concepts of QUANTUM MECHANICS and its modern interpretations. The book begins with an introduction to the historical background and foundational principles of quantum theory, highlighting the limitations of classical mechanics and the emergence of quantum concepts such as wave–particle duality and quantization. It then systematically develops the mathematical framework of concepts of QUANTUM MECHANICS, including the Schrödinger equation, wave functions, operators, eigenvalue problems, and measurement theory. Key quantum systems and applications are discussed with careful attention to physical interpretation and problem-solving strategies. Special emphasis has been placed on clarity of explanation, step-by-step derivations, and the use of illustrative examples to help students develop a strong conceptual understanding. Each chapter is organized in a structured manner to support effective learning and includes solved problems and exercises that reinforce theoretical concepts and analytical skills. This book is intended for undergraduate and postgraduate students of physics, engineering, and allied disciplines, and it will also serve as a useful reference for educators and researchers. The content has been aligned with standard university curricula and is suitable for both classroom instruction and self-study. It is the author’s sincere hope that this book will make the study of concepts of QUANTUM MECHANICS more accessible and intellectually rewarding, encouraging readers to develop a deeper appreciation for the quantum nature of the physical world. Constructive feedback and suggestions from readers are welcome and will be valuable for improving future editions of this book.