by Manjit Kumar
97 See Stuewer (1975).
98 Visible light does undergo the ‘Compton effect’. But the difference in wavelengths for the primary and scattered visible light is so much smaller than for X-rays that the effect is not detectable by the eye, although it can be measured in the lab.
99 Compton (1924), p. 70.
100 Compton (1924), p. 70.
101 Compton (1961). A short paper by Compton recounting the experimental evidence and the theoretical considerations that led to the discovery of the ‘Compton effect’.
102 The American chemist Gilbert Lewis proposed the name photon in 1926 for atoms of light.
103 Fölsing (1997), quoted p. 541.
104 Pais (1991), quoted p. 234.
105 Compton (1924), p. 70.
106 Pais (1982), quoted p. 414.
CHAPTER 6: THE PRINCE OF DUALITY
1 Ponte (1981), quoted p. 56.
2 Unlike Duc, Prince was not a French title. With the death of his brother, the French title took precedence and Louis became a Duc.
3 Pais (1994), quoted p. 48. Letter from Einstein to Hendrik Lorentz, 16 December 1924.
4 Abragam (1988), quoted p. 26.
5 Abragam (1988), quoted pp. 26–7.
6 Abragam (1988), quoted p. 27.
7 Abragam (1988), quoted p. 27.
8 Ponte (1981), quoted p. 55.
9 See Abragam (1988), p. 38.
10 Corps du Génie in French.
11 Ponte (1981), quoted pp. 55–6.
12 Pais (1991), quoted p. 240.
13 Abragam (1988), quoted p. 30.
14 Abragam (1988), quoted p. 30.
15 Abragam (1988), quoted p. 30.
16 Abragam (1988), quoted p. 30.
17 Abragam (1988), quoted p. 30.
18 Wheaton (2007), quoted p. 58.
19 Wheaton (2007, quoted pp. 54–5.
20 Elsasser (1978), p. 66.
21 Gehrenbeck (1978), quoted p. 325.
22 CPAE, Vol. 5, p. 299. Letter from Einstein to Heinrich Zangger, 12 May 1912.
23 Weinberg (1993), p. 51.
CHAPTER 7: SPIN DOCTORS
1 Meyenn and Schucking (2001), quoted p. 44.
2 Born (2005), p. 223.
3 Born (2005), p. 223.
4 Paul Ewald, AHQP interview, 8 May 1962.
5 Enz (2002), quoted p. 15.
6 Enz (2002), quoted p. 9.
7 Pais (2000), quoted p. 213.
8 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, quoted p. 378.
9 Enz (2002), quoted p. 49.
10 Cropper (2001), quoted p. 257.
11 Cropper (2001), quoted p. 257.
12 Cropper (2001), quoted p. 257.
13 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, p. 384.
14 Pauli (1946b), p. 27.
15 Mehra and Rechenberg (1982), Vol. 1, Pt. 1, quoted p. 281.
16 CPAE, Vol. 8, p. 467. Letter from Einstein to Hedwig Born, 8 February 1918.
17 Greenspan (2005), quoted p. 108.
18 Born (2005), p. 56. Letter from Born to Einstein, 21 October 1921.
19 Pauli (1946a), p. 213.
20 Pauli (1946a), p. 213.
21 Lorentz assumed that oscillating electrons inside atoms of the incandescent sodium gas emitted the light that Zeeman had analysed. Lorentz showed that a spectral line would split into two closely spaced lines (a doublet) or three lines (a triplet) depending on whether the emitted light was viewed in the direction parallel or perpendicular to that of the magnetic field. Lorentz calculated the difference in the wavelengths of the two adjacent lines and obtained a value in agreement with Zeeman’s experimental results.
22 Pais (1991), quoted p. 199.
23 Pais (2000), quoted p. 221.
24 Pauli (1946a), p. 213.
25 In 1916, 28-year-old German physicist Walther Kossel, whose father had been awarded the Nobel Prize for chemistry, was the first to establish an important connection between the quantum atom and the periodic table. He noticed that the difference between the atomic numbers 2, 10, 18 of the first three noble gases, helium, neon, argon, was 8, and argued that the electrons in such atoms orbited in ‘closed shells’. The first contained only 2 electrons, the second and third, 8 each. Bohr acknowledged the work of Kossel. But neither Kossel nor others went as far as the Dane in elucidating the distribution of electrons throughout the periodic table, the culmination of which was the correct labelling of hafnium as not a rare earth element.
26 BCW, Vol. 4, p. 740. Postcard from Arnold Sommerfeld to Bohr, 7 March 1921.
27 BCW, Vol. 4, p. 740. Letter from Arnold Sommerfeld to Bohr, 25 April 1921.
28 Pais (1991), quoted p. 205.
29 If n=3, then k=1, 2, 3. If k=1, then m=0 and the energy state is (3,1,0). If k=2, then m=–1, 0, 1 and the energy states are (3,2,–1), (3,2,0), and (3,2,1). If k=3, then m=–2, –1, 0, 1, 2 and the energy states are (3,3,–2), (3,3,–1), (3,3,0), (3,3,1) and (3,3,2). The total number of energy states in the third shell n=3 is 9 and the maximum number of electrons 18. For n=4, the energy states are (4,1,0), (4,2,–1), (4,2,0), (4,2,1), (4,3,–2), (4,3,–1), (4,3,0), (4,3,1), (4,3,2), (4,4,–3), (4,4,–2), (4,4,–1), (4,4,0), (4,4,1), (4,4,2), (4,4,3). The number of electron energy states for a given n was simply equal to n2. For the first four shells, n=1, 2, 3 and 4, the number of energy states are 1, 4, 9, 16.
30 The first edition of Atombau und Spektrallinien was published in 1919.
31 Pais (2000), quoted p. 223.
32 Recall that in his model of the quantum atom, Bohr introduced the quantum into the atom through the quantisation of angular momentum (L = nh/2 = mvr). An electron moving in a circular orbit possesses angular momentum. Labelled L in calculations, the angular momentum of the electron is nothing more than the value obtained by multiplying its mass by its velocity by the radius of its orbit (in symbols, L=mvr). Only those electron orbits were permitted that had an angular momentum equal to nh/2, where n was 1, 2, 3 and so on. All others orbits were forbidden.
33 Calaprice (2005), quoted p. 77.
34 Pais (1989b), quoted p. 310.
35 Goudsmit (1976), p. 246.
36 Samuel Goudsmit, AHQP interview, 5 December 1963.
37 Pais (1989b), quoted p. 310.
38 Pais (2000), quoted p. 222.
39 Actually, the two values are +1/2(h/2) and –1/2(h/2) or equivalently +h/4 and –h/4.
40 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, quoted p. 702.
41 Pais (1989b), quoted p. 311.
42 George Uhlenbeck, AHQP interview, 31 March 1962.
43 Uhlenbeck (1976), p. 253.
44 BCW, Vol. 5, p. 229. Letter from Bohr to Ralph Kronig, 26 March 1926.
45 Pais (2000), quoted p. 304.
46 Robertson (1979), quoted p. 100.
47 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, quoted p. 691.
48 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, quoted p. 692.
49 Ralph Kronig, AHQP interview, 11 December 1962.
50 Ralph Kronig, AHQP interview, 11 December 1962.
51 Pais (2000), quoted p. 305.
52 Pais (2000), quoted p. 305.
53 Pais (2000), quoted p. 305.
54 Pais (2000), quoted p. 305.
55 Uhlenbeck (1976), p. 250.
56 Pais (2000), quoted p. 305.
57 Pais (2000), quoted p. 305.
58 Pais (2000), quoted p. 230.
59 Enz (2002), quoted p. 115.
60 Enz (2002), quoted p. 117.
61 Goudsmit (1976), p. 248.
62 Jammer (1966), p. 196.
63 Mehra and Rechenberg (1982), Vol. 2, Pt. 2, quoted p. 208. Letter from Pauli to Ralph Kronig, 21 May 1925.
64 Mehra and Rechenberg (1982), Vol. 1, Pt. 2, quoted p. 719.
CHAPTER 8: THE QUANTUM MAGICIAN
1 Mehra and Rechenberg (1982), Vol. 2, quoted p. 6.
2 Heisenberg (1971), p. 16.
3 Heisenberg (1971), p. 16.
4 Heisenberg (1971), p. 16.
/> 5 Heisenberg (1971), p. 16.
6 Werner Heisenberg, AHQP interview, 30 November 1962.
7 Heisenberg (1971), p. 24.
8 Heisenberg (1971), p. 24.
9 Werner Heisenberg, AHQP interview, 30 November 1962.
10 Heisenberg (1971), p. 26.
11 Heisenberg (1971), p. 26.
12 Heisenberg (1971), p. 26.
13 Heisenberg (1971), p. 38.
14 Heisenberg (1971), p. 38.
15 Werner Heisenberg, AHQP interview, 30 November 1962.
16 Heisenberg (1971), p. 42.
17 Born (1978), p. 212.
18 Born (2005), p. 73. Letter from Born to Einstein, 7 April 1923.
19 Born (1978), p. 212.
20 Cassidy (1992), quoted p. 168.
21 Mehra and Rechenberg (1982), Vol. 2, quoted pp. 140–1. Letter from Heisenberg to Pauli, 26 March 1924.
22 Mehra and Rechenberg (1982), Vol. 2, quoted p. 133. Letter from Pauli to Bohr, 11 February 1924.
23 Mehra and Rechenberg (1982), Vol. 2, quoted p. 135. Letter from Pauli to Bohr, 11 February 1924.
24 Mehra and Rechenberg (1982), Vol. 2, quoted p. 142.
25 Mehra and Rechenberg (1982), Vol. 2, quoted p. 127. Letter from Born to Bohr, 16 April 1924.
26 Mehra and Rechenberg (1982), Vol. 2, quoted p. 3.
27 Mehra and Rechenberg (1982), Vol. 2, quoted p. 150.
28 Frank Hoyt, AHQP interview, 28 April 1964.
29 Mehra and Rechenberg (1982), Vol. 2, quoted p. 209. Letter from Heisenberg to Bohr, 21 April 1925.
30 Heisenberg (1971), p. 8.
31 Pais (1991), quoted p. 270.
32 Mehra and Rechenberg (1982), Vol. 2, quoted p. 196. Letter from Pauli to Bohr, 12 December 1924.
33 Cassidy (1992), quoted p. 198.
34 Pais (1991), quoted p. 275.
35 Heisenberg (1971), p. 60.
36 Heisenberg (1971), p. 60.
37 Heisenberg (1971), p. 61.
38 Heisenberg (1971), p. 61.
39 Heisenberg (1971), p. 61.
40
41 Enz (2002), quoted p. 131. Letter from Heisenberg to Pauli, 21 June 1925.
42 Cassidy (1992), quoted p. 197. Letter from Heisenberg to Pauli, 9 July 1925.
43 Mehra and Rechenberg (1982), quoted p. 291.
44 Enz (2002), quoted p. 133.
45 Cassidy (1992), quoted p. 204.
46 Heisenberg (1925), p. 276.
47 Born (2005), p. 82. Letter from Born to Einstein, 15 July 1925. Born may have discovered that Heisenberg’s multiplication rule was exactly the same as that for matrix multiplication by the time he wrote to Einstein. Born recalled on one occasion that Heisenberg gave him the paper on 11 or 12 July. However, on another occasion he believed the date of his identifying the strange multiplication with matrix multiplication was 10 July.
48 Born (2005), p. 82. Letter from Born to Einstein, 15 July 1925.
49 Cropper (2001), quoted p. 269.
50 Born (1978), p. 218.
51 Schweber (1994), quoted p. 7.
52 Born (2005), p. 80. Letter from Born to Einstein, 15 July 1925.
53 In 1925 and 1926, Heisenberg, Born and Jordan never used the term ‘matrix mechanics’. They always spoke about the ‘new mechanics’ or ‘quantum mechanics’. Others initially referred to ‘Heisenberg’s mechanics’ or ‘Göttingen mechanics’ before some mathematicians started referring to it as ‘Matrizenphysik’, ‘matrix physics’. By 1927 it was routinely referred to as ‘matrix mechanics’, a name that Heisenberg always disliked.
54 Born (1978), p. 190.
55 Born (1978), p. 218.
56 Mehra and Rechenberg (1982), Vol. 3, quoted p. 59. Letter from Born to Bohr, 18 December 1926.
57 Greenspan (2005), quoted p. 127.
58 Pais (1986), quoted p. 255. Letter from Einstein to Paul Ehrenfest, 20 September 1925.
59 Pais (1986), quoted p. 255.
60 Pais (2000), quoted p. 224.
61 Born (1978), p. 226.
62 Born (1978), p. 226.
63 Kursunoglu and Wigner (1987), quoted p. 3.
64 Paul Dirac, AHQP interview, 7 May 1963.
65 Kragh (2002) quoted p. 241.
66 Dirac (1977), p. 116.
67 Dirac (1977), p. 116.
68 Born (2005), p. 86. Letter from Einstein to Mrs Born, 7 March 1926.
69 Bernstein (1991), quoted p. 160.
CHAPTER 9: ‘A LATE EROTIC OUTBURST’
1 Moore (1989), quoted p. 191.
2 Born (1978), p. 270.
3 Moore (1989), quoted p. 23.
4 Moore (1989), quoted pp. 58–9.
5 Moore (1989), quoted p. 91.
6 Moore (1989), quoted p. 91.
7 Mehra and Rechenberg (1987) Vol. 5, Pt. 1, quoted p. 182.
8 Moore (1989), quoted p. 145.
9 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 412.
10 Bloch (1976), p. 23. Although there is some doubt when exactly Schrödinger delivered his talk at the colloquium, 23 November is the most probable date that fits the known facts better than any alternative.
11 Bloch (1976), p. 23.
12 Bloch (1976), p. 23.
13 Abragam (1988), p. 31.
14 Bloch (1976), pp. 23–4.
15 The equation was rediscovered in 1927 by Oskar Klein and Walter Gordon and became known as the Klein-Gordon equation. It applies only to spin zero particles.
16 Moore (1989), quoted p. 196.
17 Moore (1989), quoted p. 191.
18 The title of Schrödinger’s paper signalled that in his theory the quantisation of an atom’s energy levels was based on the allowed values, or eigenvalues, of electron wavelengths. In German, eigen means ‘proper’ or ‘characteristic’. The German word eigenwert was only half-heartedly translated into English as eigenvalue.
19 Cassidy (1992), quoted p. 214.
20 Moore (1989), quoted p. 209. Letter from Planck to Schrödinger, 2 April 1926.
21 Moore (1989), quoted p. 209. Letter from Einstein to Schrödinger, 16 April 1926.
22 Przibram (1967), p. 6.
23 Moore (1989), quoted p. 209. Letter from Einstein to Schrödinger, 26 April 1926.
24 Cassidy (1992), quoted p. 213.
25 Pais (2000), quoted p. 306.
26 Moore (1989), quoted p. 210.
27 Mehra and Rechenberg (1987), Vol. 5, Pt. 1, quoted p. 1. Letter from Pauli to Pascual Jordan, 12 April 1926.
28 Cassidy (1992), quoted p. 213.
29 Cassidy (1992), quoted p. 213. Letter from Heisenberg to Pascual Jordan, 19 July 1926.
30 Cassidy (1992), quoted p. 213.
31 Cassidy (1992), quoted p. 213. Letter from Born to Schrödinger, 16 May 1927.
32 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
33 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
34 Pauli, Dirac and the American Carl Eckhart all independently showed that Schrödinger was correct.
35 Mehra and Rechenberg (1987), Vol. 5 Pt. 2, quoted p. 639. Letter from Schrödinger to Wilhelm Wien, 22 February 1926.
36 Moore (1989), quoted p. 211.
37 Moore (1989), quoted p. 211.
38 Cassidy (1992), quoted p. 215. Letter from Heisenberg to Pauli, 8 June 1926.
39 Cassidy (1992), quoted p. 213. Letter from Heisenberg to Pascual Jordan, 8 April 1926.
40 Heisenberg’s paper was received by the Zeitschrift für Physik on 24 July and was published on 26 October 1926.
41 Pais (2000), quoted p. 41. Letter from Born to Einstein, 30 November 1926. Not included in Born (2005).
42 Bloch (1976), p. 320. In the original German:
ar Manches rechnet Erwin schon
Mit seiner Wellenfunktion.
Nur wissen möcht’ man gerne wohl
Was man sich dabei vorstell’n soll.
43 Str
ictly speaking it should be the square of the ‘modulus’ of the wave function. Modulus is the technical term for taking the absolute value of a number regardless of whether it is positive or negative. For example, if x=–3, then the modulus of x is 3. Written as: |x|=|–3|= 3. For a complex number z=x+iy, the modulus of z is given by |z|= x+y2.
44 The square of a complex number is calculated as follows: z=4+3i, z2 is in fact not z×z, but z×z* where z* is called the complex conjugate. If z=4+3i, then z*=4–3i. Hence, z2=z×z*=(4+3i)×(4–3i)=16–12i+12i–9i2=16–9(–1)2=16–9(–1)=16+9=25. If z=4+3i, then the modulus of z is 5.
45 Born (1978), p. 229.
46 Born (1978), p. 229.
47 Born (1978), p. 230.
48 Born (1978), p. 231.
49 Born (2005), p. 81. Letter from Born to Einstein, 15 July 1925.
50 Born (2005), p. 81. Letter from Born to Einstein, 15 July 1925.
51 Pais (2000), quoted p. 41.
52 Pais (1986), quoted p. 256.
53 Pais (2000), quoted p. 42.
54 The second paper was published in the Zeitschrift für Physik on 14 September.
55 Pais (1986), quoted p. 257.
56 Pais (1986), quoted p. 257.
57 Once again, technically speaking it is the absolute or modulus square of the wave function. Also, technically, rather than the ‘probability’, the absolute square of the wave function gives the ‘probability density’.
58 Pais (1986), quoted p. 257.
59 Pais (1986), quoted p. 257.
60 Pais (2000), quoted p. 39.
61 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 827. Letter from Schrödinger to Wien, 25 August 1926.
62 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 828. Letter from Schrödinger to Born, 2 November 1926.
63 Heitler (1961), quoted p. 223.
64 Moore (1989), quoted p. 222.
65 Moore (1989), quoted p. 222.
66 Heisenberg (1971), p. 73.
67 Cassidy (1992), quoted p. 222. Letter from Heisenberg to Pascual Jordan, 28 July 1926.
68 Cassidy (1992), quoted p. 222. Letter from Heisenberg to Pascual Jordan, 28 July 1926.
69 Mehra and Rechenberg (1987), Vol. 5, Pt. 2, quoted p. 625. Letter from Bohr to Schrödinger, 11 September 1926.
70 Heisenberg (1971), p. 73.
71 Heisenberg (1971), p. 73.
72 See Heisenberg (1971), pp. 73–5 for the complete reconstruction of this particular exchange between Schrödinger and Bohr.
73 Heisenberg (1971), p. 76.
74 Moore (1989), p. 228. Letter from Schrödinger to Wilhelm Wien, 21 October 1926.