Oxford University Press eBooks

3. Magic wand

J. L. Heilbron

Published Jan 23, 2020• 0 citations

Abstract

‘Magic wand’ refers to the ‘correspondence principle’ that Bohr devised and deployed to investigate the interface between quantum and ordinary (‘classical’) physics. The chapter covers various lines of work, some inspired by his approach and some independent of it, all of which confirmed its fertility. The mobilization of the international brotherhood of physicists for the Great War gave Bohr breathing space to develop the correspondence principle with the help of Hendrik Kramers, who had come to neutral Denmark to study with him, and in friendly competition with Arnold Sommerfeld, who made important formal extensions of the theory.

DOI: 10.1093/actrade/9780198819264.003.0003

Related papers

A Magic Wand

Helge Kragh

In a major work of 1918 (‘On the quantum theory of line-spectra’) Bohr reconsidered the general principles of quantum and atomic theory. Apart from reinterpreting his original theory, he introduced the correspondence principle as a crucial connection between quantum and classical physics. What was the nature of this principle and what role did it play in the understanding of atomic structure? In applying the new principle, Bohr and his assistant H. A. Kramers relied on Einstein’s radiation theory. Bohr used the correspondence principle as a selection principle, and Kramers showed how it could account quantitatively for the Stark effect. However, not all physicists appreciated the Copenhagen ‘magic wand’ and Bohr’s use of it. Sommerfeld was the most prominent of the sceptics, but not the only one. The chapter also briefly considers the role of the correspondence principle in the early phase of the new quantum mechanics.

Oxford University Press eBooksMay 17, 20120 citations

Quantum Physics

Suman Seth

This article discusses the history of quantum physics, beginning with an analysis of the process through which a community of quantum theorists and experimentalists came into being. In particular, it traces the roots and fruits of Max Planck’s papers in irreversible processes in nature. It proceeds by exploring the origin and subsequent development of Niels Bohr’s so-called ‘planetary model’ of the atom, focusing on the extension of the model by Arnold Sommerfeld and members of his school as well to Bohr’s use of his principles of correspondence and adiabatic invariance. It also considers the post-war years, as the problems of atomic spectroscopy sparked the development of new methodological approaches to quantum theory. Finally, it offers a history of the two distinct new forms of quantum mechanics put forward in the mid-1920s: Werner Heisenberg, Max Born, and Pascual Jordan’s matrix mechanics, and Erwin Schrödinger’s wave mechanics.

Oxford University Press eBooksJul 6, 20173 citations

From quantum mechanics toward quantum electrodynamics

Arthur I. Miller

Prior to and into the first decade of Niels Bohr's 1913 atomic theory, physicists dealt with physical systems in which the usual space and time pictures of classical physics were assumed trustworthy and so could be extrapolated to any sort of matter in motion, for example, electrons move like billiard balls and light behaves analogously to water waves. In the German scientific milieu this visual imagery was accorded a reality status higher than viewing merely with the senses and was referred to as ‘ordinary intuition [ gewöhnliche Anschauung ]’. Ordinary intuition is the visual imagery abstracted from phenomena that we have actually witnessed in the world of sense perceptions. The concept of ordinary intuition was much debated during 1923–27 by physicists like Niels Bohr, Werner Heisenberg, Wolfgang Pauli and Erwin Schrödinger, all of whom used this term with proper Kantian overtones, and all of whom lamented its loss in the new quantum mechanics. Ordinary intuition is associated with the strong causality of classical mechanics. According to the law of causality, initial conditions (position and velocity or momentum and energy) can be ascertained with in-principle perfect accuracy. Consequently any system's continuous development in space and time can be traced with in-principle perfect accuracy using Newton's laws of motion and conservation of energy and momentum. Any limitations to the accuracy of measurements are assumed not to be intrinsic to the phenomena, that is they are interpreted to be systematic measurement errors that ideally can be made to vanish.

Cambridge University Press eBooksJan 6, 19940 citations

The Correspondence Principle and theory choice in physics

Youssef Samadi Aliabadi

A conception of the Correspondence Principle which Bohr deployed implicitly in developing a new theory of atomic constitution in 1913, is made explicit through an extensive examination of his classic paper of that year. Arguments are considered which purport to show that the application of the principle must be restricted to few isolated cases. These arguments are either defused or rejected. In particular an extensive review of issues concerning the interpretation of Quantum Mechanics is made to counter the claims that an insurmountable conceptual gap exits between the tenets of this theory and those of Classical Mechanics which makes it logically impossible for the latter to be regarded as the 'limiting case' of the former. In the light of a particular interpretation adopted and defended, a proposal is made that suggests that the Hamilton-Jacobi formulation of Classical Mechanics, as well as Maxwell's electromagnetic theory, can be viewed as 'limiting cases' of Quantum Mechanics. Having established a case for the global validity of the requirement imposed on physics by the Correspondence Principle, it is then argued that this requirement is indispensable if a particular brand of realism is adopted for the interpretation of theories in physics. Taking on board the assumption that an ultimate theory exists which mirrors the underlying physical constitution of the world, it is subsequently argued that the intertheory order established by the global imposition of the principle in physics, can be used to solve the problem of rational theory choice for this brand of realism.

Jan 1, 19971 citation

Guiding Principles

Anthony Duncan A, Michel Janssen B

Abstract The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.

Aug 29, 20191 citation

5. The Correspondence Principle as an Intermediary Hypothesis

Slobodan Perović

As the chapter explains, the correspondence principle was gradually devised by Bohr as a constructive versatile intermediary hypothesis. It argues the principle was essential in developing and refining his full-scale model of the atom and connecting it with lower-level experimental hypotheses.

University of Chicago Press eBooksJan 1, 20210 citations