Despite its status as a core part of contemporary physics, there is no consensus among physicists on the question of what, if anything, the success of quantum theory is telling us about the physical world. This gives rise to the collection of debates and discussions known as "the interpretation of quantum mechanics". Describing quantum mechanics is complicated by there being so many interpretations of it. In text books, classical mechanics is an approximation of the quantum mechanics when ℏ → 0. In a first part, we recall the fundamental differences between the classical mechanics in different formalisms: Newtonian, Lagrangian and Hamiltonian (Jacobi). A second part is dedicated to the deep similarities and differences between classical and quantum mechanics. The third part deals with the misunderstanding between scientific communities about the meaning ℏ → 0. The last part deals with the porous frontier between classical and quantum physics to the light of the algebraic topology illustrated by two major theorems: Borsuk Ulam and Non squeezing Gromov's theorem.
Despite its status as a core part of contemporary physics, there is no consensus among physicists on the question of what, if anything, the success of quantum theory is telling us about the physical world. This gives rise to the collection of debates and discussions known as "the interpretation of quantum mechanics". Describing quantum mechanics is complicated by there being so many interpretations of it. In text books, classical mechanics is an approximation of the quantum mechanics when ℏ → 0. In a first part, we recall the fundamental differences between the classical mechanics in different formalisms: Newtonian, Lagrangian and Hamiltonian (Jacobi). A second part is dedicated to the deep similarities and differences between classical and quantum mechanics. The third part deals with the misunderstanding between scientific communities about the meaning ℏ → 0. The last part deals with the porous frontier between classical and quantum physics to the light of the algebraic topology illustrated by two major theorems: Borsuk Ulam and Non squeezing Gromov's theorem.
Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists.
Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists.
There are many important questions that do not fall neatly into any one discipline; rather, their full investigation requires the integration of two or more distinct fields. This book is about just such a question – one that arises at the intersection of physics, philosophy, and history. The question can be simply stated as “What is the relation between classical and quantum mechanics?” The simplicity of the question, however, belies the complexity of the answer. Classical mechanics and quantum mechanics are two of the most successful scientific theories ever developed, and yet how these two very different theories can successfully describe one and the same world – the world we live in – is far from clear. One theory is deterministic, the other indeterministic; one theory describes a world in which chaotic behavior is pervasive, and the other a world in which it is almost entirely absent. Did quantum mechanics simply replace classical mechanics as the new universal theory? Do they each describe their own distinct domains of phenomena? Or is one theory really just a continuation of the other? In the philosophy literature, this sort of issue is known as the problem of intertheoretic relations. Currently, there are two accepted philosophical frameworks for thinking about intertheoric relations: the first is reductionism, and the second, pluralism. As we shall see, these labels each actually describe a family of related views.
"Owing to efforts in both theoretical and experimental research, a better understanding of the interpretation and many fundamental principles of quantum mechanics has been achieved. These include the complementarity principle, the geometrical phase, the topological phase, the boundary between quantum and classical mechanics, quantum mechanics on the macroscopic level, and so on. Part of this book is devoted to introducing these developments. Significant progress in the frontier research in various branches of physics has been achieved by making use of the insights and judgements originating from quantum mechanics. Part of this book is devoted to introducing some of these fields, namely quantum information, cavity quantum electrodynamics, the quantum Hall effect and the Bose-Einstein condensation. Basic physical ideas and methods are emphasized, instead of going into technical details. The Yang-Baxter system has become a prosperous field of mathematical physics. The last part of the book is devoted to introducing its application to some basic problems in quantum mechanics, and again basic physical ideas are emphasized."
Abstract The purpose of this book is to present an interpretation of quantum mechanics. But what are we talking about when we speak of “quantum mechanics?” Are we talking about a single theory or about many related theories? And what do we mean by “interpretation” here? In this chapter, I will address these questions in an introductory way. Of course, I do not intend to take part in the extensive discussions about what a scientific theory is, what is meant by interpreting a theory, in what situation we encounter equivalent theories, and many other questions related to or derived from these. My aim here is to present some preliminary ideas in a way that I hope will be sufficient to avoid misunderstandings in the following chapters. But, above all, I will state my position as to why, after so many years and so much literature on the subject, the interpretation of quantum mechanics deserves further discussion.