Early Mental Models

Hentschel, Klaus

doi:10.1007/978-3-319-95252-9_4

Klaus Hentschel³

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Abstract

The mental models by early actors are presented. Sect 4.1 discusses Isaac Newton’s “globuli of light” along with amendments by some of his important adherents; the next two sections cover Einstein’s mental model of light quanta around 1909 as singularities in the radiation field, along with his doubts about it 1910–15. Sects. 4.4–4.6 review the mental models of three influential experimental physicists: Johannes Stark’s light quanta, J.J. Thomson’s model of hard x rays, and W.H. Bragg’s neutral pair model for -rays. Sect. 4.7 treats the mental model argued by Planck, Peter Debye and Arnold Sommerfeld to relegate the quantization of energy and momentum to the material resonators in a black body. Sect. 4.8 deals with Gilbert Lewis’s mental model of photons by which this American physical chemist introduced the term ‘photon’ in his reflections about the temporal symmetry between emission and absorption but still attaching to it the completely wrong notion of photon number being conserved.

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Notes

1.
For further examples and for a methodological discussion, cf. Gentner and Stevens (1983).
2.
Newton’s complex methodology is discussed by Harper (2011) and Achinstein (2013) with further literature cited there.
3.
MS Add. 3996, Cambridge University Library, Cambridge, UK, fol. 104v, on-line at http://www.enlighteningscience.sussex.ac.uk/view/texts/normalized/THEM00092 ; cf. ibid., fol. 98r and Herivel (1965) p. 122 for an exact hydrodynamical analogue to the above sketch: a sphere with water flowing around it with a head wave in front (right) and eddies behind (left).
4.
The above quotations are taken from Newton’s Questiones, dated 1664–65 in the critical edition of this notebook ed. by J.E. McGuire and Martin Tamny, Cambridge Univ. Press, 1983, pp. 384–385.
5.
For details see Newton (1675a) pp. 256ff., resp., (1675b) pp. 186ff.; furthermore Hall (1993), Sepper (1994), Shapiro (2009).
6.
See Hentschel (2001) on Snel’s discovery of the law of refraction.
7.
See Cantor (1983), Eisenstaedt (2007) and standard histories of optics such as Park (1997) or Darrigol (2012) as well as here Sect. 3.1.
8.
See his collected papers (CPAE). Initially a comprehensive publication of all of Einstein’s surviving letters, the later volumes are unfortunately becoming increasingly selective for reasons of economy.
9.
Einstein (1909a) quote on p. 499 (CPAE, vol. 2, doc. 60, transl. ed., p. 394). And similarly, in the subsequent discussion to Einstein (1909a) p. 826 (CPAE, vol. 2, doc. 61). In a letter to Sommerfeld on 29 Sep. 1909 (CPAE, vol. 5, transl. ed., p. 135), Einstein writes analogously not about particles but about an “arrangement of light energy around discrete points moving with the speed of light.”
10.
Heinrich Kayser’s memoirs (1936), ed. by Matthias Dörries and K. Hentschel in 1996, pp. 228f., or pp. 250f. of the original typescript.
11.
Einstein (1909ab) pp. 499–500 (CPAE, vol. 2, transl. ed., p. 394). Kojevnikov (2002) pp. 188ff., interprets these passages as a mental extension of the nonmechanical, noncorpuscular conception of electrons by Lorentz. I rather view them as anticipating quantized field theories. ‘Undulatory’ generally means wave-shaped with the meaning here of “described by Maxwell’s equations.”
12.
Max Planck discussing Einstein (1909aa) p. 825 (CPAE, vol. 2, doc. 61, transl. ed., quotes on pp. 395 and 396).
13.
Einstein (1909a) pp. 825, 826 original emphasis (CPAE, vol. 2, doc. 61, transl. ed., p. 396).
14.
Einstein (1909a) p. 826 (CPAE, vol. 2, doc. 61, transl. ed., p. 397). For Stark’s reaction to this, see Sect. 4.4 below.
15.
A. Einstein to H.A. Lorentz, 27 Jan. 1911, CPAE, vol. 5, doc. 250, p. 276 (transl. ed., p. 175).
16.
See, e.g., Lorentz to Einstein, 6 May 1909, CPAE, vol. 5, doc. 153, Kox (2008) as well as Lorentz (1910a) pp. 354–355 and Lorentz (1910b) p. 1249. Such coherence lengths of trains of interfering waves can currently be made to measure some meters with modern lamps; ones with lasers can be kilometers long. That’s a far cry from ‘point shaped.’
17.
Lorentz to Einstein, 6 May 1909, CPAE, vol. 5, doc. 153, p. 174 (transl. ed., p. 110), original emphasis. He was to be proven right with the former but not with the latter.
18.
Ibid., doc. 153, p. 176 (transl. ed., p. 112), original emphasis. The draft of this letter (Einstein archives, EA 16-417) states in Dutch: “Deze bezwaren jammer want theorie lichtquanta wel mooi.” On Vaihinger’s fictionalism and its application in physics, see Hentschel (1990) sec. 4.4, Hentschel (2014a) and the primary sources cited there.
19.
See, e.g., Lorentz (1910a) p. 354: “The aforesaid ought to suffice to show that there can be no question of light quanta which while propagating remain concentrated within small spaces and always undivided.”
20.
Prior to this, Einstein described Lorentz to others in glowing terms, such as, in his letter to Jakob Laub on 17 May 1909, CPAE, vol. 5, doc. 160, p. 187 (transl. ed., p. 119): “H.A. Lor[entz] and Planck. The former is an amazingly profound and at the same time lovable man.”
21.
A. Einstein to J. Laub, 4 Nov. 1910, CPAE, vol. 5, doc. 231, pp. 260–261 (transl. ed., p. 166), original emphasis. Cf. Einstein to Laub, 27 Aug. 1910, ibid., doc. 224, p. 254 (transl. ed., p. 162): “I have not made any progress regarding the question of the constitution of light. There is something very fundamental at the bottom of it.”
22.
Einstein to Besso, 13 Mai 1911, in Speziali (1972) pp. 19–20, resp. CPAE 5, doc. 267, p. 295, our translation.
23.
Einstein (1911/12) p. 347 (CPAE, vol. 3, doc. 26, transl. ed., p. 419) and the discussion, p. 359 (doc. 27, transl. ed., p. 431). The German translation of these French proceedings appeared late, in 1914.
24.
Sommerfeld (1911a) p. 31.
25.
Millikan (1913) pp. 132–133; similarly in Millikan (1916a) p. 384: “Einstein himself, I believe, no longer holds to it.”
26.
Einstein (1916a, b) is discussed further in Sect. 3.9.
27.
Einstein (1916a) p. 322 (CPAE, vol. 6, doc. 34, transl. ed., pp. 215–216).
28.
Albert Einstein to Michele Besso, 9 Mar. 1917, in Speziali (1972) p. 103 (CPAE, vol. 8, doc. 306, transl. ed., p. 293).
29.
Albert Einstein in a letter to Michele Besso, 12 Dec. 1951, in: Speziali (1972) p. 453 (transl. in Hentschel and Grasshoff (2005) p. 60).
30.
On Stark’s career and complicity in the Nazi regime, see Hoffmann (1982), Kleinert (1983), Hentschel (1996) and Eckert in Hoffmann and Walker (2007).
31.
This early contact between Stark and Einstein is covered by Hermann (1969/71), see also CPAE, vols. 1–2.
32.
Johannes Stark in the discussion following Einstein (1909a) on p. 826, resp. CPAE, vol. 2, doc. 61, p. 586 (transl. ed., p. 397).
33.
Ibid. Thereupon Einstein developed his hypotheses about singularities surrounded by vector fields already described above in Sect. 4.2.
34.
Stark (1909a) p. 583. For consistency I have substituted \(\nu \) for Stark’s n for the frequency.
35.
Stark (1909a, b, 1910a, b).
36.
Stark (1908b, 1912a, b).
37.
Stark (1909b c, 1912c).
38.
Stark (1908b) p. 889 and Stark (1908a).
39.
On the latter, see Stark (1908c).
40.
Stark (1927, 1930).
41.
Stark (1909a) p. 584; cf. also the contrast set between a “pragmatic” and “dogmatic way of working” in Stark (1922) Chap. I and Stark (1950) Chap. VII, where the methodical opposition alluded to here is brought to a polemical extreme.
42.
Stark (1950) p. 22 in sec. II.5 headed: “Die Existenz von Lichtkörperchen” or in the motto on p. 5. Stark chose a more careful formulation on p. 50 (ibid.), however: as “merely a suggestion that might stimulate further observations” (“lediglich ein Vorschlag, der zu weiteren Beobachtungen anregen mag”). But this passage comes from a draft paper that Stark had subsequently incorporated into his final book. It had originally attempted to persuade his “dogmatic opponents”; hence it is rather strategic in character. Nevertheless, it shows how tactical Stark was to the very last—as far as the ontological status of “light vortices” was concerned (see below).
43.
Einstein (1912a) pp. 837–838 (CPAE, vol. 4, doc. 2, transl. ed., p. 94), directly quoted by Stark (1912a) p. 468.
44.
See Stark (1908a) p. 889: “It is in keeping with the fundamental importance of such a general principle as the light quantum hypothesis that it allow the prediction of new phenomena as well as allow one to recognize the importance of processes that had hitherto received little attention. [...] in the second part of the present communication an attempt is made to apply this [light-quantum] hypothesis to photochemistry for the first time, which application yields three fundamental photochemical laws.”
45.
Stark (1912a) p. 468; analogously also Stark (1909a) p. 583: “On the grounds of applications of the light-quantum hypothesis to experiments on x-rays, I arrive along a different route from Einstein’s, which is perhaps shorter and simpler, at the same conclusion as Einstein’s.”
46.
Einstein (1912c) p. 888 (CPAE 4, doc. 6, transl. ed., p. 125); further details in Stark (1908b).
47.
Stark (1912a) p. 496.
48.
See Hermann (1968).
49.
H. Nagaoka to E. Rutherford, 22 Feb. 1911, quoted after Stuewer (2014) p. 147.
50.
See Stark (1922) and the scathing book review by Max von Laue (1923a) p. 30 (transl. in Hentschel (1996) p. 7): “All in all, we would have wished that this book had remained unwritten, that is, in the interest of science in general, of German science in particular, and not least of all in the interest of the author himself.”
51.
See Stark (1927) p. 29 and Kleinert (2002) for further sources and related analyses. In a subsequent article in Annalen der Physik, Stark (1930) p. 687, Stark revealed that this concept “had been developed [...] out of the Newtonian idea of the light corpuscle.”
52.
Stark (1927) p. 33. These light and quantum vortices could be viewed as Stark’s graphic reinterpretation of photon and electron spin, which is conserved in emissive and absorptive processes. It is indicative that even Stark’s coworkers Robert Döpel and Rudolf von Hirsch refused to associate themselves with this manuscript and declined being named as coauthors: see Hirsch and Döpel (1928) and Kleinert (2002) p. 217.
53.
Stark (1950) pp. 61ff.
54.
Stark (1950) p. 22; analogously also ibid., p. 31 and pp. 62f.
55.
Ibid., p. 40. These passages remind one of Michael Faraday’s visual thinking.
56.
Ibid. pp. 41–50, which reproduces Stark’s eight-page manuscript, “Experimentelle Untersuchungen über die Natur des Lichtes,” for which he had been unable to find a publisher. At this time his improvised laboratory on his son’s farm in Eppenstatt had been requisitioned as housing for refugees. Stark had been expelled from his own property in Traunstein by Military Governor Thom in 1947 (ibid., p. 61).
57.
On this ‘Deutsche Physik’ group and its weak influence see, e.g., Hentschel (1996) pp. lxx–lxxvii, Hentschel (2005) pp. 90–95, Eckert in Hoffmann and Walker (2007) and Schneider (2015) along with the cited secondary sources. Lenard and Stark also served as scapegoats for the physics community’s bid of being otherwise uncensurable.
58.
See Millikan (1913) p. 130, Millikan (1916b) esp. p. 383.
59.
For these experimental findings see, e.g., Thomson (1903, 1908a), Barkla (1906, 1907, 1908a, b, 1910), W.H. Bragg (1907, 1908a, b, 1912/13), Sommerfeld (1911a), Millikan (1913) p. 128 and further primary citations there.
60.
Thomson (1893) pp. 4 and 43. On J.J. Thomson’s model of light and aether at this time, see McCormmach (1967), Navarro (2005), Bordoni (2009, 1890) and further primary sources cited there.
61.
Millikan (1913) pp. 130 and 133; analogously also Millikan (1916b) p. 383: “we must abandon the Thomson-Einstein hypothesis of localized energy [...] which seems at present to be wholly untenable.”
62.
See, e.g., Millikan (1916b) p. 383, (1917) p. 237, (1924) in his Nobel prize lecture, p. 61 and the quote on p. 64, furthermore in his autobiography from 1950.
63.
Curie (1904) p. 41.
64.
On W.H. Bragg’s background as an Australian trained in England who later immigrated permanently in 1909 after having returned home to Australia, and on his work, see Wheaton (1983) pp. 81ff., Jenkin (2004, 2007). See above in Sect. 3.3 about his opponent Barkla, whose experiments confirmed the polarizability of x-rays in 1905.
65.
For the first time in Bragg (1907) pp. 440f. These pairs of particles that Bragg occasionally also called ‘neutrons’ are not identical with what are currently being referred to by that name: those chargeless nuclear components also known as hadrons!
66.
Bragg (1912/13) p. vi: “the three forms of radiation [“\(\upalpha \), \(\upbeta \) and X or \(\upgamma \) rays”] differ in degree rather than in kind.” Cf. Bragg (1912/13) pp. IV–V, where he argued that from this aspect, no difference apart from wavelength existed between x-rays, \(\upgamma \)-rays and light.
67.
Bragg (1912) p. 106 the want of proof of diffraction is also discussed there.
68.
Bragg (1912) p. 138. Further analyses and references to Bragg’s corpuscular theory of x-rays and \(\upgamma \)-rays are provided by Stuewer (1971, 1975a) pp. 6–23 and Wheaton (1983) pp. 81ff.
69.
See, e.g., Bragg (1907, 1908a) p. 270.
70.
Barkla (1907) p. 662.
71.
See, e.g., Bragg (1908a) p. 270: “the kathode [sic] radiations from a given stratum of matter traversed by \(\upgamma \) rays possess momentum in the original direction of motion of the rays, and this shows that the rays are material.”
72.
The controversy between Sommerfeld and Stark on this point is discussed by Hermann (1968), and Wheaton (1983) pp. 116ff., 135ff.; see also the cited primary sources and correspondence there.
73.
See Pohl (1912) pp. VI, 18.
74.
On the former: Kleeman (1907) pp. 638, 662; the latter developed into \(\upgamma \)-spectroscopy.
75.
E. Regener, c. 1912, p. 103: ‘Die Strahlen der radioaktiven Substanzen,’ separate offprint of a chapter from an unidentifiable book, among Regener’s papers at the Archive of the University of Stuttgart. Similarly also in Regener (1915) p. 8: “In essence, so-called ‘\(\upgamma \)-rays are similar to roentgen rays.” Egon von Schweidler (1910) unsuccessfully tried to reach an experimental decision.
76.
Bragg (1912) pp. vi, 105f., Chap. XII; see similarly Bragg (1907) p. 442, Bragg and Marsden (1908a) pp. 938 and 670: “The x-rays resemble the \(\upgamma \) rays so closely that it is practically inconceivable that the two radiations should be essentially different.”
77.
Bragg (1912/13) p. 191.
78.
On this point see esp. Bragg and Marsden (1908a) p. 670, (1908b).
79.
Bragg (1912/13) pp. 192–193; cf. Bragg (1912/13) pp. 237f.
80.
See Rutherford and Andrade (1914a) and supplementarily Meitner (1922) p. 382.
81.
Bruce Wayne, an American plant physiologist at Cornell University who also developed some alternative models of his own, offers a good survey of the literature in Wayne (2009) pp. 23ff.
82.
Planck to Robert Williams Wood, 7 Oct. 1931, quoted by Hermann (1969/71b) p. 23. Cf. p. 14 above for the context of Planck’s research around 1900.
83.
See Ehrenfest (1911) p. 92.
84.
Planck to Robert Williams Wood, 7 Oct. 1931; cf. p. 14 above for a text-critical evaluation of the full quotation.
85.
On Planck’s second quantum theory, see Planck (1910b)–(1913), as well as Needell (1980), Whitaker (1985), Gearhart in Hoffmann (2010) p. 116 and Kragh (2014c).
86.
Debye and Sommerfeld (1913) p. 875.
87.
Debye and Sommerfeld (1913) p. 874 (original emphasis omitted).
88.
In this sense, see also Planck (1907), Sommerfeld (1911a).
89.
Debye and Sommerfeld (1913) p. 923; cf. further Niedderer (1982) p. 43.
90.
Sommerfeld (1909) p. 976.
91.
Millikan (1913) pp. 123–124 (original emphasis).
92.
Debye and Sommerfeld (1913) pp. 927–928.
93.
See Sects. 3.4, 3.5, 3.6 above and, e.g., Ramsauer (1914).
94.
See Debye (1909), von Laue (1914) as well as, e.g., the Wikipedia article on wave packets and Brandt and Dahmen (1985) pp. 20 ff. on their visualization.
95.
On this point see the exchanges of letters: H.A. Lorentz to E. Schrödinger 27 May 1926 and Schrödinger to Planck 31 May 1926 and to Lorentz 6 Jun. 1926, both exchanges reproduced in Przibram (1963), esp. pp. 9, 43–45 and 54.
96.
Schrödinger (1926b) p. 501, with reference to Debye (1909) and von Laue (1914).
97.
Schrödinger (1926b) p. 500, citing Debye (1909) and von Laue (1914).
98.
Schrödinger (1926a) pp. 59–60 and Schrödinger (1927b) on wave mechanics. Compare further Brandt and Dahmen (1985) Chaps. 3–4.
99.
See Schrödinger (1926b) and Schrödinger’s letter to Planck, 11 June 1926, in Przibram (1963) p. 14. The probability interpretation of the \(\Psi \)-function comes from Max Born (1926).
100.
The powerful influence of Schrödinger’s wave mechanics on the history of quantum mechanics generally is covered by Rechenberg (1982ff.) vol. 5, Darrigol (1986, 1992), also citing sources.
101.
Thus the programmatic title of Schrödinger (1926a).
102.
Compare Brandt and Dahmen (1985) pp. 40–49.
103.
Einstein (1927) p. 546, for instance, mentions “Hunderttausende oder Millionen von Schwingungen” as being necessary to generate the wave. Heisenberg (1927) showed that the relation between the duration \(\Delta t\) and the breadth of the energy spectrum \(\Delta E\) connected with his uncertainty relation, \(\Delta E \cdot \Delta t \ge \hbar \), demands very large times t in order to make the energetic uncertainty \(\Delta E\) and thus also the frequency uncertainty \(\Delta \nu \) sufficiently small.
104.
Lewis (1926c) p. 874. On Compton’s scattering experiments and Bothe & Geiger, see here pp. 126ff. and 131f.
105.
Lewis (1926c) p. 875.
106.
See Sect. 2.6 and further references there about its history and statistics.

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Section for History of Science and Technology, History Department, University of Stuttgart, Stuttgart, Baden-Württemberg, Germany
Klaus Hentschel

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Hentschel, K. (2018). Early Mental Models. In: Photons. Springer, Cham. https://doi.org/10.1007/978-3-319-95252-9_4

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DOI: https://doi.org/10.1007/978-3-319-95252-9_4
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