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Cambridge University Press eBooks

Wave-particle duality

Dugald R. Murdoch

Published Nov 5, 1987• 0 citations
Publisher

Abstract

Niels Bohr's theory of complementarity was an attempt to solve the enormous problems of interpretation – especially the problem of wave particle duality – that beset the quantum theory in the mid-twenties. By 1920 electromagnetic radiation could be conceived of either in terms of the wave model or in terms of the particle model, though neither conception alone was wholly adequate to the empirical data. By the mid-twenties the duality problem was quite general, applying to matter as well as to radiation. Quantum mechanics, the new quantum theory, could be interpreted partially in terms of one or other of the two models but not comprehensively in terms of either. Bohr's theory can be fully understood only against the background of the interpretative problems which it was intended to solve; and the root of these problems goes back to the very origin of the quantum theory, viz. the quantum hypothesis to the effect that in certain physical processes energy is transferred discontinuously in discrete amounts. Wave-particle duality was a development of the continuity-discontinuity duality which the quantum hypothesis introduced into physics. How did wave-particle duality arise?

DOI
10.1017/cbo9780511564307.003

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arXiv:2303.15185•Quantum•Oct 11, 2023•3 citations
Niels Bohr's theory of complementarity was an attempt to solve the enormous problems of interpretation – especially the problem of wave particle duality – that beset the quantum theory in the mid-twenties. By 1920 electromagnetic radiation could be conceived of either in terms of the wave model or in terms of the particle model, though neither conception alone was wholly adequate to the empirical data. By the mid-twenties the duality problem was quite general, applying to matter as well as to radiation. Quantum mechanics, the new quantum theory, could be interpreted partially in terms of one or other of the two models but not comprehensively in terms of either. Bohr's theory can be fully understood only against the background of the interpretative problems which it was intended to solve; and the root of these problems goes back to the very origin of the quantum theory, viz. the quantum hypothesis to the effect that in certain physical processes energy is transferred discontinuously in discrete amounts. Wave-particle duality was a development of the continuity-discontinuity duality which the quantum hypothesis introduced into physics. How did wave-particle duality arise?
Bohr's response in 1925 to the failure of the Bohr–Kramers–Slater theory was, as we have seen, to regard wave–particle duality as having a formal, rather than realistic, significance; he saw it as a ‘limitation of our usual means of visualization’. That same year, however, wave–particle duality was generalised by Louis-Victor de Broglie to cover the theory of matter. Moreover, the advent of quantum mechanics (i.e. matrix mechanics and wave mechanics), rather than dispelling the duality problem, heightened it. How did Bohr respond to these new developments in the quantum theory? A matter of waves In the autumn of 1923 de Broglie put forward the extremely bold hypothesis that any particle whatever is associated with a wave whose wavelength λ and frequency ν are proportional to the particle's momentum and energy respectively: λ = h / p , v = E / h . De Broglie regarded his hypothesis as the basis of a new mechanics, a wave mechanics related to classical mechanics in the same way as wave optics is related to ray optics. On this view the trajectory of a particle corresponds to the ray of the wave associated with it (i.e. the normal to the equiphase surface of the wave), and the velocity of the particle corresponds to the group velocity of the wave. De Broglie suggested, moreover, that in certain circumstances particles should exhibit diffraction effects: a stream of electrons, for example, which passes through a slit in a screen should undergo diffraction.
Bohr's general thesis of complementarity conveys the idea that we can, and perhaps must, make use of the classical physical concepts in quantum physics, notwithstanding the inadequacies of these concepts; but we can use them only within the limits circumscribed by the quantum of action – beyond these limits the classical concepts cease to be well defined. This idea originated in his thesis that the conceptual structure of the quantum theory is in a sense a generalisation of the conceptual scheme of classical mechanics; and this thesis was a corollary of the correspondence principle. During the first months of 1927 Bohr regarded quantum mechanics as the quantum-theoretical generalisation of classical mechanics to which he had been looking forward. He came also to think that quantum mechanics required in a sense the generalisation of the two classical models of particle and wave. In classical physics these two models generally pertain to different theories, the particle model to the mechanical theory of matter, the wave model to the electromagnetic theory of radiation. In quantum physics, however, the two models pertain to one theory, quantum mechanics, and each is applicable to matter and radiation. Where discontinuity obtains, the standard classical models of matter and radiation cease to be well defined, and the alternative, non-standard models may be used. There is no logical inconsistency in this dual use of the models since each is appropriately applicable only in different empirical circumstances.
What was Bohr's response to the problem of wave-particle duality? Before considering this question in detail it will be useful to survey briefly Bohr's work in physics between 1911 and 1923. Bohr and the ‘old’ quantum theory In 1911 Bohr completed his doctoral dissertation on the classical electron theory of metals. Developed by Sir J.J. Thomson and Lorentz, the theory explained electrical, magnetic and thermal properties of metals in terms of the motions of free electrons. Although Bohr made no use of the quantum hypothesis in his dissertation, he noted that classical electrodynamics was incapable of explaining Planck's radiation law and entailed the ultraviolet catastrophe. After completing his dissertation Bohr pursued his post-graduate studies under Thomson at Cambridge University. Finding that Thomson was little interested in his work, Bohr went on to Manchester University in March 1912, to work under Ernest Rutherford. Bohr's move to Manchester was very opportune: the quantum hypothesis was just beginning to receive a wider recognition, thanks largely to the first Solvay Conference in 1911, which Rutherford attended; Rutherford's laboratory, moreover, was one of the most active centres in the investigation of radio-activity. In order to explain the results of experiments on the passage of alpha and beta particles through matter Rutherford had revived Hantaro Nagaoka's (1904) planetary model of the atom. On this model an atom consists of a positively charged nucleus which is orbited by negatively charged electrons, the number of which corresponds to the number of charges on the nucleus.
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.