by Manjit Kumar
CHAPTER 10: UNCERTAINTY IN COPENHAGEN
1 Heisenberg (1971), p. 62.
2 Heisenberg (1971), p. 62.
3 Heisenberg (1971), p. 62.
4 Heisenberg (1971), p. 62.
5 Heisenberg (1971), p. 63.
6 Heisenberg (1971), p. 63.
7 Heisenberg (1971), p. 63.
8 Werner Heisenberg, AHQP interview, 30 November 1962.
9 Heisenberg (1971), p. 63.
10 Heisenberg (1971), p. 63.
11 Heisenberg (1971), p. 64.
12 Heisenberg (1971), p. 64.
13 Heisenberg (1971), p. 64.
14 Heisenberg (1971), p. 65.
15 Cassidy (1992), quoted p. 218.
16 Pais (1991), quoted p. 296. Letter from Bohr to Rutherford, 15 May 1926.
17 Heisenberg (1971), p. 76.
18 Cassidy (1992), quoted p. 219.
19 Pais (1991), quoted p. 297.
20 Robertson (1979), quoted p. 111.
21 Pais (1991), quoted p. 300.
22 Heisenberg (1967), p. 104.
23 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 235. Letter from Einstein to Paul Ehrenfest, 28 August 1926.
24 Werner Heisenberg, AHQP interview, 25 February 1963.
25 Werner Heisenberg, AHQP interview, 25 February 1963.
26 Werner Heisenberg, AHQP interview, 25 February 1963.
27 Heisenberg (1971), p. 77.
28 Heisenberg (1971), p. 77.
29 Heisenberg (1971), p. 77.
30 Heisenberg (1971), p. 77.
31 In another of his later writings, Heisenberg expressed the crucial switch in the question to answer: ‘Instead of asking: How can one in the known mathematical scheme express a given experimental situation? The other question was put: Is it true, perhaps, that only such experimental situations can arise in nature as can be expressed in the mathematical formalism?’ Heisenberg (1989), p. 30.
32 Heisenberg (1971), p. 78.
33 Heisenberg (1971), p. 78.
34 Heisenberg (1971), p. 79.
35 Momentum is preferred over velocity because it appears in fundamental equations of both classical and quantum mechanics. Both physical variables are intimately connected by the fact that momentum is just mass times velocity – even for a fast-moving electron with corrections imposed by the special theory of relativity.
36 As pointed out by Max Jammer (1974), Heisenberg used Ungenauigkeit (inexactness, imprecision) or Genauigkeit (precision, degree of precision). These two terms appear more than 30 times in his paper, whereas Unbestimmtheit (indeterminacy) appears only twice and Unsicherheit (uncertainty) three times.
37 Heisenberg in his published paper actually put it as pq~h, or p times q is approximately Planck’s constant.
38 There were occasions over the years when Heisenberg seemed to suggest that it was our knowledge of the atomic world that was indeterminate: ‘The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of the various quantities with which quantum theory deals…’, rather than an intrinsic feature of nature. See Heisenberg (1949), p. 20.
39 Heisenberg (1927), p. 68. An English translation can be found in Wheeler and Zurek (1983), pp. 62–84. All page references refer to this reprint.
40 Heisenberg (1927), p. 68.
41 Heisenberg (1927), p. 68.
42 Heisenberg (1989), p. 30.
43 Heisenberg (1927), p. 62.
44 Heisenberg (1989), p. 31.
45 Heisenberg (1927), p. 63.
46 Heisenberg (1927), p. 64.
47 Heisenberg (1927), p. 65.
48 Heisenberg (1989), p. 36.
49 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 146. Letter from Pauli to Heisenberg, 19 October 1926.
50 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 147. Letter from Pauli to Heisenberg, 19 October 1926.
51 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 146. Letter from Pauli to Heisenberg, 19 October 1926.
52 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 93.
53 Pais (1991), quoted p. 304. Letter from Heisenberg to Bohr, 10 March 1927.
54 Pais (1991), quoted p. 304.
55 Cassidy (1992), quoted p. 241. Letter from Heisenberg to Pauli, 4 April 1927.
56 Werner Heisenberg, AHQP interview, 25 February 1963.
57 Werner Heisenberg, AHQP interview, 25 February 1963.
58 Werner Heisenberg, AHQP interview, 25 February 1963.
59 Heisenberg (1927), p. 82.
60 The original German title was: ‘Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik’, Zeitschrift für Physik, 43, 172–98 (1927). See Wheeler and Zurek (1983), pp. 62–84.
61 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 182. Letter from Heisenberg to Pauli, 4 April 1927.
62 Bohr (1949), p. 210.
63 There was a subtle difference between wave-particle complementarity and that involving any pair of physical observables like position and momentum. According to Bohr, the complementary wave and particle aspects of an electron or light are mutually exclusive. It is one or the other. However, only if either position or momentum of an electron, for example, is measured with pinpoint certainty are position and momentum mutually exclusive. Otherwise, the precision with which both can be measured and therefore known is given by the position-momentum uncertainty relation.
64 BCW, Vol. 6, p. 147.
65 BCW, Vol. 3, p. 458.
66 Werner Heisenberg, AHQP interview, 25 February 1963.
67 Werner Heisenberg, AHQP interview, 25 February 1963.
68 Bohr (1949), p. 210.
69 Bohr (1928), p. 53.
70 BCW, Vol. 6, p. 91.
71 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 187. Letter from Bohr to Einstein, 13 April 1927.
72 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 187. Letter from Bohr to Einstein, 13 April 1927.
73 BCW, Vol. 6, p. 418. Letter from Bohr to Einstein, 13 April 1927.
74 Mackinnon (1982), quoted p. 258. Letter from Heisenberg to Pauli, 31 May 1927.
75 Cassidy (1992), quoted p. 243. Letter from Heisenberg to Pauli, 16 May 1927. Heisenberg uses the symbol that means ‘approximately’.
76 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 183. Letter from Heisenberg to Pauli, 16 May 1927.
77 Heisenberg (1927), p. 83.
78 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 184. Letter from Heisenberg to Pauli, 3 June 1927.
79 Heisenberg (1971), p. 79.
80 Pais (1991), quoted p. 309. Letter from Heisenberg to Bohr, 18 June 1927.
81 Pais (1991), quoted p. 309. Letter from Heisenberg to Bohr, 21 August 1927.
82 Cassidy (1992), quoted p. 218. Letter from Heisenberg to his parents, 29 April 1926.
83 Pais (2000), quoted p. 136.
84 Pais (1991), quoted p. 309. Letter from Heisenberg to Pauli, 16 May 1927.
85 Heisenberg (1989), p. 30.
86 Heisenberg (1989), p. 30.
87 Heisenberg (1927), p. 83.
88 Heisenberg (1927), p. 83.
89 Heisenberg (1927), p. 83.
90 Heisenberg (1927), p. 83.
CHAPTER 11: SOLVAY 1927
1 Mehra (1975), quoted p. xxiv.
2 CPAE, Vol. 5, p. 222. Letter from Einstein to Heinrich Zangger, 15 November 1911.
3 Mehra (1975), quoted p. xxiv. Lorentz’s Report to the Administrative Council, Solvay Institute, 3 April 1926.
4 Mehra (1975), quoted p. xxiv.
5 Mehra (1975), quoted p. xxiii. Letter from Ernest Rutherford to B.B. Boltwood, 28 February 1921.
6 Mehra (1975), quoted p. xxii.
7 The statute of the League of Nations was drawn up in April 1919.
8 In 1936 Hitler violated the Locarno treaties when he sent German troops into the demilitarised Rhineland.
9 William H. Bragg resigned from th
e committee in May 1927 citing other commitments, and though invited did not attend. Edmond Van Aubel, though still on the committee, refused to attend because the Germans had been invited.
10 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 232.
11 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 241. Letter from Einstein to Hendrik Lorentz, 17 June 1927.
12 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 241. Letter from Einstein to Hendrik Lorentz, 17 June 1927.
13 Bohr (1949), p. 212.
14 Bacciagaluppi and Valentini (2006), quoted p. 408.
15 Bacciagaluppi and Valentini (2006), quoted p. 408.
16 Bacciagaluppi and Valentini (2006), quoted p. 432.
17 Bacciagaluppi and Valentini (2006), quoted p. 437.
18 Mehra (1975), quoted p. xvii.
19 Bacciagaluppi and Valentini (2006), quoted p. 448.
20 Bacciagaluppi and Valentini (2006), quoted p. 448.
21 Bacciagaluppi and Valentini (2006), quoted p. 470.
22 Bacciagaluppi and Valentini (2006), quoted p. 472.
23 Bacciagaluppi and Valentini (2006), quoted p. 473.
24 Pais (1991), quoted p. 426. ‘Could one not keep determinism by making it an object of belief? Must one necessarily elevate indeterminism to a principle?’ (Bacciagaluppi and Valentini (2006), p. 477.)
25 Bohr (1963c), p. 91.
26 Bohr was partly to blame for the confusion, since on occasions he referred to his contribution during the general discussion as a ‘report’. He did so, for example, in his lecture ‘The Solvay Meetings and the Development of quantum Physics’, reprinted in Bohr (1963c).
27 Bohr (1963c), p. 91.
28 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 240.
29 Bohr (1928), p. 53.
30 Bohr (1928), p. 54.
31 Petersen (1985), quoted p. 305.
32 Bohr (1987), p. 1.
33 Einstein (1993), p. 121. Letter from Einstein to Maurice Solovine, 1 January 1951.
34 Einstein (1949a), p. 81.
35 Heisenberg (1989), p. 174.
36 Bacciagaluppi and Valentini (2006), quoted p. 486. The translation is based on notes in the Einstein archives. The published French translation reads: ‘I have to apologize for not having gone deeply into quantum mechanics. I should nevertheless want to make some general remarks.’
37 Bohr (1949), p. 213.
38 Bacciagaluppi and Valentini (2006), quoted p. 487.
39 Bacciagaluppi and Valentini (2006), quoted p. 487.
40 See Chapter 9, note 43.
41 Bacciagaluppi and Valentini (2006), quoted p. 487.
42 Bacciagaluppi and Valentini (2006), quoted p. 489.
43 Bacciagaluppi and Valentini (2006), quoted p. 489.
44 Bohr (1949).
45 Bohr (1949), p. 217.
46 Bohr (1949), p. 218.
47 Bohr (1949), p. 218.
48 Bohr (1949), p. 218.
49 Bohr (1949), p. 218.
50 Bohr (1949), p. 222.
51 De Broglie (1962), p. 150.
52 Heisenberg (1971), p. 80.
53 Heisenberg (1967), p. 107.
54 Heisenberg (1967), p. 107.
55 Heisenberg (1967), p. 107.
56 Heisenberg (1983), p. 117.
57 Heisenberg (1983), p. 117.
58 Heisenberg (1971), p. 80.
59 Bohr (1949), p. 213.
60 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, pp. 251–3. Letter from Paul Ehrenfest to Samuel Goudsmit, George Uhlenbeck and Gerhard Diecke, 3 November 1927.
61 Bohr (1949), p. 218.
62 Bohr (1949), p. 218.
63 Bohr (1949), p. 206.
64 Brian (1996), p. 164.
65 Cassidy (1992), quoted p. 253. Letter from Einstein to Arnold Sommerfeld, 9 November 1927.
66 Marage and Wallenborn (1999), quoted p. 165.
67 Cassidy (1992), quoted p. 254.
68 Werner Heisenberg, AHQP interview, 27 February 1963.
69 Gamov (1966), p. 51.
70 Calaprice (2005), p. 89.
71 Fölsing (1997), quoted p. 601. Letter from Einstein to Michele Besso, 5 January 1929.
72 Brian (1996), quoted p. 168.
73 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 256.
74 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted p. 266. Letter from Schrödinger to Bohr, 5 May 1928.
75 Mehra and Rechenberg (2000), Vol. 6, Pt. 1, quoted pp. 266–7. Letter from Bohr to Schrödinger, 23 May 1928.
76 Przibram (1967), p. 31. Letter from Einstein to Schrödinger, 31 May 1928.
77 Fölsing (1997), quoted p. 602. Letter from Einstein to Paul Ehrenfest, 28 August 1928.
78 Brian (1996), quoted p. 169.
79 Pais (2000), quoted p. 215. Letter from Pauli to Hermann Weyl, 11 July 1929.
80 Pais (1982), quoted p. 31.
CHAPTER 12: EINSTEIN FORGETS RELATIVITY
1 Rosenfeld (1968), p. 232.
2 Pais (2000), quoted p. 225.
3 Rosenfeld (1968), p. 232.
4 Rosenfeld (1968), p. 232.
5 Rosenfeld, AHQP interview.
6 Clark (1973) quoted p. 198.
7 ‘The Fabric of the Universe’, The Times, 7 November 1919.
8 Thorne (1994), p. 100.
9 Alternatively, since the uncontrollable transfer of momentum to the light box when the pointer and scale is illuminated causes the box to move about unpredictably, the clock inside is now moving in a gravitational field. The rate at which it ticks (the flow of time) changes unpredictably, leading to an uncertainty in the precise time when the shutter is opened and the photon escapes. Once again, the chain of uncertainties obeys the limits set by Heisenberg’s uncertainty principle.
10 Pais (1982), quoted p. 449.
11 Pais (1982), quoted p. 515. Einstein had pointed out to the Swedish Academy that the achievements of Heisenberg and Schrödinger were so significant that it would not be appropriate to divide a Nobel Prize between them. However, ‘who should get the prize first is hard to answer’, he admitted, before suggesting Schrödinger. He had first nominated Heisenberg and Schrödinger in 1928 when he suggested that de Broglie and Davisson be given precedence. The other options he put forward involved one prize to be shared by de Broglie and Schrödinger and another by Born, Heisenberg and Jordan. The 1928 prize was deferred until 1929, when it was awarded to the British physicist Owen Richardson. As Einstein suggested, Louis de Broglie was the first of the new generation of quantum theorists to be honoured when he was awarded the 1929 prize.
12 Fölsing (1997), quoted p. 630.
13 Brian (1996), quoted p. 200.
14 Calaprice (2005), p. 323.
15 Brian (1996), quoted p. 201.
16 Brian (1996), quoted p. 201.
17 Brian (1996), quoted p. 201.
18 Henig (1998), p. 64.
19 Brian (1996), quoted p. 199.
20 Fölsing (1997), quoted p. 629.
21 Brian (1996), quoted p. 199. Letter from Sigmund Freud to Arnold Zweig, 7 December 1930.
22 Brian (1996), quoted p. 204.
23 Levenson (2003), quoted p. 410.
24 Brian (1996), quoted p. 237.
25 Fölsing (1997), quoted p. 659. Letter from Einstein to Margarete Lenbach, 27 February 1933.
26 Clark (1973), quoted p. 431.
27 Fölsing (1997), quoted p. 661 and Brian (1996), p. 244.
28 Fölsing (1997), quoted p. 662. Letter from Planck to Einstein, 19 March 1933.
29 Fölsing (1997), quoted p. 662. Letter from Planck to Einstein, 31 March 1933.
30 Friedländer (1997), quoted p. 27.
31 Physics: Albert Einstein (1921), James Franck (1925), Gustav Hertz (1925), Erwin Schrödinger (1933), Viktor Hess (1936), Otto Stern (1943), Felix Bloch (1952), Max Born (1954), Eugene Wigner (1963), Hans Bethe (1967), and Dennis Gabor (1971). Chemistry: Fritz Haber (1918), Pieter Debye (1936), Georg von Hevesy (1943), and Gerhard Hertzber
g (1971). Medicine: Otto Meyerhof (1922), Otto Loewi (1936), Boris Chain (1945), Hans Krebs (1953), and Max Delbrück (1969).
32 Heilbron (2000), quoted p. 210.
33 Heilbron (2000), quoted p. 210.
34 Beyerchen (1977), quoted p. 43. This section does not appear in the account published in Heilbron (2000), pp. 210–11, which ends with: ‘So saying, he hit himself hard on the knee, spoke faster and faster, and flew into such a rage that I could only remain silent and withdraw.’
35 Forman (1973), quoted p. 163.
36 Holton (2005), quoted pp. 32–3.
37 Greenspan (2005), quoted p. 175.
38 Born (1971), p. 251.
39 Greenspan (2005), quoted p. 177.
40 Born (2005), p. 114. Letter from Born to Einstein, 2 June 1933.
41 Born (2005), p. 114. Letter from Born to Einstein, 2 June 1933.
42 Born (2005), p. 111. Letter from Einstein to Born, 30 May 1933.
43 Cornwell (2003), quoted p. 134.
44 Jungk (1960), quoted p. 44.
45 Clark (1973), quoted p. 472.
46 Pais (1982), quoted p. 452. Letter from Abraham Flexner to Einstein, 13 October 1933.
47 Fölsing (1997), quoted p. 682.
48 Fölsing (1997), quoted p. 682. Letter from Einstein to the Board of Trustees of the Institute for Advanced Study, November 1933.
49 Fölsing (1997), quoted pp. 682–3. Letter from Einstein to the Board of Trustees of the Institute for Advanced Study, November 1933.
50 Moore (1989), quoted p. 280.
51 Cassidy (1992), quoted p. 325. Letter from Heisenberg to Bohr, 27 November 1933.
52 Greenspan (2005), quoted p. 191. Letter from Heisenberg to Born, 25 November 1933.
53 Born (2005), p. 200. Letter from Born to Einstein, 8 November 1953.
54 Mehra (1975), quoted p. xxvii. Letter from Einstein to Queen Elizabeth of Belgium, 20 November 1933.
CHAPTER 13: QUANTUM REALITY
1 Smith and Weiner (1980), p. 190. Letter from Robert Oppenheimer to Frank Oppenheimer, 11 January 1935.
2 Smith and Weiner (1980), p. 190. Letter from Robert Oppenheimer to Frank Oppenheimer, 11 January 1935.
3 Born (2005), quoted p. 128.
4 Bernstein (1991), quoted p. 49.
5 James Chadwick was awarded the Nobel Prize for Physics in 1935 and Enrico Fermi in 1938.
6 Brian (1996), quoted p. 251.
7 Einstein (1950), p. 238.
8 Moore (1989), quoted p. 305, Letter from Einstein to Schrödinger, 8 August 1935.
9 Jammer (1985), quoted p. 142.