This Resource Letter provides a guide to the literature that is concerned with the connections between classical and quantum mechanics. After the three centuries of classical mechanics, this fundamental problem in physics became one of the important issues at the beginning of the twentieth century, in the transitional period from 1900 to 1925. It then lost some of its urgency during the modern period from the discovery of Schrödinger’s equation to the middle of the 1960s, when the validity of quantum mechanics was tested in all the areas of application. The most recent 30 years are called the Post-Modern Period because both the classical and quantal aspects of nature are seen in their full complexity, and the advantages of viewing one in the light of the other have brought a better understanding of many special fields. The literature is divided into these four periods, and the list of references in each of them is subdivided according to the main areas of interest. Most of the bibliographic descriptions are accompanied by a short comment that is supposed to complete the information in the title.
This Resource Letter provides a guide to the literature that is concerned with the connections between classical and quantum mechanics. After the three centuries of classical mechanics, this fundamental problem in physics became one of the important issues at the beginning of the twentieth century, in the transitional period from 1900 to 1925. It then lost some of its urgency during the modern period from the discovery of Schrödinger’s equation to the middle of the 1960s, when the validity of quantum mechanics was tested in all the areas of application. The most recent 30 years are called the Post-Modern Period because both the classical and quantal aspects of nature are seen in their full complexity, and the advantages of viewing one in the light of the other have brought a better understanding of many special fields. The literature is divided into these four periods, and the list of references in each of them is subdivided according to the main areas of interest. Most of the bibliographic descriptions are accompanied by a short comment that is supposed to complete the information in the title.
This Resource Letter provides a guide to the literature on the foundations of quantum mechanics over approximately the past 20 years. Topics covered include Bell’s theorem, interpretation of the quantum state concept, the theory of measurement, and experimental tests of fundamental aspects of the quantum theory of matter and the electromagnetic field. The letter E after an item indicates elementary level of material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
Quantum mechanics is one of the great success stories of modern physics, making sense of the very small just as Einstein's theory of relativity made sense of the very large. But, for most students, the ideas that make quantum mechanics powerful can be confusing and counterintuitive. This volume in the Greenwood Guides to Great Ideas in Science series provides a history of quantum mechanics from the early breakthroughs of Planck and Einstein, at the beginning of the 20th century, to the present frontiers of quantum computing and quantum gravity. The approach is entirely non-technical, and is aimed at the general reader who may not have much mathematical background but who has a strong curiosity about some of the most important developments in modern science. Quantum Mechanics: A Historical Perspectivetraces the history of this powerful theory, including: ; The early discoveries by Max Planck and Albert Einstein regarding the quantization of radiation ; The early quantum theory, including Neils Bohr's theory of the atom ; The birth of modern quantum mechanics through the work of Heisenberg, Schrodinger, Born, Dirac and others ; Applications of quantum mechanics in chemistry, nuclear physics, electronics, and many other areas ; Recent work in quantum computation and quantum information theory The book emphasizes the fact that despite the great success of quantum mechanics, many exciting intellectual frontiers remain open for further researchers to explore. It includes a glossary, a timeline, and a bibliography of accessible resources for further research.
Abstract Following the path by which humanity learned quantum mechanics can lead to an improved understanding of the theory and the origins of its perceived limitations. Our goal is to retrace the development by investigating primary sources, including original published papers and letters, with attention to their timing and influence. Quantum mechanics began in 1900 with the introduction of Planck’s constant, which lead to the “old” quantum theory and Bohr’s model of the atom. With the introduction of matter waves in 1924, a second more intense period began. By 1928 the complete fundamental structure of quantum mechanics was established with the introduction of the Schrödinger equation, the proof of its equivalence to Heisenberg’s matrix mechanics, and the introduction of the relativistic Dirac equation. The theory retains the same essential form today, fueling the technological revolution that began in the last century. We culminate with an introduction to quantum information and computing. This completely new physical scientific paradigm was developed largely in Germany during a period of enormous social, economic, and political upheaval—in a hostile intellectual environment—that parallels the overturning of classical physics. It is striking that all the problems debated today were immediately recognized by the founders of the theory and instructive to see how they dealt with the various issues. We emphasize the centrality of the often neglected second quantization form of the theory for questions of interpretation and give a detailed examination of von Neumann’s widely misunderstood hidden variable theorem.
Introduction While it might appear that the nineteenth-century physics presented in this chapter has no place in a topic as quantum mechanically oriented as atomic physics, this is simply not the case. The purpose of this first chapter is to try to convince the readers that the material learned in their early years of studying physics is not disjoint from modern topics, but in fact can provide a foundation for their further understanding. Other examples will occur later. The reader may be a bit surprised to see that the results of the classical description turn out to be so close to the quantum mechanical results. Where there are significant disagreements between classical and quantum descriptions, it is necessary to explain why these occur. The correspondence principle requires that in the limit of large quantum numbers the complete quantum mechanical description must agree with the classical one. It is always better to need fewer of these explanations and to be able to treat physics as a coherent whole instead of a collection of topics. The consequences of classical physics are intuitively familiar, and this is often most helpful in gaining deeper understanding. In fact, the approach taken in very many of the chapters in this book is to start with a purely classical description of a topic, and then transport it directly into the Schrödinger equation. Radiation from an accelerated charge, as treated here in the harmonic case, provides an ideal setting for such pedagogy. Even though classical mechanics is used in place of quantum mechanics, for the case of harmonic motion, the results are quite compatible. The early history of atomic physics contains many topics that are well worth reading about, especially the experimental facilities. For example, there were no electric motors, wire was not readily available, and making even a crude vacuum was an experimental tour de force. Very many textbooks have discussions of these topics, and so they will not be presented here. But the reader is warned that certain oft-repeated modern descriptions are simply wrong. Perhaps the most important notion to be gained from this chapter is that the classical description of a harmonically bound electron provides quite accurate results about the interaction between atoms and light. Of course, the utility of this description is limited because the classical harmonic oscillator has no internal structure, is infinitely deep, and has a continuous energy spectrum.
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.
On August 15, 1932 Niels Bohr gave opening address of International Congress on Therapy held in Copenhagen. Bohr's title was Light and Life, and his purpose was to draw attention to epistemological implications for life sciences of fundamental changes that quantum theory had brought to conception of natural law (Bohr 1933). He thought that these changes, which extend to very idea of nature of scientific explanation, were important not only for a full appreciation of new situation brought to physics by quantum theory. According to Bohr, these developments had also created an entirely new background for viewing problems of biology, especially as concerns our views on position of living organisms in realm of natural science. In particular, Bohr proposed that notion of complementarity, which he had first presented 5 years earlier at International Congress of Physics in Como, relevant also for physiological and psychological aspects of life. Bohr began his address by stating what nowadays stigmatized as reductionist credo, namely that subtle character of riddle of life notwithstanding, any scientific explanation of biological phenomena necessarily must consist of reducing description of more complex phenomena to that of simpler ones. But, Bohr continued, discovery of an essential limitation of mechanical description of natural phenomena, as revealed by recent development of atomic theory, has lent new interest to old problem of how far program of reductive biological explanations can be carried. Bohr then presented a brief historical account of rise of quantum theory in connection with study of light, which he thought is perhaps least complex of all physical phenomena. Yet, it turned out that despite its lack of complexity, phenomenon of light cannot be given a coherent mechanical explanation, inasmuch as from viewpoint of classical physical theories, the quantum of action . . . must be considered as an irrational notion. The spatial continuity of light propagation, on one hand, and atomicity of light effects on other hand, must, therefore, be considered as complementary aspects of one reality, in sense that each expresses an important feature of phenomena of light. Those aspects are complementary, because, although they are conceptually irreconcilable from a mechanical point of view, they can never be shown to be in direct, or empirical, contradiction. The reason for this that any closer analysis of either wave aspect or particle aspect of light demands mutually exclusive observational arrangements.