Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality
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Wave mechanics A version of quantum mechanics developed in 1926 by Erwin Schrödinger.
Wave packet A superposition of many different waves that cancel each other out everywhere except within a small confined region of space, allowing the representation of a particle.
Wave-particle duality Electrons and photons, matter and radiation, may behave either like waves or like particles depending upon the experiment performed.
Wavelength () The distance between two successive peaks or troughs of a wave. The wavelength of electromagnetic radiation determines which part of the electromagnetic spectrum it belongs to.
Wien’s displacement law Wilhelm Wien discovered in 1893 that as the temperature of a blackbody increases, the wavelength at which it emits the greatest intensity of radiation shifts to ever-shorter wavelengths.
Wien’s distribution law A formula discovered by Wilhelm Wien in 1896 that described the distribution of blackbody radiation in accordance with the experimental data then available.
X-rays The radiation discovered by Wilhelm Röntgen in 1895 for which he was awarded the first Nobel Prize for physics in 1901. X-rays were later identified as electromagnetic waves of extremely short wavelength, emitted when very fast-moving electrons strike a target.
Zeeman effect The splitting of spectral lines when atoms are placed in a magnetic field.
NOTES
PROLOGUE: THE MEETING OF MINDS
1 Pais (1982), p. 443.
2 Mehra (1975), quoted p. xvii.
3 Mehra (1975), quoted p. xvii.
4 Excluding the three professors (de Donder, Henriot and Piccard) from the Free University of Brussels invited as guests, Herzen representing the Solvay family, and Verschaffelt there in his capacity as the scientific secretary, then seventeen out of the 24 participants had already or would in due course receive a Nobel Prize. They were: Lorentz, 1902; Curie, 1903 (physics) and 1911 (chemistry); W.L. Bragg, 1915; Planck, 1918; Einstein, 1921; Bohr, 1922; Compton, 1927; Wilson, 1927; Richardson, 1928; de Broglie, 1929; Langmuir, 1932 (chemistry); Heisenberg, 1932; Dirac, 1933; Schrödinger, 1933; Pauli, 1945; Debye, 1936 (chemistry); and Born 1954. The seven who did not were Ehrenfest, Fowler, Brillouin, Knudsen, Kramers, Guye and Langevin.
5 Fine (1986), quoted p. 1. Letter from Einstein to D. Lipkin, 5 July 1952.
6 Snow (1969), p. 94.
7 Fölsing (1997), quoted p. 457.
8 Pais (1994), quoted p. 31.
9 Pais (1994), quoted p. 31.
10 Jungk (1960), quoted p. 20.
11 Gell-Mann (1981), p. 169.
12 Hiebert (1990), quoted p. 245.
13 Mahon (2003), quoted p. 149.
14 Mahon (2003), quoted p. 149.
CHAPTER 1: THE RELUCTANT REVOLUTIONARY
1 Planck (1949), pp. 33–4.
2 Hermann (1971), quoted p. 23. Letter from Planck to Robert Williams Wood, 7 October 1931.
3 Mendelssohn (1973), p. 118.
4 Heilbron (2000), quoted p. 5.
5 Mendelssohn (1973), p. 118.
6 Hermann (1971), quoted p. 23. Letter from Planck to Robert Williams Wood, 7 October 1931.
7 Heilbron (2000), quoted p. 3.
8 In the seventeenth century it was well known that passing a beam of sunlight through a prism resulted in the production of a spectrum of colours. It was believed that this rainbow of colours was the result of some sort of transformation of light as a result of passing through the prism. Newton disagreed that somehow the prism adds colour and conducted two experiments. In the first he passed a beam of white light through a prism to produce the spectrum of colours and allowed a single colour to pass through a slit in a board and strike a second prism. Newton argued that if the colour had been the result of some change that light had undergone by passing through the first prism, passing it through a second would produce another change. Alas he found that, no matter which colour was selected as he repeated the experiment, passing it through a second prism left the original colour unchanged. In his second experiment Newton succeeded in mixing light of different colours to create white light.
9 Herschel made his serendipitous discovery on 11 September 1800, but it was published the following year. The spectrum of light can be viewed horizontally and vertically, depending on the arrangement apparatus. The prefix ‘infra’ came from the Latin word meaning ‘below’, when the light spectrum was viewed as a vertical strip with violet at the top and red at the bottom.
10 The wavelengths of red light and its various shades lie between 610 and 700 nanometres (nm), where a nanometre is a billionth of a metre. Red light of 700nm has a frequency of 430 trillion oscillations per second. At the opposite end of the visible spectrum, violet light ranges over 450nm to 400nm with the shorter wavelength having a frequency of 750 trillion oscillations per second.
11 Kragh (1999), quoted p. 121.
12 Teichmann et al. (2002), quoted p. 341.
13 Kangro (1970), quoted p. 7.
14 Cline (1987), quoted p. 34.
15 In 1900, London had a population of approximately 7,488,000, Paris of 2,714,000, and Berlin of 1,889,000.
16 Large (2001), quoted p. 12.
17 Planck (1949), p. 15.
18 Planck (1949), p. 16.
19 Planck (1949), p. 15.
20 Planck (1949), p. 16.
21 Planck (1949), p. 16.
22 Heat is not a form of energy as is commonly assumed, but a process that transfers energy from A to B due a temperature difference.
23 Planck (1949), p. 14.
24 Planck (1949), p. 13.
25 Lord Kelvin had also formulated a version of the second law: it is impossible for an engine to convert heat into work with 100 per cent efficiency. It was equivalent to Clausius. Both were saying the same thing but in two different languages.
26 Planck (1949), p. 20.
27 Planck (1949), p. 19.
28 Heilbron (2000), quoted p. 10.
29 Heilbron (2000), quoted p. 10.
30 Planck (1949), p. 20.
31 Planck (1949), p. 21.
32 Jungnickel and McCormmach (1986), quoted p. 52, Vol. 2.
33 Otto Lummer and Ernst Pringsheim christened Wien’s discovery ‘the displacement law’ (Verschiebungsgesetz) only in 1899.
34 Given the inverse relationship between frequency and wavelength, as the temperature increases so does the frequency of the radiation of maximum intensity.
35 When the wavelength is measured in micrometres and the temperature in degrees Kelvin, then the constant is 2900.
36 In 1898 the Berlin Physical Society (Berliner Physikalische Gesellschaft), founded in 1845, changed its name to the German Physical Society (Deutsche Physikalische Gesellschaft zu Berlin).
37 The infrared part of the spectrum can be subdivided into roughly four wavelength bands: the near infrared, near the visible spectrum (0.0007–0.003mm), the intermediate infrared (0.003–0.006mm), the far infrared (0.006–0.015mm) and the deep infrared (0.015–1mm).
38 Kangro (1976), quoted p. 168.
39 Planck (1949), pp. 34–5.
40 Jungnickel and McCormmach (1986), Vol. 2, quoted p. 257.
41 Mehra and Rechenberg (1982), Vol. 1, Pt. 1, quoted p. 41.
42 Jungnickel and McCormmach (1986), Vol. 2, quoted p. 258.
43 Kangro (1976), quoted p. 187.
44 Planck (1900a), p. 79.
45 Planck (1900a), p. 81.
46 Planck (1949), pp. 40–1.
47 Planck (1949), p. 41.
48 Planck (1949), p. 41.
49 Planck (1993), p. 106.
50 Mehra and Rechenberg (1982), Vol. 1, p. 50, footnote 64.
51 Hermann (1971), quoted p. 23. Letter from Planck to Robert Williams Wood, 7 October 1931.
52 Hermann (1971), quoted p. 23. Letter from Planck to Robert Williams Wood, 7 October 1931.
53 Hermann (1971), quoted p. 24. Letter from Planck to Robert Williams Wood, 7 October 1931.
54 Hermann (1971), quoted p. 23. Letter from Planck to
Robert Williams Wood, 7 October 1931.
55 Heilbron (2000), quoted p. 14.
56 Planck (1949), p. 32.
57 Hermann (1971), quoted p. 16.
58 Planck (1900b), p. 84.
59 The numbers have been rounded up.
60 Planck (1900b), p. 82.
61 Born (1948), p. 170.
62 Planck was also pleased because he had devised a way of measuring length, time and mass using a new set of units that would be valid and easily reproducible anywhere in the universe. It was a matter of convention and convenience that had led to the introduction of various measuring systems at different places and times in human history, the latest being the measurement of length in metres, time in seconds, and mass in kilograms. Using h and two other constants, the speed of light c and Newton’s gravitational constant G, Planck calculated values of length, mass and time that were unique and could serve as the basis of a universal scale of measurement. Given the smallness of the values of h and G, it could not be used for practical everyday purposes, but it would be the scale of choice to communicate with an extraterrestrial culture.
63 Heilbron (2000), quoted p. 38.
64 Planck (1949), pp. 44–5.
65 James Franck, Archive for the History of quantum Physics (AHQP) interview, 7 September 1962.
66 James Franck, AHQP interview, 7 September 1962.
CHAPTER 2: THE PATENT SLAVE
1 Hentschel and Grasshoff (2005), quoted p. 131.
2 Collected Papers of Albert Einstein (CPAE), Vol. 5, p. 20. Letter from Einstein to Conrad Habicht, 30 June–22 September 1905.
3 Fölsing (1997), quoted p. 101.
4 Hentschel and Grasshoff (2005), quoted p. 38.
5 Einstein (1949a), p. 45.
6 CPAE, Vol. 5, p. 20. Letter from Einstein to Conrad Habicht, 18 or 25 May 1905.
7 CPAE, Vol. 5, p. 20. Letter from Einstein to Conrad Habicht, 18 or 25 May 1905.
8 Brian (1996), quoted p. 61.
9 CPAE, Vol. 9, Doc. 366.
10 CPAE, Vol. 9, Doc. 366.
11 Calaprice (2005), quoted p. 18.
12 CPAE, Vol. 1, xx, M. Einstein.
13 Einstein (1949a), p. 5.
14 Einstein (1949a), p. 5.
15 Einstein (1949a), p. 5.
16 Einstein (1949a), p. 8.
17 Oktoberfest started in 1810 as a fair to celebrate the marriage between the Bavarian Crown Prince Ludwig (the future King Ludwig I) and Princess Thérèse on 17 October. The event was so popular that it has been repeated annually ever since. It begins not in October, but September. It lasts sixteen days and ends on the first Sunday in October.
18 CPAE, Vol. 1, p. 158.
19 Fölsing (1997), quoted p. 35.
20 With 6 being the highest mark, Einstein received the following marks: algebra 6, geometry 6, history 6, descriptive geometry 5, physics 5–6, Italian 5, chemistry 5, natural history 5, German 4–5, geography 4, artistic drawing 4, technical drawing 4, and French 3.
21 CPAE, Vol. 1, pp. 15–16.
22 Einstein (1949a), p. 17.
23 Einstein (1949a), p. 15.
24 Fölsing (1997), quoted pp. 52–3.
25 Overbye (2001), quoted p. 19.
26 CPAE, Vol. 1, p. 123. Letter from Einstein to Mileva Maric, 16 February 1898.
27 Cropper (2001), quoted p. 205.
28 Einstein (1949a), p. 17.
29 CPAE, Vol. 1, p. 162. Letter from Einstein to Mileva Maric, 4 April 1901.
30 CPAE, Vol. 1, pp. 164–5. Letter from Hermann Einstein to Wilhelm Ostwald, 13 April 1901.
31 CPAE, Vol. 1, pp. 164–5. Letter from Hermann Einstein to Wilhelm Ostwald, 13 April 1901.
32 CPAE, Vol. 1, p. 165. Letter from Einstein to Marcel Grossmann, 14 April 1901.
33 CPAE, Vol. 1, p. 177. Letter from Einstein to Jost Winteler, 8 July 1901.
34 The advert appeared in the Bundesblatt (Federal Gazette) of 11 December 1901. CPAE, Vol. 1, p. 88.
35 CPAE, Vol. 1, p. 189. Letter from Einstein to Mileva Maric, 28 December 1901.
36 Berchtold V, Duke of Zähringen, founded the city in 1191. According to legend, Berchtold went hunting nearby and named the city Bärn after his first kill, a bear (Bär in German).
37 CPAE, Vol. 1, p. 191. Letter from Einstein to Mileva Maric, 4 February 1902.
38 Pais (1982), quoted pp. 46–7.
39 Einstein (1993), p. 7.
40 CPAE, Vol. 5, p. 28.
41 Hentschel and Grasshoff (2005), quoted p. 37.
42 Fölsing (1997), quoted p. 103.
43 Fölsing (1997), quoted p. 103.
44 Highfield and Carter (1994), quoted p. 210.
45 See CPAE, Vol. 5, p. 7. Letter from Einstein to Michele Besso, 22 January 1903.
46 CPAE, Vol. 5, p. 20. Letter from Einstein to Conrad Habicht, 30 June–22 September 1905.
47 Hentschel and Grasshoff (2005), quoted p. 23.
48 CPAE, Vol. 1, p. 193. Letter from Einstein to Mileva Maric, 17 February 1902.
49 Fölsing (1997), quoted p. 101.
50 Fölsing (1997), quoted p. 104.
51 Fölsing (1997), quoted p. 102.
52 Born (1978), p. 167.
53 Einstein (1949a), p. 15.
54 Einstein (1949a), p. 17.
55 CPAE, Vol. 2, p. 97.
56 Einstein (1905a), p. 178.
57 Einstein (1905a), p. 183.
58 Einstein also used his quantum of light hypothesis to explain Stoke’s law of photoluminescence and the ionisation of gases by ultraviolet light.
59 Mulligan (1999), quoted p. 349.
60 Susskind (1995), quoted p. 116.
61 Pais (1982), quoted p. 357.
62 During his Nobel Lecture, entitled ‘The Electron and the light-quanta from the experimental point of view’, Millikan also said: ‘After ten years of testing and changing and learning and sometimes blundering, all efforts being directed from the first toward the accurate experimental measurement of the energies of emission of photo-electrons, now as a function of the temperature, now of wavelength, now of material, this work resulted, contrary to my own expectations, in the first direct experimental proof in 1914 of the exact validity, within narrow limits of experimental errors, of the Einstein equation, and the first direct photoelectric determination of Planck’s constant h.’
63 CPAE, Vol. 5, pp. 25–6. Letter from Max Laue to Einstein, 2 June 1906.
64 CPAE, Vol. 5, pp. 337–8. Proposal for Einstein’s Membership in the Prussian Academy of Sciences, dated 12 June 1913 and signed by Max Planck, Walther Nernst, Heinrich Rubens and Emil Warburg.
65 Park (1997), quoted p. 208. Written in English, Opticks was first published in 1704.
66 Park (1997), quoted p. 208.
67 Park (1997), quoted p. 211.
68 Robinson (2006), quoted p. 103.
69 Robinson (2006), quoted p. 122.
70 Robinson (2006), quoted p. 96.
71 In German: ‘War es ein Gott der diese Zeichen schrieb?’
72 Baierlein (2001), p. 133.
73 Einstein (1905a), p. 178.
74 Einstein (1905a), p. 193.
75 CPAE, Vol. 5, p. 26. Letter from Max Laue to Einstein, 2 June 1906.
76 In 1906 Einstein published On the Theory of Brownian Motion in which he presented his theory in a more elegant and extended form.
77 CPAE, Vol. 5, p. 63. Letter from Jakob Laub to Einstein, 1 March 1908.
78 CPAE, Vol. 5, p. 120. Letter from Einstein to Jakob Laub, 19 May 1909.
79 CPAE, Vol. 5, p. 120. Letter from Einstein to Jakob Laub, 19 May 1909.
80 CPAE, Vol. 5, p. 120. Letter from Einstein to Jakob Laub, 19 May 1909.
81 CPAE, Vol. 5, p. 120. Letter from Einstein to Jakob Laub, 19 May 1909.
82 CPAE, Vol. 2, p. 563.
83 CPAE, Vol. 5, p. 140. Letter from Einstein to Michele Besso, 17 November 1909.
84 Jammer (1966), quoted p. 57.
85 CPAE, Vol. 5, p. 187. Letter from Einstein to Michele Besso, 13 May 1911.<
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86 CPAE, Vol. 5, p. 190. Letter and invitation to the Solvay Congress from Ernst Solvay to Einstein, 9 June 1911.
87 CPAE, Vol. 5, p. 192. Letter from Einstein to Walter Nernst, 20 June 1911.
88 Pais (1982), quoted p. 399.
89 CPAE, Vol. 5, p. 241. Letter from Einstein to Michele Besso, 26 December 1911.
90 Brian (2005), quoted p. 128.
91 CPAE, Vol. 5, p. 220. Letter from Einstein to Heinrich Zangger, 7 November 1911.
CHAPTER 3: THE GOLDEN DANE
1 Niels Bohr Collected Works (BCW), Vol. 1, p. 559. Letter from Bohr to Harald Bohr, 19 June 1912.
2 Pais (1991), quoted p. 47. Since 1946 it has housed Copenhagen University’s museum of medical history.
3 Pais (1991), quoted p. 46.
4 Pais (1991), quoted p. 99.
5 Pais (1991), quoted p. 48.
6 A second university in Aarhus was founded only in 1928.
7 Pais (1991), quoted p. 44.
8 Pais (1991), quoted p. 108.
9 Moore (1966), quoted p. 28.
10 Rozental (1967), p. 15.
11 Pais (1989a), quoted p. 61.
12 Niels Bohr, AHQP interview, 2 November 1962.
13 Niels Bohr, AHQP interview, 2 November 1962.
14 Heilbron and Kuhn (1969), quoted p. 223. Letter from Bohr to Margrethe Nørland, 26 September 1911.
15 BCW, Vol. 1, p. 523. Letter from Bohr to Ellen Bohr, 2 October 1911.
16 Weinberg (2003), quoted p. 10.
17 Aston (1940), p. 9.
18 Pais (1991), quoted p. 120.
19 BCW, Vol. 1, p. 527. Letter from Bohr to Harald Bohr, 23 October 1911.
20 BCW, Vol. 1, p. 527. Letter from Bohr to Harald Bohr, 23 October 1911.
21 There is no definitive historical evidence, but it is possible that Bohr attended a lecture given by Rutherford in Cambridge about his atomic model in October.
22 Bohr (1963b), p. 31.
23 Bohr (1963c), p. 83. The official report of the first Solvay Council was published in French in 1912 and in German in 1913. Bohr read the report as soon as it became available.