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Routledge eBooks

Introduction

Kefu Zhu

Published Aug 22, 2025• 0 citations
Publisher

Abstract

This chapter, along with the next two chapters, sets the basic context for the readers to go into the topic of this book. Physicists, mathematicians, and philosophers struggle to clarify the foundations of quantum mechanics and debate on the interpretations of quantum mechanics. What is the foundation of quantum mechanics and how to interpret the formalism of quantum mechanics are the core issues of concern in the philosophy of physics. These two questions also involve fundamental issues in the general philosophy of science and even metaphysics and epistemology. This chapter introduces the original thoughts, historical developments, and current status of the interpretation of quantum mechanics, as well as its connection with the philosophy of science and metaphysics; it also analyzes the classifications by Bell, Leifer, and Cabello on the spectrum of interpretations of quantum mechanics, which can be regarded as a sort of “navigation map”. On this basis, the main object of discussion in this book is introduced – the quantum histories interpretation.

DOI
10.4324/9781003662860-1

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This chapter, along with the next two chapters, sets the basic context for the readers to go into the topic of this book. Physicists, mathematicians, and philosophers struggle to clarify the foundations of quantum mechanics and debate on the interpretations of quantum mechanics. What is the foundation of quantum mechanics and how to interpret the formalism of quantum mechanics are the core issues of concern in the philosophy of physics. These two questions also involve fundamental issues in the general philosophy of science and even metaphysics and epistemology. This chapter introduces the original thoughts, historical developments, and current status of the interpretation of quantum mechanics, as well as its connection with the philosophy of science and metaphysics; it also analyzes the classifications by Bell, Leifer, and Cabello on the spectrum of interpretations of quantum mechanics, which can be regarded as a sort of “navigation map”. On this basis, the main object of discussion in this book is introduced – the quantum histories interpretation.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.
Quantum mechanics approaches its centenary with an impressive record. It became the backbone of most research in physics, led to applications such as the transistor and laser, and prompted an upheaval in the philosophy of science. Its scope and its precision have been constantly growing, and it is now promising more powerful computers and safer cryptography. This century of conquests has also been a time of ongoing debates about the foundations and interpretation of the theory, which has been referred to as the quantum controversy. The controversy has been unusually long and remains open. Jammer called it “a story without an ending” and Laloë described this coexistence of successes and doubts with the metaphor of the colossus with feet of clay. This Handbook is a survey on this history. Some of the so-called “interpretations” are not interpretations of a fixed formalism, they are different theories, thus it has been a debate about the interpretations and the foundations of quantum mechanics. In this volume, the “history of interpretations” is used for the sake of brevity. The successive parts of the Handbook deal with the scientific and philosophical issues under debate, historical landmarks, places and contexts, historical and philosophical theses, and the proliferation of interpretations. This Handbook may serve those interested in the history of quantum mechanics and those who are engaged with, or attracted by current research on quantum information, as it may give them a flavor of the history that led to or lay the groundwork for the current investigations.
In this introductory chapter, which actually is the core of the entire book, we make a serious effort to bring together a variety of ideas from philosophy and physics. We first lay the epistemological foundations for our approach to particle physics. These philosophical foundations, combined with tools borrowed from the amazingly sophisticated, but still not entirely satisfactory, mathematical apparatus of present-day quantum field theory and augmented by some new ideas, are then employed to develop a mathematical representation of fundamental particles and their interactions. In this process, also the relation between “fundamental particle physics” and “quantum field theory” is going to be clarified. This first chapter consists of two voluminous sections: a number of philosophical contemplations followed by a discussion of mathematical and physical elements . The reader might wonder why these massive sections are not presented as two separate chapters. The reason for keeping them together is the desire to emphasize the intimate relation between these two sections: the selection and construction of the mathematical and physical elements is directly based on our philosophical contemplations. The beauty of the entire approach is a fruit of this intimate relationship. The presentation of the material in this chapter is based on the assumption that the reader has a basic working knowledge of linear algebra and quantum mechanics. If that is not the case, the reader might want to consult the equally entertaining and serious introduction Quantum Mechanics: The Theoretical Minimum by Susskind and Friedman [4]. The book Quantum Mechanics and Experience by Albert [5] offers a fascinating introduction with a strong focus on the measurement problem. An almost equation-free discussion of the history and foundations of quantum mechanics can be found in the book Einstein, Bohr and the Quantum Dilemma: From Quantum Theory to Quantum Information by Whitaker [6]. Complex vector spaces, Hilbert space vectors and density matrices for describing states of quantum systems, bosons and fermions, canonical commutation relations, Heisenberg's uncertainty relation, the Schrodinger and Heisenberg pictures for the time evolution of quantum systems, as well as a basic idea of the measurement process are all referred or alluded to in Section 1.1; these basics of quantum mechanics are recapped only very briefly in Section 1.2. The crucial construct of Fock spaces is explained in a loose way in Section 1.1.3 and later elaborated in full detail in Section 1.2.1.
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins with a non-mathematical introduction to some of the more controversial topics in the foundations of quantum mechanics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by a detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensures the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and the philosophy of science interested in the foundations of quantum mechanics.