Quantum mechanics has played a significant role in the development of various disciplines of physics. It was propounded in 1925 and has reigned supreme ever since, extending its domain over the years; of course, in its own domain it has always been in excellent agreement with experiments. It has long since become the language of physics and anyone who tries to understand the basic principles of physics without having a grasp of this subject is doomed to fade away in the darkness of ignorance. In this book an attempt has been made to provide a logical, lucid and user-friendly treatment of this elegant and fascinating subject.
Quantum mechanics has played a significant role in the development of various disciplines of physics. It was propounded in 1925 and has reigned supreme ever since, extending its domain over the years; of course, in its own domain it has always been in excellent agreement with experiments. It has long since become the language of physics and anyone who tries to understand the basic principles of physics without having a grasp of this subject is doomed to fade away in the darkness of ignorance. In this book an attempt has been made to provide a logical, lucid and user-friendly treatment of this elegant and fascinating subject.
The more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science. This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information
Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information