Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality
Page 45
24 Kay (1963), p. 131.
25 Keller (1983), quoted p. 55.
26 Nitske (1971), quoted p. 5.
27 Nitske (1971), p. 5.
28 Kragh (1999), p. 30.
29 Wilson (1983), quoted p. 127.
30 Often in textbooks and scientific histories, the French scientist Paul Villard is credited with the discovery of gamma rays in 1900. In fact Villard discovered that radium emitted gamma rays, but it was Rutherford who reported them in his first paper on uranium radiation, published in January 1899, but finished on 1 September 1898. Wilson (1983), pp. 126–8 outlines the facts and makes a convincing case for Rutherford.
31 Eve (1939), quoted p. 55.
32 Andrade (1964), quoted p. 50.
33 More accurate measurements gave a half-life of 56 seconds.
34 Howorth (1958), quoted p. 83.
35 Wilson (1983), quoted p. 225.
36 Wilson (1983), quoted p. 225.
37 Wilson (1983), quoted p. 286.
38 Wilson (1983), quoted p. 287.
39 Pais (1986), quoted p. 188.
40 Cropper (2001), quoted p. 317.
41 Wilson (1983), quoted p. 291.
42 Marsden (1948), p. 54.
43 Rhodes (1986), quoted p. 49.
44 Thomson began working on a detailed mathematical version of this model only after he came across a similar idea proposed by Kelvin in 1902.
45 Badash (1969), quoted p. 235.
46 From quoted remarks by Geiger, Wilson (1983), p. 296.
47 Rowland (1938), quoted p. 56.
48 Cropper (2001), quoted p. 317.
49 Wilson (1983), quoted p. 573.
50 Wilson (1983), quoted p. 301. Letter from William Henry Bragg to Ernest Rutherford, 7 March 1911. Received on 11 March.
51 Eve (1939), quoted p. 200. Letter from Hantaro Nagaoka to Ernest Rutherford, 22 February 1911.
52 Nagaoka had been inspired by James Clerk Maxwell’s famous analysis of the stability of Saturn’s rings, which had puzzled astronomers for more than 200 years. In 1855, in a bid to attract the best physicists to attack the problem, it was chosen as the topic for Cambridge University’s prestigious biennial competition, the Adams Prize. Maxwell submitted the only entry to be received by the closing date in December 1857. Rather than diminish the significance of the prize and Maxwell’s achievement, it only served to enhance his growing reputation by once again demonstrating the difficulty of the problem. No one else had even succeeded in completing a paper worth entering. Although when seen through telescopes they appeared to be solid, Maxwell showed conclusively that the rings would be unstable if they were either solid or liquid. In an astonishing display of mathematical virtuosity, he demonstrated that the stability of Saturn’s rings was due to them being composed of an enormous number of particles revolving around the planet in concentric circles. Sir George Airy, the Astronomer Royal, declared that Maxwell’s solution was ‘one of the most remarkable applications of Mathematics to Physics that I have ever seen’. Maxwell was duly rewarded with the Adams Prize.
53 Rutherford (1906), p. 260.
54 Rutherford (1911a), reprinted in Boorse and Motz (1966), p. 709.
55 In their paper, published in April 1913, Geiger and Marsden argued that their data was ‘strong evidence of the correctness of the underlying assumptions that an atom contains a strong charge at the centre of dimensions, small compared with the diameter of the atom’.
56 Marsden (1948), p. 55.
57 Niels Bohr, AHQP interview, 7 November 1962.
58 Niels Bohr, AHQP interview, 2 November 1962.
59 Niels Bohr, AHQP interview, 7 November 1962.
60 Rosenfeld and Rüdinger (1967), quoted p. 46.
61 Pais (1991), quoted p. 125.
62 Andrade (1964), quoted p. 210.
63 Andrade (1964), p. 209, note 3.
64 Rosenfeld and Rüdinger (1967), quoted p. 46.
65 Bohr (1963b), p. 32.
66 Niels Bohr, AHQP interview, 2 November 1962.
67 Howorth (1958), quoted p. 184.
68 Soddy (1913), p. 400. He also suggested ‘isotopic elements’ as an alternative.
69 Radiothorium, radioactinium, ionium and uranium-X were later identified as only four of the 25 isotopes of thorium.
70 Niels Bohr, AHQP interview, 2 November 1962.
71 Bohr (1963b), p. 33.
72 Bohr (1963b), p. 33.
73 Bohr (1963b), p. 33.
74 Niels Bohr, AHQP interview, 2 November 1962.
75 Niels Bohr, AHQP interview, 31 October 1962.
76 Niels Bohr, AHQP interview, 31 October 1962.
77 Boorse and Motz (1966), quoted p. 855.
78 Georg von Hevesy, AHQP interview, 25 May 1962.
79 Pais (1991), quoted p. 125.
80 Pais (1991), quoted p. 125.
81 Bohr (1963b), p. 33.
82 Blaedel (1985), quoted p. 48.
83 BCW, Vol. 1, p. 555. Letter from Bohr to Harald Bohr, 12 June 1912.
84 BCW, Vol. 1, p. 555. Letter from Bohr to Harald Bohr, 12 June 1912.
85 BCW, Vol. 1, p. 561. Letter from Bohr to Harald Bohr, 17 July 1912.
CHAPTER 4: THE QUANTUM ATOM
1 Margrethe Bohr, Aage Bohr and Léon Rosenfeld, AHQP interview, 30 January 1963.
2 Margrethe Bohr, Aage Bohr and Léon Rosenfeld, AHQP interview, 30 January 1963.
3 Margrethe Bohr, AHQP interview, 23 January 1963.
4 Rozental (1998), p. 34.
5 Bohr decided to delay publication of the paper until experiments being conducted in Manchester on the velocity of alpha particles became available. The paper, ‘On the Theory of the Decrease of Velocity of Moving Electrified Particles on Passing through Matter’, was published in 1913 in the Philosophical Magazine.
6 See Chapter 3, note 6.
7 Nielson (1963), p. 22.
8 Rosenfeld and Rüdinger (1967), quoted p. 51.
9 BCW, Vol. 2, p. 577. Letter from Bohr to Ernest Rutherford, 6 July 1912.
10 Niels Bohr, AHQP interview, 7 November 1962.
11 BCW, Vol. 2, p. 136.
12 BCW, Vol. 2, p. 136.
13 Niels Bohr, AHQP interview, 1 November 1962.
14 Niels Bohr, AHQP interview, 31 October 1962.
15 BCW, Vol. 2, p. 577. Letter from Bohr to Ernest Rutherford, 4 November 1912.
16 BCW, Vol. 2, p. 578. Letter from Ernest Rutherford to Bohr, 11 November 1912.
17 Pi () is the numerical value of the ratio of the circumference of a circle to its diameter.
18 One electron volt (eV) was equivalent to 1. 6×10–19 joules of energy. A 100-watt light bulb converts 100 joules of electrical energy into heat in one second.
19 BCW, Vol. 2, p. 597. Letter from Bohr to Ernest Rutherford, 31 January 1913.
20 Niels Bohr, AHQP interview, 31 October 1962.
21 In Balmer’s day and well into the twentieth century, wavelength was measured in a unit named in honour of Anders Ångström. 1 Ångström = 10–8cm, one hundred-millionth of a centimetre. It is equal to one-tenth of a nanometre in modern units.
22 See Bohr (1963d), with introduction by Léon Rosenfeld.
23 In 1890 the Swedish physicist Johannes Rydberg developed a more general formula than Balmer’s. It contained a number, later called Rydberg’s constant, which Bohr was able to calculate from his model. He was able rewrite Rydberg’s constant in terms of Planck’s constant, the electron’s mass and the electron’s charge. He was able to derive a value for Rydberg’s constant that was almost an identical match for the experimentally determined value. Bohr told Rutherford that he believed it to be an ‘enormous and unexpected development’. (See BCW, Vol. 2, p. 111.)
24 Heilbron (2007), quoted p. 29.
25 Gillott and Kumar (1995), quoted p. 60. Lectures delivered by Nobel Prize-winners are available at www.nobelprize.org.
26 BCW, Vol. 2, p. 582. Letter from Bohr to Ernest Rutherford, 6 March 1913.
27 Eve (1939), quoted p. 221.
28 Eve (1939), quoted p. 221.
29 BCW, Vol. 2, p. 583. Letter from Ernest Rutherford to Bohr, 20 March 1913.
30 BCW, Vol. 2, p. 584. Letter from Ernest Rutherford to Bohr, 20 March 1913.
31 BCW, Vol. 2, pp. 585–6. Letter from Bohr to Ernest Rutherford, 26 March 1913.
32 Eve (1939), p. 218.
33 Wilson (1983), quoted p. 333.
34 Rosenfeld and Rüdinger (1967), quoted p. 54.
35 Wilson (1983), quoted p. 333.
36 Blaedel (1988), quoted p. 119.
37 Eve (1939), quoted p. 223.
38 Cropper (1970), quoted p. 46.
39 Jammer (1966), quoted p. 86.
40 Mehra and Rechenberg (1982), Vol. 1, quoted p. 236.
41 Mehra and Rechenberg (1982), Vol. 1, quoted p. 236.
42 BCW, Vol. 1, p. 567. Letter from Harald Bohr to Bohr, autumn 1913.
43 Eve (1939), quoted p. 226.
44 Moseley was also able to resolve some anomalies that had arisen in the placing of three pairs of elements in the periodic table. According to atomic weight, argon (39.94) should be listed after potassium (39.10) in the periodic table. This would conflict with their chemical properties, as potassium was grouped with the inert gases and argon with the alkali metals. To avoid such chemical nonsense, the elements were placed with the atomic weights in reverse order. However, using their respective atomic numbers they are placed in the correct order. Atomic number also allowed the correct positioning of two other pairs of elements: tellurium–iodine and cobalt–nickel.
45 Pais (1991), quoted p. 164.
46 BCW, Vol. 2, p. 594. Letter from Ernest Rutherford to Bohr, 20 May 1914.
47 Pais (1991), quoted p. 164.
48 CPAE, Vol. 5, p. 50. Letter from Einstein to Arnold Sommerfeld, 14 January 1908.
49 It was discovered later that Sommerfeld’s k could not be equal to zero. So k was set equal to l+1 where l is the orbital angular momentum number. l = 0, 1, 2…n–1 where n is the principal quantum number.
50 There are actually two types of Stark effect. Linear Stark effect is one in which splitting is proportional to the electric field and occurs in excited states of hydrogen. All other atoms exhibit the quadratic Stark effect, where the splitting of the lines is proportional to the square of the electric field.
51 BCW, Vol. 2, p. 589. Letter from Ernest Rutherford to Bohr, 11 December 1913.
52 BCW, Vol. 2, p. 603. Letter from Arnold Sommerfeld to Bohr, 4 September 1913.
53 In modern notation m is written ml. For a given l there are 2l+1 values of ml that range from –l to +l. If l=1, then there are three values of ml: –1,0,+1.
54 Pais (1994), quoted p. 34. Letter from Arnold Sommerfeld to Bohr, 25 April 1921.
55 Pais (1991), quoted p. 170.
56 In 1965, when Bohr would have been 80, it was renamed the Niels Bohr Institute.
CHAPTER 5: WHEN EINSTEIN MET BOHR
1 Frank (1947), quoted p. 98.
2 CPAE, Vol. 5, p. 175. Letter from Einstein to Hendrik Lorentz, 27 January 1911.
3 CPAE, Vol. 5, p. 175. Letter from Einstein to Hendrik Lorentz, 27 January 1911.
4 CPAE, Vol. 5, p. 187. Letter from Einstein to Michele Besso, 13 May 1911.
5 Pais (1982), quoted p. 170.
6 Pais (1982), quoted p. 170.
7 CPAE, Vol. 5, p. 349. Letter from Einstein to Hendrik Lorentz, 14 August 1913.
8 Fölsing (1997), quoted p. 335.
9 CPAE, Vol. 8, p. 23. Letter from Einstein to Otto Stern, after 4 June 1914.
10 CPAE, Vol. 8, p. 10. Letter from Einstein to Paul Ehrenfest, before 10 April 1914.
11 CPAE, Vol. 5, p. 365. Letter from Einstein to Elsa Löwenthal, before 2 December 1913.
12 CPAE, Vol. 8, pp. 32–3. Memorandum from Einstein to Mileva Einstein-Maric, 18 July 1914.
13 CPAE, Vol. 8, p. 41. Letter from Einstein to Paul Ehrenfest, 19 August 1914.
14 Fromkin (2004), quoted pp. 49–50.
15 Russia, France, Britain and Serbia were joined by Japan (1914), Italy (1915), Portugal and Romania (1916), the USA and Greece (1917). The British dominions also fought with the allies. Germany and Austria-Hungary were supported by Turkey (1914) and Bulgaria (1915).
16 CPAE, Vol. 8, p. 41. Letter from Einstein to Paul Ehrenfest, 19 August 1914.
17 CPAE, Vol. 8, p. 41. Letter from Einstein to Paul Ehrenfest, 19 August 1914.
18 Heilbron (2000), quoted p. 72.
19 Fölsing (1997), quoted p. 345.
20 Fölsing (1997), quoted p. 345.
21 Gilbert (1994), quoted p. 34.
22 Fölsing (1997), quoted p. 346.
23 Fölsing (1997), quoted p. 346.
24 Large (2001), quoted p. 138.
25 CPAE, Vol. 8, p. 77. Letter from Einstein to Romain Rolland, 22 March 1915.
26 CPAE, Vol. 8, p. 422. Letter from Einstein to Hendrik Lorentz, 18 December 1917.
27 CPAE, Vol. 8, p. 422. Letter from Einstein to Hendrik Lorentz, 18 December 1917.
28 CPAE, Vol. 5, p. 324. Letter from Einstein to Arnold Sommerfeld, 29 October 1912.
29 CPAE, Vol. 8, p. 151. Letter from Einstein to Heinrich Zangger, 26 November 1915.
30 CPAE, Vol. 8, p. 22. Letter from Einstein to Paul Ehrenfest, 25 May 1914.
31 CPAE, Vol. 8, p. 243. Letter from Einstein to Michele Besso, 11 August 1916.
32 CPAE, Vol. 8, p. 243. Letter from Einstein to Michele Besso, 11 August 1916.
33 CPAE, Vol. 8, p. 246. Letter from Einstein to Michele Besso, 6 September 1916.
34 CPAE, Vol. 6, p. 232.
35 CPAE, Vol. 8, p. 613. Letter from Einstein to Michele Besso, 29 July 1918.
36 Born (2005), p. 22. Letter from Einstein to Max Born, 27 January 1920.
37 Analogy courtesy of Jim Baggott (2004).
38 Born (2005), p. 80. Letter from Einstein to Max Born, 29 April 1924.
39 Large (2001), quoted p. 134.
40 CPAE, Vol. 8, p. 300. Letter from Einstein to Heinrich Zangger, after 10 March 1917.
41 CPAE, Vol. 8, p. 88. Letter from Einstein to Heinrich Zangger, 10 April 1915.
42 In a weak gravitational field, general relativity predicts the same bending as Newton’s theory.
43 Pais (1994), quoted p. 147.
44 Brian (1996), quoted p. 101.
45 In the wake of the huge interest in his work, the first English translation of Relativity appeared in 1920.
46 CPAE, Vol. 8, p. 412, Letter from Einstein to Heinrich Zangger, 6 December 1917.
47 Pais (1982), quoted p. 309.
48 Brian (1996), quoted p. 103.
49 Calaprice (2005), quoted p. 5. Letter from Einstein to Heinrich Zangger, 3 January 1920.
50 Fölsing (1997), quoted p. 421.
51 Fölsing (1997), quoted p. 455. Letter from Einstein to Marcel Grossmann, 12 September 1920.
52 Pais (1982), quoted p. 314. Letter from Einstein to Paul Ehrenfest, 4 December 1919.
53 Everett (1979), quoted p. 153.
54 Elon (2003), quoted pp. 359–60.
55 Moore (1966), quoted p. 103.
56 Pais (1991), quoted p. 228. Postcard from Einstein to Planck, 23 October 1919.
57 CPAE, Vol. 5, p. 20. Letter from Einstein to Conrad Habicht, sometime between 30 June and 22 September 1905.
58 CPAE, Vol. 5, pp. 20–1. Letter from Einstein to Conrad Habicht, sometime between 30 June and 22 September 1905.
59 CPAE, Vol. 5, p. 21. Letter from Einstein to Conrad Habicht, sometime between 30 June and 22 September 1905.
60 Einstein (1949a), p. 47.
61 Moore (1966), quoted p. 104.
62 Moore (1966), quoted p. 106.
63 Pais (1991) quoted p. 232.
64 CPAE, Vol. 6, p. 232.
65 Fölsing (1997), quoted p. 477. Letter from Einstein to Bohr, 2 May 1920.
66 Fölsing (1997), quoted p. 477. Letter from Einstein to Paul Ehrenfest, 4 May 1920.
67 Fölsing (1997), quoted p. 477. Letter from Bohr
to Einstein, 24 June 1920.
68 Pais (1994), quoted p. 40. Letter from Einstein to Hendrik Lorentz, 4 August 1920.
69 Arbeitsgemeinschaft deutscher Naturforscher zur Erhaltung reiner Wissenschaft.
70 Born (2005), p. 34. Letter from Einstein to the Borns, 9 September 1920.
71 Born (2005), p. 34. Letter from Einstein to the Borns, 9 September 1920.
72 Pais (1982), quoted p. 316. Letter from Einstein to K. Haenisch, 8 September 1920.
73 Fölsing (1997), quoted p. 512. Letter from Einstein to Paul Ehrenfest, 15 March 1922.
74 BCW, Vol. 3, pp. 691–2. Letter from Bohr to Arnold Sommerfeld, 30 April 1922.
75 What Bohr was calling electron shells were really a set of electron orbits. The primary orbits were numbered from 1 to 7, with 1 being nearest to the nucleus. Secondary orbits were designated by the letters s, p, d, f (from the terms ‘sharp’, ‘principal’, ‘diffuse’ and fundamental’, used by spectroscopists to describe the lines in atomic spectra). The orbit nearest to the nucleus is just a single orbit and is labelled 1s, the next is a pair of orbits labelled 2s and 2p, the next a trio of orbits 3s, 3p and 3d, and so on. Orbits can hold increasing numbers of electrons the further from the nucleus they are. The s can hold 2 electrons, the p ones 6, the d ones 10, and the f ones 14.
76 Brian (1996), quoted p. 138.
77 Einstein (1993), p. 57. Letter from Einstein to Maurice Solovine, 16 July 1922.
78 See Fölsing (1997), p. 520. Letter from Einstein to Marie Curie, 11 July 1922.
79 Einstein (1949a), pp. 45–7.
80 French and Kennedy (1985), quoted p. 60.
81 Mehra and Rechenberg (1982), Vol. 1, Pt. 1, p. 358. Letter from Bohr to James Franck, 15 July 1922.
82 Moore (1966), quoted p. 116.
83 Moore (1966), quoted p. 116.
84 BCW, Vol. 4, p. 685. Letter from Bohr to Einstein, 11 November 1922.
85 Pais (1982), quoted p. 317.
86 BCW, Vol. 4, p. 686. Letter from Einstein to Bohr, 11 January 1923.
87 Pais (1991), quoted p. 308.
88 Pais (1991), quoted p. 215.
89 Bohr’s banquet speech is available at www.nobelprize.org.
90 Bohr (1922), p. 7.
91 Bohr (1922), p. 42.
92 Robertson (1979), p. 69.
93 Weber (1981), p. 64.
94 Bohr (1922), p. 14.
95 Stuewer (1975), quoted p. 241.
96 Stuewer (1975), quoted p. 241.