Abstract This chapter elaborates and reflects on the authors’ use of the “arch-and-scaffold” metaphor to characterize the transition from classical mechanics, via the old quantum theory, to modern quantum mechanics. It discusses in detail why this metaphor does justice to both continuous and discontinuous aspects of this transition, as well the various ways in which the metaphor applies to the contents of both volumes of the work. It contrasts the account of this transition based on the “arch-and-scaffold” metaphor with an account based on Kuhn’s notion of a paradigm shift. This shift occurs, resulting in the understanding in which the continuous aspects of the transition from classical to quantum mechanics are lost.
Abstract This chapter elaborates and reflects on the authors’ use of the “arch-and-scaffold” metaphor to characterize the transition from classical mechanics, via the old quantum theory, to modern quantum mechanics. It discusses in detail why this metaphor does justice to both continuous and discontinuous aspects of this transition, as well the various ways in which the metaphor applies to the contents of both volumes of the work. It contrasts the account of this transition based on the “arch-and-scaffold” metaphor with an account based on Kuhn’s notion of a paradigm shift. This shift occurs, resulting in the understanding in which the continuous aspects of the transition from classical to quantum mechanics are lost.
Abstract This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the twentieth century. It covers the period 1923–1927. It traces how the old quantum theory of Bohr and Sommerfeld gave way to the matrix mechanics of Heisenberg and others, and to the wave mechanics of Schrödinger. It then turns to the emergence of statistical transformation theory and the Hilbert space formalism unifying these two forms of the new quantum theory. It uses the metaphor of an arch built on a scaffold to capture these developments. The volume provides detailed analyses of the classic papers of Heisenberg, Born, Jordan, Pauli, Dirac, De Broglie, Einstein, Schrödinger, von Neumann, and others, which helped to lay the foundations of modern quantum mechanics. Drawing on correspondence and later reminiscences of these authors and synthesizing much of the extensive secondary literature on the breakthrough to modern quantum mechanics in the mid-1920s, this volume presents an authoritative new account of the genesis of quantum mechanics.
Abstract This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.
The most discussed of ``live'' metaphors in physical sciences is that of the Schrödinger cat. Introduced in the early, but mature days of the new quantum theory, in 1935, the parable of the cat has provoked and enlivened debates on the meaning of the quantum theory, on the ontology of the quantum wavefunction, on the puzzle of the collapse of the wavefunction, on the meaning of quantum measurement, and on the boundary between the quantum world and the classical world. In this article, I will discuss these issues of the quantum theory focussing on various aspects of the metaphor of the Schrödinger cat.
In this monograph I present the basic structure of an interpretation of quantum mechanics. Chapter 1 outlines the central ideas behind the interpretation and illustrates them by means of examples: Subsequent chapters fill in the details of the interpretation. But it is important to begin by explaining what I take an interpretation of quantum mechanics to be, and why any further interpretation needs to be offered. After all, quantum mechanics (in some form) is by now both a foundation for much of contemporary physics and a veteran of more than sixty years of intermittent but sometimes intense reflection on its content and meaning. What more can be, or should be, said about the interpretation of this theory? Many physicists believe that no more needs to be said: that there is basically only one way of understanding quantum mechanics, due to Bohr, Heisenberg, Pauli, and others, and that the only remaining interpretative task is that of the physics teacher, who seeks to perfect ways of conveying this understanding to new generations of students. Sir Rudolf Peierls, one of the more lucid and distinguished of these physicists, even objects to the use of the familiar term ‘Copenhagen interpretation’ to refer to the way of understanding quantum mechanics due to Bohr, Heisenberg, Pauli, and others. Because this sounds as if there were several interpretations of quantum mechanics. There is only one. There is only one way in which you can understand quantum mechanics.[…]
The report by Born and Heisenberg on ‘quantum mechanics’ may seem surprisingly difficult to the modern reader. This is partly because Born and Heisenberg are describing various stages of development of the theory that are quite different from today's quantum mechanics. Among these, it should be noted in particular that the theory developed by Heisenberg, Born and Jordan in the years 1925–6 and known today as matrix mechanics (Heisenberg 1925b [1], Born and Jordan 1925 [2], Born, Heisenberg and Jordan 1926 [4]) a differs from standard quantum mechanics in several important respects. At the same time, the interpretation of the theory (the topic of Section II of the report) also appears to have undergone important modifications, in particular regarding the notion of the state of a system. Initially, Born and Heisenberg insist on the notion that a system is always in a stationary state (performing quantum jumps between different stationary states). Then the notion of the wave function is introduced and related to probabilities for the stationary states. At a later stage, probabilistic notions (in particular, what one now calls transition probabilities) are extended to arbitrary observables, but it remains somewhat unclear whether the wave function itself should be regarded as a fundamental entity or merely as an effective one. This may reflect the different routes followed by Born and by Heisenberg in the development of their ideas. The common position presented by Born and Heisenberg emphasises the probabilistic aspect of the theory as fundamental, and the conclusion of the report expresses strong confidence in the resulting picture.
Quantum mechanics is a most intriguing theory, the empirical success of which is as great as its departure from the basic intuitions of previous theories. Its history has attracted much attention. In the 1960s, three leading contributors to this history, Thomas Kuhn, Paul Forman, and John Heilbron, put together the Archive for the History of Quantum Physics (AHQP), which contains manuscripts, correspondence, and interviews of early quantum physicists. In the same period, Martin Klein wrote clear and penetrating essays on Planck, Einstein, and early quantum theory; and Max Jammer published The Conceptual Development of Quantum Mechanics , still the best available synthesis. Since then, this subfield of the history of science has grown considerably, as demonstrated in accounts such as the five-volume compilation by Jagdish Mehra and Helmut Rechenberg; the philosophically sensitive studies by Edward MacKinnon, John Hendry, and Sandro Petruccioli; Bruce Wheaton’s work on the empirical roots of wave-particle dualism; my own book on the classical analogy in the history of quantum theory; and a number of biographies. These sources nicely complement one another. There have been, however, a couple of bitter controversies. Historians notoriously disagree about the nature of Planck’s quantum work around 1900. Whereas Klein sees in it a sharp departure from classical electrodynamics, Kuhn denies that Planck introduced any quantum discontinuity before Einstein. Here I take Kuhn’s side, although it follows from Allan Needell’s insightful dissertation that neither Klein nor Kuhn fully identified Planck’s goals.