Abstract
Notwithstanding the broad philosophical implications of Niels Bohr’s thought reaching far beyond the confines of physics, quantum theory was from the beginning, and remains to be, the field of primary importance with which his idea of complementarity is concerned. Understanding of his thought therefore requires at least a brief survey of quantum physics as it historically developed in the early twentieth century. In this opening chapter, I wish accordingly to offer a sketch of the development of quantum theory – including the central role played by Bohr – within which his path toward the idea of complementarity is situated.
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Notes
- 1.
According to Thomas S. Kuhn, Planck’s change of vocabulary from “element” to “quantum” signals a change in meaning of the quantity hν “from a mental subdivision of the energy continuum to a physically separable atom of energy” (Kuhn 1978, 363, cf. 201).
- 2.
- 3.
Einstein suggested that the ‘photoelectric effect’ and some other light phenomena may be accounted for by the light-quantum hypothesis, although the photoelectric effect did not constitute his principal concern in this work (see 1905, 144ff.). See also Jammer (1989, 22), Kuhn (1978, 221), and Murdoch (1987, 5f.).
- 4.
Although since early modern times the nature of light was a controversial issue, it was in the nineteenth century that the wave theory of light became predominant by virtue of the discovery that light exhibits the phenomena of diffraction and interference. This wave theory of light was further developed by James Clerk Maxwell, whose theory of electromagnetism offered an elaborate account of light as an electromagnetic wave (see PWNB, 1:27). With the general acceptance of Maxwell’s theory, the wave nature of light appeared to be firmly established before the advent of quantum theory.
- 5.
Bohr stayed in Britain for postdoctoral research from 1911 to 1912. After working at J. J. Thomson’s laboratory in Cambridge, he transferred in early 1912 to Manchester University to work with Rutherford. See Pais (1991, 117–31).
- 6.
Niels Bohr, “On the Constitution of Atoms and Molecules,” The Philosophical Magazine 26 (1913): 1–25, 476–502, 853–75; reprinted in NBCW, 2:161–233.
- 7.
As Max Jammer comments, in the trilogy Bohr gives three different formulations of the quantum rule (Jammer 1989, 78ff.), the simplest of which assumes that “the ratio between the total energy, emitted during the formation of the configuration, and the frequency of revolution of the electron is an entire multiple of h/2.” In the case of a circular orbit, this is equivalent to the assumption that “the angular momentum of the electron round the nucleus is equal to an entire multiple of h/2π” (NBCW, 2:233; cf. 164f., 184f.). See also Darrigol (1992, 86ff.).
- 8.
Furthermore, the radiation mechanism in Bohr’s theory differs essentially from that in classical physics: According to classical electrodynamics, the basic frequency and the higher harmonics are emitted in one atomic process, while in Bohr’s theory every quantum frequency originates from a separate atomic transition. See Radder (1988, 130f.).
- 9.
In 1913, Bohr spoke of “the most beautiful analogi [sic] between the old electrodynamics and the considerations used in my paper.” Letter from Bohr to Rutherford, March 21, 1913 (NBCW, 2:584f.). Further, in 1917, he used the expression: “the formal analogy between the ordinary theory of radiation and the [quantum] theory” (NBCW, 3:100). See Chevalley (1995, 15).
- 10.
Bohr began to extend his idea of ‘agreement’ by combining it with generalized quantum conditions introduced by Sommerfeld in 1915 (see PWNB, 1:38).
- 11.
In Hans Radder’s account, the development of Bohr’s correspondence principle may be divided into three consecutive phases: the first (1913–1915), the second (1916–1922), and the third (1923–1925). While the initial form of correspondence as Bohr conceived it in the first phase concerned numerical agreement or “agreement of calculations,” he came in the second phase to assume also conceptual continuity between his quantum theory and the classical theories (Radder 1988, 129, 133; cf. 1996, 55).
- 12.
In 1923, Bohr characterized the correspondence principle as a “general law holding for all quantum numbers” (NBCW, 3:577).
- 13.
Niels Bohr, Hendrik A. Kramers, and John C. Slater, “The Quantum Theory of Radiation,” The Philosophical Magazine 47 (1924): 785–802; reprinted in NBCW, 5:101–18 as well as in van der Waerden (1967, 159–76). Kramers was Bohr’s assistant at his Institute for Theoretical Physics, while Slater made a short visit at the institute in early 1924 (see Murdoch 1987, 24f.). After being founded in 1921, the Institute for Theoretical Physics of Copenhagen University served as an international center of the research of quantum theory in which many foreign physicists stayed and collaborated with Bohr and with each other. See Pais (1991, 171).
- 14.
According to Radder, Bohr’s correspondence principle at this third and final stage assumes an agreement only for large quantum numbers, and a formal and numerical correspondence rather than a conceptual continuity between classical and quantum theories (Radder 1988, 140, 143). That is, this principle came again to concern a non-conceptual correspondence, but, unlike in the first stage, took on a formal character in distancing itself from intuitive space-time pictures. See also Radder (1996, 55f.).
- 15.
In this Bohr-Kramers-Slater paper, the authors still assumed a critical attitude toward the light quantum hypothesis by saying that, despite its “great heuristic value,” “the theory of light-quanta can obviously not be considered as a satisfactory solution of the problem of light propagation” (NBCW, 5:103).
- 16.
Bohr remarked: “Since now a unique coupling of atomic processes seems actually to be a fact even for radiation phenomena, the approach taken in this paper [based on the Bohr-Kramers-Slater theory] must probably be abandoned” (NBCW, 5:205).
- 17.
- 18.
See Jammer (1974, 91). Bohr further maintained that a generalization of classical electrodynamics would “require a fundamental revolution in the concepts upon which the description of nature has been based until now” (NBCW, 5:191/205).
- 19.
- 20.
Werner Heisenberg, “Über die quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,” Zeitschrift für Physik 33 (1925): 879–93; reprinted in Heisenberg 1984ff., A1:382–96; Eng. trans. “Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations,” in van der Waerden 1967, 261–76.
- 21.
Trans. van der Waerden (1967, 262).
- 22.
It was Max Born who realized that the multiplication rule for oscillator amplitudes found out by Heisenberg was nothing other than the basic rule for multiplying matrices. See Jammer (1989, 215).
- 23.
Bohr at the time considered de Broglie’s hypothesis of matter waves to be purely formal and devoid of realistic significance, just as Einstein’s theory of light quanta. It is not until 1927 that the idea of matter waves would be supported by Davisson and Germer’s experiments, which offered striking evidence of electron diffraction. See Murdoch (1987, 35f., 53).
- 24.
In the same year, 1926, Max Born offered an interpretation of the wave function ψ different from Schrödinger’s own. According to Born, the square of the wave function, |ψ|2, represents the probability of the associated particle’s presence. See Jammer (1989, 301ff.).
- 25.
Letter from Bohr to Schrödinger, December 2, 1926 (NBCW, 6:462f., on 462). See Murdoch (1987, 46). On the role of Bohr’s dialogue with Schrödinger in the formation of his idea of complementarity, see Catherine Chevalley’s “Introduction” to Bohr (1991, 17–147, on 66ff.). See also Beller (1999, 122ff.).
- 26.
Letter from Bohr to Einstein, April 13, 1927 (NBCW, 6:421/23).
- 27.
Letter from Bohr to Einstein, April 13, 1927 (NBCW, 6:418–21/21–24, on 419/21). Just before the quotation in the same letter, Bohr also wrote: “how intimately the difficulties of quantum theory are connected with the concepts or rather the words that are used in the customary description of nature, and which all have their origin in the classical theories.”
- 28.
In Bohr’s account, “the definition of every concept or rather every word presupposes the continuity of the phenomena and hence becomes ambiguous as soon as this presupposition cannot be upheld.” Letter from Bohr to Schrödinger, December 2, 1926 (NBCW, 6:462).
- 29.
Letter from Bohr to Einstein, April 13, 1927 (NBCW, 6:421/23).
- 30.
- 31.
Letter from Bohr to Schrödinger, December 2, 1926 (NBCW, 6:462). See Held (1994, 890).
- 32.
In 1925, commenting on the rise of matrix mechanics, Bohr said that “[i]n contrast to ordinary mechanics, the new quantum mechanics does not deal with a space-time description of the motion of atomic particles” (PWNB, 1:48; see Jammer 1974, 91).
- 33.
Werner Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Zeitschrift für Physik 43 (1927): 172–98; reprinted in Heisenberg (1984ff., A1:478–504); Eng. trans. J. A. Wheeler and W. H. Zurek, “The Physical Content of Quantum Kinematics and Mechanics,” in Wheeler and Zurek (1983, 62–84).
- 34.
According to some commentators, as is suggested by the title of the paper, Heisenberg here restored the notion of visualizablity or intuitiveness (Anschaulichkeit) – which he had once abandoned in 1925 – through a “subtle redefinition” of the term anschaulich (Camilleri 2009, 49; see Beller 1999, 49, 67ff.).
- 35.
In Heisenberg’s account, the change in the momentum of the electron “is the greater the smaller the wavelength of the light employed – that is, the more exact the determination of the position.” Since this change itself cannot be determined, “[a]t the instant at which the position of the electron is known, its momentum […] can be known up to magnitudes which correspond to that discontinuous change” (1984ff., A1:481; trans. Wheeler and Zurek 1983, 64).
- 36.
Trans. Wheeler and Zurek (1983, 64).
- 37.
Trans. Wheeler and Zurek (1983, 68).
- 38.
As Heisenberg recalled later, at the time he still considered Schrödinger’s wave mechanics “as an extremely useful tool for solving the mathematical problems of quantum mechanics, but not more” (1967, 102).
- 39.
In a letter from around the same period, Bohr noted that “the uncertainty mentioned is not only connected to the presence of discontinuities, but also to the very impossibility of a detailed description in accordance with those properties of material particles and light that find expression in the wave theory.” Letter from Bohr to Einstein, April 13, 1927 (NBCW, 6:418–21/21–23, on 421/23).
- 40.
See Heisenberg (1967, 106). Similar to his 1925 work on quantum mechanics, Heisenberg’s 1927 uncertainty paper also tends toward a positivist view of science according to which “physics should only formally describe the relation between perceptions” (1984ff., A1:503; cf. 480, 491). As we will see later on, this positivist idea was not shared by Bohr, although their positions were often confounded by others. It is also noteworthy that, as suggested by some commentors, the early Heisenberg’s positivist tendency may not so much constitute a definite philosophical commitment, but rather serve as a “post facto justification” of his approach to quantum mechanics (Camilleri 2009, 17; see also Beller 1999, 52ff.; Schiemann 2008, 45).
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Katsumori, M. (2011). Bohr and the Development of Quantum Theory: A Brief Review. In: Niels Bohr's Complementarity. Boston Studies in the Philosophy of Science, vol 286. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1748-0_1
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