Abstract
Today, many physicists use the expressions ‘particle’ and ‘field’ more or less synonymously. This is an obvious consequence of the transformations of the particle concept discussed in the last chapter. Particle physics started from the classical particle concept and arrived at a group theoretical concept which deals with the conserved dynamic quantities of fields. The quantum particles discussed in Sects. 6.2 and 6.4 are neither particles nor fields in a classical sense. They have wavelike and particle-like features. Quantum mechanical systems are described in terms of plane waves and more or less sharply localized wave packets. Quantized fields may be either in a sharp number state or in a state of well-defined phase but not in both states at once. For photons, the coherent states with minimum unsharpness of occupation number and phase are closest to the description of a classical field.
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References
See Wheaton 1983, 286–301.
See Sect. 3.2.2 and Wheaton 1983, 279–281, but also Greenstein and Zajonc 1997, 23–35, and my remarks at the end of Sect. 3.2.2.
Bohr et al. 1924. Bohr worked on this theory after Einstein had received the Nobel prize for the light quantum hypothesis. See Jammer 1966, 183–187; Wheaton 1983, 281; Beller 1999. The role of the BKS theory in the development of Bohr’s thought is investigated in Pringe 2006.
Bohr 1928. See Sect. 7.2.2.
Planck 1901, Einstein 1905.
Einstein 1917, de Broglie 1923.
Davisson and Germer 1927. For an early visualization of wave-particle duality see Fig. 1.2 in Sect. 1.5, where the magnetic deflection of electron diffraction is shown.
Von Neumann 1932.
Born 1926b, 803. My translation. Here, ‘guiding field’ is the literal translation of ‘Führungsfeld’.
Jammer 1974, 41.
Bohm 1952.
Hughes 1989, 302, following the ‘latency’ interpretation Margenau 1954.
Born 1926a, 51; translation from Wheeler and Zurek 1983, 54. See the full quotation in Sect. 6.1.
According to Howard 2002, however, what is today called the Copenhagen interpretation is due to Heisenberg, whereas Bohr’s own view is just the complementarity view.
See Meyer-Abich 1965, Falkenburg 1998, Pringe 2006.
A careful analysis is found in Scheibe 1971, 29–35. See also Meyer-Abich 1965; Murdoch 1981; Folse 1985. Greenstein and Zajonc 1997 give a short systematic account in the context of quantum optics.
Bohr 1937 and later writings; see Scheibe 1971, 31–32; or Redhead 1987, 50: “Complementarity is a relationship that exists between mutually exclusive QM phenomena. Although complementary phenomena cannot occur simultaneously, their mutual possibility is necessary for the complete description of quantum-mechanical reality.” However, at least implicitly this is already assumed in the Como lecture.
Bohr 1928, 90.
Bohr 1928, 92.
Bohr 1928, 91. Here, Bohr considers the wave and particle descriptions of free subatomic particles to be complementary. This is on the lines of the Planck-Einstein and Einstein-de Broglie relations.
Bohr 1928, 92–94; equations (1) on p. 92 and (2) on p. 94.
There is no time operator in quantum mechanics. The only formal relation ΔEΔν ≥ h which can be derived in a quantum theory holds for the line width and the lifetime of unstable quantum states. The derivation requires quantum field theory. For a more detailed discussion, see Messiah 1969, Sect. 4.2.4.
Bohr 1928, 95. The sense of’ symbolic’ in Bohr’s views is clarified in Pringe 2006.
Bohr 1928, 90.
Bohr 1928, 94.
Bohr 1928, 91. In addition, it can be shown in detail that he considered the complementarity between spatio-temporal and causal description as a rational generalization of Kant’s account of physical reality. See Pringe 2006.
Other complementarities which do not directly concern wave-particle duality have to be added (see Bohr 1928 and Pringe 2006): the possibilities of defining physical objects and measuring their properties; Schrödinger’s wave mechanics and Heisenberg’s matrix theory: “Indeed, the two formulations of the interaction problem might be said to be complementary in the same sense as the wave and particle idea in the description of the free individuals” (Bohr 1928, 111); and more.
In the Como lecture, Bohr only mentions Born’s probabilistic interpretation but he claims that “wave mechanics just as the matrix theory [...] represents a symbolic transcription of the problem of motion of classical mechanics adapted to the requirements of quantum theory and only to be interpreted by an explicit use of the quantum postulate” (Bohr 1928, 586; my emphasis).
Heisenberg 1927, 174–175 and 198. See also Heisenberg 1930b, 21–23. In contradistinction to Bohr’s Como lecture, Heisenberg’s paper makes use of the probabilistic interpretation in the statistical calculation of a particle track (Heisenberg 1927, 186–188).
Bohr 1949; Feynman et al. 1965, 1-4–1-9. From these thought experiments emerged the recent which-way experiments of quantum optics; see Scully et al. 1991 and Sects. 7.4–7.5.
Heisenberg 1930a, 4; my translation. The English version is much shorter here. It does not contain any explanation of the particle concept; see Heisenberg 1930b, 4.
Heisenberg 1930b, 10; similarly, Heisenberg 1930a, 7.
Born 1926a,b; von Neumann 1932.
Bohr 1928; Heisenberg 1930; Einstein et al. 1935; Bohr 1935; Bohr 1949. According to Howard 2002, in addition Heisenberg’s post-war views about the measurement process were decisive for what was finally called ‘the’ Copenhagen interpretation.
Clifton and Halvorson 2002.
Von Neumann 1932.
See Einstein et al. 1935.; Aspect 1982.
Born 1926b, 803.
See Dürr 2006.
The double-slit experiment with single electrons is, e.g., reported in Greenstein and Zajonc 1997, 1–7.
Grangier et al. 1986. For a discussion of different single photon light sources, see Greenstein and Zajonc 1997, 32–35.
Keller et al. 2004.
Pfleegor and Mandel 1967. See Greenstein and Zajonc 1997, 43 (the nice title “Two Lasers, One Photon” of this paragraph is taken from there) and the discussion there, 43–53.
Dirac 1958, 4–7. A nice computer simulation can be found at http://www.physik.uni-muenchen.de/didaktik/Computer/interfer/.
See Walls and Milburn 1994, 51–52; Busch et al. 1995, 9–10 and 177–180.
Remember Born’s remark in Born 1926a, quoted in Sect. 7.2.
Heisenberg 1927, 174–175 and 1930b, 21–23.
See Bohr 1949.
Einstein et al. 1935. Bohr’s reply in 1935 was primarily philosophical. For the simple reason that it was too hard to understand, it did not convince any physicist opposed to Bohr’s views.
Bohr 1949, 215–216. By the way, this is one of the few probabilistic arguments in Bohr’s reasoning.
Feynman et al. 1965, 1-4–1-9.
Aspect et al. 1982. See also Greenstein and Zajonc 1997, Chap. 2.
Scully et al. 1991.
Scully et al. 1991, 113, referring to Englert et al. 1990. The claim that Heisenberg’s uncertainty relation is not therefore employed in wave-particle duality gave rise here to a debate within quantum optics; see below.
Scully et al. 1991, 111.
Scully et al. 1991, 114. They emphasize that the micromasers will not serve as which-way detectors if they contain classical microwave radiation with a large average photon number N and the associated fluctuations of √N ≫ 1; ibid.
In comparison to Scully et al. 1991, 113–115, the following technical details are omitted: the wave function of the internal state of the atom which does not add any new terms to the sums below in (7.8–7.11); the assignment of the field states to the cavities 1 and 2 which must be symmetrized in the end (here, the field states are simply given in terms of occupation numbers); and the probability density of the entangled detector-screen states which describes the correlations of photon detection in the cavity wall and atom detection on the screen.
Scully et al. 1991, 115.
The antisymmetric part of the wave function of the detector atom (which does not couple to the photon field states of the cavities) is entangled with ∣ΨPM〉 in such a way that anticorrelations between the screen and the photon detector and corresponding antifringes are measured; see Scully et al. 1991, 115, and the discussion in Sect. 7.5. The original double slit wave function would be re-established by simply removing the wall between the cavities. This requires another experimental arrangement, namely an opening between the cavities and a shutter which can be closed. Such an arrangement would give rise to another kind of quantum eraser which is similar to the polarization experiment discussed in Sect. 7.3 rather than to the EPR correlations.
This point is emphasized several times in the paper; see Scully et al. 1991, 111; 113, where the calculations concerning the negligible momentum transfer are reported; and 114, where they “emphasize once more that the micromaser welcher weg detectors are recoil-free; there is no significant change in the spatial wave functions of the atoms,” before they come to explain the quantum eraser.
Einstein et al. 1935.
Scully et al. 1991, 114, after Jaynes 1980.
Scully et al. 1991, 111. For a related discussion of the following topics, see also Busch and Lahti 2005; Shillady and Busch 2006.
Bohr 1949, 225–226; Feynman et al. 1965, 1-4–1-9; Heisenberg 1927; 1930a, 15; 1930b, 21.
Scully et al. 1991, 111.
Ibid.
Scully et al. 1991, 112.
Feynman et al. 1965, 1–9.
Scully et al. 1991, 112., referring to Scully et al. 1989, Scully and Walther 1989, and Englert et al. 1990.
Scully et al. 1991, 114.
Scully et al. 1991, 112; see above.
Storey et al. 1994, 626.
Storey et al. 1994, 627.
Storey et al. 1994, 627. See also the above discussion of Bohr 1928 in Sect. 7.2.2.
Englert et al. 1995, 367–368. Indeed, Scully et al. 1994 do not suggest any position measurement in the sense of Storey et al. 1994. As they emphasize in Englert et al. 1995, they propose to place the micromaser cavities before the double slit, in order to avoid precise position measurements.
Storey et al. 1995, 368.
See Wiseman and Harrison 1995.
Wiseman and Harrison 1995.
Scully et al. 1991; see above.
See Englert 1998. The experiment is Dürr et al. 1998a,b, Dürr and Rempe 2000a, discussed in Sect. 7.4. Englert 1998 gives a short report of the experiment and the debate. Obviously, he includes Wiseman and Harrison 1995 amongst the opponents of the claim that the proposed experimental scheme aims at path information without substantial momentum transfer.
Robertson 1929.
Dürr and Rempe 2000b, 1022.
Mittelstaedt et al. 1987. A which-way experiment with path information and incomplete quantum erasure has the same effect; see Dürr et al. 2000a, 60–65.
Busch et al. 1995.
Mittelstaedt et al. 1987. See also Dürr et al. 1998b, Dürr and Rempe 2000b.
Englert 1996.
Dürr et al. 1998b, 5705, claim that |w1 − w2| gives rise to “an a priori WW [=which-way, B.F.] knowledge due to the difference between the probabilities, w+ and w−, that the particle takes one way or the other.”
Englert 1996; Dürr et al. 1998a,b; Dürr and Rempe 2000b; Scully et al. 1991.
Englert 1996, Jaeger et al. 1995.
Dürr et al. 2000b, 64: “Note that the distinguishability (as well as the visibility) is an ensemble property.”
Englert 1996, Jaeger et al. 1995.
Dürr and Rempe 2000b.
Ibid.
Dürr and Rempe 2000b, 1023–1024.
Zou et al. 1990; based on the proposals Scully and Drühl 1982, Zajonc 1983. The experiment is discussed in Greenstein and Zajonc 1997, 206–209. Another realization of Scully and Drühl 1982 is Kim et al. 1999.
Greenstein and Zajonc 1997, 208–209.
Dürr et al. 1998a,b, 2000a. In the following, all technical details are omitted.
Dürr et al. 2000a, 57.
Dürr and Rempe 2000a, 55.
Walborn et al. 2003, 341.
Walborn et al. 1993, 343.
Afshar 2003.
This point is also criticized in Kastner 2005, 653.
In his note 23, Afshar attributes this idea to Wheeler, but this seems hardly compatible with Wheeler’s views, e.g., expressed in Wheeler 1979–1981.
Dirac 1958, 9.
Einstein et al. 1935.
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(2007). Wave-Particle Duality. In: Particle Metaphysics. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33732-4_7
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