Reappraising Einstein's 1909 application of fluctuation theory to Planckian radiation

American Journal of Physics

Volumn 72, Issue 8, 2004, Pages 1059-1067

  Irons, F E ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

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EID: 4344593016     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1767098     Document Type: Article

References (84)

1. A. Einstein, "On the present status of the radiation problem," Phys. Z. 10, 185-193 (1909), Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 56. For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 56.
2. Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 56.
3. Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 56. For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 56.
4. A. Einstein, "On the development of our views concerning the nature and constitution of radiation," Phys. Z. 10, 817-826 (1909). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 60. For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 60.
5. A. Einstein, "On the development of our views concerning the nature and constitution of radiation," Phys. Z. 10, 817-826 (1909). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 60. For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 60.
6. A. Einstein, "On the development of our views concerning the nature and constitution of radiation," Phys. Z. 10, 817-826 (1909). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 60. For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 60.
7. See, for example, G. Greenstein and A. G. Zajonic, The Quantum Challenge (Jones and Bartlett, Boston, 1997), Chap, 2, particularly Sec. 2.2.
8. Y. Rocard and C. R. S. Manders, Thermodynamics (Isaac Pitman, London, 1961), Chap. 35; W. Greiner, L. Neise, and H. Stöcker, Thermodynamics and Statistical Mechanics, translated by D. Rischke (Springer-Verlag, New York, 1995), pp. 191-194; J. R. Waldram, The Theory of Thermodynamics (Cambridge U.P., Cambridge, UK, 1985), Chap. 16.
9. Y. Rocard and C. R. S. Manders, Thermodynamics (Isaac Pitman, London, 1961), Chap. 35; W. Greiner, L. Neise, and H. Stöcker, Thermodynamics and Statistical Mechanics, translated by D. Rischke (Springer-Verlag, New York, 1995), pp. 191-194; J. R. Waldram, The Theory of Thermodynamics (Cambridge U.P., Cambridge, UK, 1985), Chap. 16.
10. Y. Rocard and C. R. S. Manders, Thermodynamics (Isaac Pitman, London, 1961), Chap. 35; W. Greiner, L. Neise, and H. Stöcker, Thermodynamics and Statistical Mechanics, translated by D. Rischke (Springer-Verlag, New York, 1995), pp. 191-194; J. R. Waldram, The Theory of Thermodynamics (Cambridge U.P., Cambridge, UK, 1985), Chap. 16.
11. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Dover, New York, 1960), Chap. VII.
12. A. Einstein, "On the general molecular theory of heat," Ann. Phys. (Leipzig) 14, 354-362 (1904). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 5, For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 5.
13. A. Einstein, "On the general molecular theory of heat," Ann. Phys. (Leipzig) 14, 354-362 (1904). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 5, For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 5.
14. A. Einstein, "On the general molecular theory of heat," Ann. Phys. (Leipzig) 14, 354-362 (1904). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 5, For an English translation, see The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 5.
15. For a recent derivation of Eq. (1) as an ensemble average, see W. Greiner, L. Neise, and H. Stöcker, Ref. 4; A. Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (Clarendon, Oxford, 1982), p. 69.
16. For a recent derivation of Eq. (1) as an ensemble average, see W. Greiner, L. Neise, and H. Stöcker, Ref. 4; A. Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (Clarendon, Oxford, 1982), p. 69.
17. Editorial note in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), p. 146.
18. W. Pauli, "Einstein's contributions to quantum theory," in Albert Einstein: Philosopher-Scientist, edited by P. A. Schilpp (Tudor, New York, 1951), pp. 149-160.
19. R. C. Tolman, The Principles of Statistical Physics (Oxford Univ., Oxford, 1959), pp. 636-641.
20. M. J. Klein, "Einstein and the wave-particle duality," Natural Philos. 3, 1-49 (1964).
21. A. Kastler, "Albert Einstein and the photon concept," in Relativity, Quanta, and Cosmology in the Scientific Thought of Albert Einstein, edited by F. De Finis (Johnson Reprint, New York, 1979), Chap. 11.
22. M. J. Klein, "Einstein and the development of quantum physics," in Einstein: A Centenary Volume, edited by A. P. French (Heinemann, London, 1979), pp. 133-151.
23. M. J. Klein, "No firm foundation: Einstein and the early quantum theory," in Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, edited by H. Woolf (Addison-Wesley, Reading, MA, 1980), pp. 161-185.
24. A. Pais, Ref. 7, Secs, 4c, 4d, 21a, 21c.
25. J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory (Springer-Verlag, New York, 1982), Vol. 1, Part 1, Sec. 1,3.
26. P. W. Milonni, "Wave-particle duality of light: A current perspective," in The Wave-Particle Dualism, edited by S. Diner, D. Fargue, G. Lochak, and F. Selleri (Reidel, Dordrecht, 1984), pp. 27-67.
27. M. S. Longair, Theoretical Concepts in Physics (Cambridge U.P., Cambridge, 1984), Chap. 12.
28. A. B. Pippard, The Elements of Classical Thermodynamics (Cambridge U.P., Cambridge, 1957), pp. 83-84.
29. A. Einstein, Ref. l, p. 364 of the English translation.
30. Reference 18, pp. 245-249.
31. References 1 and 2; Ref. 18, pp. 245-249; Ref. 11, p. 12.
32. For a comment to this effect, see R. E. Kelly, "Thermodynamics of blackbody radiation," Am. J. Phys. 49, 714-719 (1981); C. V. Heer, Statistical Mechanics, Kinetic Theory, and Stochastic Processes (Academic, New York, 1972), p. 234. The photon-photon interaction predicted by quantum electrodynamics is too small to be of concern. See J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Springer-Verlag, New York, 1976), Chap. 13.
33. For a comment to this effect, see R. E. Kelly, "Thermodynamics of blackbody radiation," Am. J. Phys. 49, 714-719 (1981); C. V. Heer, Statistical Mechanics, Kinetic Theory, and Stochastic Processes (Academic, New York, 1972), p. 234. The photon-photon interaction predicted by quantum electrodynamics is too small to be of concern. See J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Springer-Verlag, New York, 1976), Chap. 13.
34. For a comment to this effect, see R. E. Kelly, "Thermodynamics of blackbody radiation," Am. J. Phys. 49, 714-719 (1981); C. V. Heer, Statistical Mechanics, Kinetic Theory, and Stochastic Processes (Academic, New York, 1972), p. 234. The photon-photon interaction predicted by quantum electrodynamics is too small to be of concern. See J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Springer-Verlag, New York, 1976), Chap. 13.
35. A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 61. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 61.
36. A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 61. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 61.
37. See, for example, F. K. Richtmyer, E. H. Kennard, and J. N. Cooper, Introduction to Modern Physics (McGraw-Hill, New York, 1969), pp. 143-146; M. Born, Atomic Physics (Blackie, Glasgow, 1962), 7th ed., pp. 343-347.
38. See, for example, F. K. Richtmyer, E. H. Kennard, and J. N. Cooper, Introduction to Modern Physics (McGraw-Hill, New York, 1969), pp. 143-146; M. Born, Atomic Physics (Blackie, Glasgow, 1962), 7th ed., pp. 343-347.
39. Of related interest is that the expansion of the universe causes the spectral distribution of the cosmic background radiation to vary, while maintaining its blackbody character. Such a variation is linked to the gravitational red shift and is not indicative of the radiation being able to thermalize. For a brief discussion, see W. Greiner, L. Neise, and H. Stöcker., Ref. 4, p. 333. For greater detail, see H. Höhl, "A contribution to the thermodynamics of the universe and to 3°K radiation," in Perspectives in Quantum Theory, edited by W. Yourgrau and A. van der Mewe (Dover, New York, 1971), Chap. 8.
40. Of related interest is that the expansion of the universe causes the spectral distribution of the cosmic background radiation to vary, while maintaining its blackbody character. Such a variation is linked to the gravitational red shift and is not indicative of the radiation being able to thermalize. For a brief discussion, see W. Greiner, L. Neise, and H. Stöcker., Ref. 4, p. 333. For greater detail, see H. Höhl, "A contribution to the thermodynamics of the universe and to 3°K radiation," in Perspectives in Quantum Theory, edited by W. Yourgrau and A. van der Mewe (Dover, New York, 1971), Chap. 8.
41. D. C. Spanner, Introduction to Thermodynamics (Academic, London, 1964), pp. 223-224.
42. S. Tomonaga, Quantum Mechanics (North-Holland, Amsterdam, 1962), Vol. I, p. 18.
43. C. V. Heer, Ref. 23, p. 234; P. G. Bergmann, Basic Theories of Physics: Heat and Quanta (Dover, New York, 1951), p. 143; E. A. Desloge, Statistical Physics (Holt, Rinehart and Winston, New York, 1966), p. 159.
44. C. V. Heer, Ref. 23, p. 234; P. G. Bergmann, Basic Theories of Physics: Heat and Quanta (Dover, New York, 1951), p. 143; E. A. Desloge, Statistical Physics (Holt, Rinehart and Winston, New York, 1966), p. 159.
45. C. V. Heer, Ref. 23, p. 234; P. G. Bergmann, Basic Theories of Physics: Heat and Quanta (Dover, New York, 1951), p. 143; E. A. Desloge, Statistical Physics (Holt, Rinehart and Winston, New York, 1966), p. 159.
46. T. S. Kuhn, Black-Body Theory and the Quantum Discontinuity 1894-1912 (Clarendon, Oxford, 1978), pp. 117-118.
47. A. Einstein, Ref. 2, p. 391 of the English translation.
48. In Ref. 2, Einstein refers to A as an increase in momentum and derives Eq. (20) of the present paper. In Ref. l Einstein refers to A as an increase in velocity, though the equation that he derives [Eq. (20) of the present paper] requires that A be viewed as the increase in momentum.
49. A. Einstein, Ref. 6, p. 76 of the English translation.
50. A. Einstein, Ref. 2, p. 386 of the English translation, For a brief account of the reception accorded Einstein's address at the Salzburg Congress of 1909, see A. Hermann, The Genesis of Quantum Theory (1899-1913) (MIT, Cambridge, MA, 1971), Chap. 3, Sec. 7; also the Editorial Note in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al (Princeton U.P., Princeton, 1989), pp. 134-148 (particularly pp. 147-148).
51. A. Einstein, Ref. 2, p. 386 of the English translation, For a brief account of the reception accorded Einstein's address at the Salzburg Congress of 1909, see A. Hermann, The Genesis of Quantum Theory (1899-1913) (MIT, Cambridge, MA, 1971), Chap. 3, Sec. 7; also the Editorial Note in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al (Princeton U.P., Princeton, 1989), pp. 134-148 (particularly pp. 147-148).
52. A. Einstein, Ref. 2, p. 386 of the English translation, For a brief account of the reception accorded Einstein's address at the Salzburg Congress of 1909, see A. Hermann, The Genesis of Quantum Theory (1899-1913) (MIT, Cambridge, MA, 1971), Chap. 3, Sec. 7; also the Editorial Note in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 1900-1909, edited by J. Stachel et al (Princeton U.P., Princeton, 1989), pp. 134-148 (particularly pp. 147-148).
53. 35 Reference 14, p. 167.
54. A. Einstein, "On the theory of light production and light absorption," Ann. Phys. (Leipzig) 20, 199-206 (1906). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 19001909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 34. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 34 (see particularly p. 196), For a commentary, see M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), pp. 26-27; T. Kuhn, Ref, 30, pp. 184-185.
55. A. Einstein, "On the theory of light production and light absorption," Ann. Phys. (Leipzig) 20, 199-206 (1906). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 19001909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 34. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 34 (see particularly p. 196), For a commentary, see M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), pp. 26-27; T. Kuhn, Ref, 30, pp. 184-185.
56. A. Einstein, "On the theory of light production and light absorption," Ann. Phys. (Leipzig) 20, 199-206 (1906). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 19001909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 34. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 34 (see particularly p. 196), For a commentary, see M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), pp. 26-27; T. Kuhn, Ref, 30, pp. 184-185.
57. A. Einstein, "On the theory of light production and light absorption," Ann. Phys. (Leipzig) 20, 199-206 (1906). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 19001909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 34. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 34 (see particularly p. 196), For a commentary, see M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), pp. 26-27; T. Kuhn, Ref, 30, pp. 184-185.
58. A. Einstein, "On the theory of light production and light absorption," Ann. Phys. (Leipzig) 20, 199-206 (1906). Reprinted in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: Writings 19001909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), Doc. 34. For an English translation, see the companion volume, The Collected Papers of Albert Einstein, translated by A. Beck (Princeton U.P., Princeton, 1989), Doc. 34 (see particularly p. 196), For a commentary, see M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), pp. 26-27; T. Kuhn, Ref, 30, pp. 184-185.
59. E. Wigner, as part of a discussion, in Some Strangeness In the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, edited by H. Woolf (Addison-Wesley, Reading, MA, 1980), p. 195 (also see the comments by Wigner on p. 194).
60. For example, R. E. Sonntag and G. J. van Wylen, Fundamentals of Statistical Thermodynamics (Wiley, New York, 1966), pp. 177-183; S. Tomonaga, Ref. 28, pp. 72-75; H. S. Leff, "Teaching the photon gas in introductory physics," Am. J. Phys. 70, 792-797 (2002).
61. For example, R. E. Sonntag and G. J. van Wylen, Fundamentals of Statistical Thermodynamics (Wiley, New York, 1966), pp. 177-183; S. Tomonaga, Ref. 28, pp. 72-75; H. S. Leff, "Teaching the photon gas in introductory physics," Am. J. Phys. 70, 792-797 (2002).
62. For example, R. E. Sonntag and G. J. van Wylen, Fundamentals of Statistical Thermodynamics (Wiley, New York, 1966), pp. 177-183; S. Tomonaga, Ref. 28, pp. 72-75; H. S. Leff, "Teaching the photon gas in introductory physics," Am. J. Phys. 70, 792-797 (2002).
63. Reference 3, Chap, 2; M. V. Klein, Optics (Wiley, New York, 1970), Sec. 6.4; W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am, J. Phys. 32, 919-926 (1964).
64. Reference 3, Chap, 2; M. V. Klein, Optics (Wiley, New York, 1970), Sec. 6.4; W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am, J. Phys. 32, 919-926 (1964).
65. Reference 3, Chap, 2; M. V. Klein, Optics (Wiley, New York, 1970), Sec. 6.4; W. Martienssen and E. Spiller, "Coherence and fluctuations in light beams," Am, J. Phys. 32, 919-926 (1964).
66. For a broad account of radiation from solids, see G. A. W. Rutgers, "Temperature radiation of solids," in Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1958), Vol. XXVI, pp. 129-170; H. Blau and H. Fischer (eds.), Radiative Transfer from Solid Materials (Macmillan, New York, 1962).
67. For a broad account of radiation from solids, see G. A. W. Rutgers, "Temperature radiation of solids," in Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1958), Vol. XXVI, pp. 129-170; H. Blau and H. Fischer (eds.), Radiative Transfer from Solid Materials (Macmillan, New York, 1962).
68. For a useful discussion of detailed balance, see R. W. Ditchburn, Light (Blackie, London, 1958), pp. 570-571; J. K. Roberts, Heat and Thermodynamics (Blackie, London, 1940), 3rd ed., pp. 385-386.
69. For a useful discussion of detailed balance, see R. W. Ditchburn, Light (Blackie, London, 1958), pp. 570-571; J. K. Roberts, Heat and Thermodynamics (Blackie, London, 1940), 3rd ed., pp. 385-386.
70. v(T)].
71. v(T)].
72. See E. U. Condon, Ref. 42, p. 374;
73. E. Mach, Principles of the Theory of Heat (Reidel, Dordrecht, 1986), pp. 139-140.
74. 2 also exhibit fluctuations owing to the emission and absorption of photons by the atoms." R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973), p. 18.
75. See F. Seitz, The Modem Theory of Solids (McGraw-Hill, New York, 1940), Sec. 96; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986), 6th ed., pp. 296-306; C. T. Walker and G. A. Slack, "Who named the-ON's?" Am. J. Phys. 38, 1380-1389 (1970), pp. 1384-1385.
76. See F. Seitz, The Modem Theory of Solids (McGraw-Hill, New York, 1940), Sec. 96; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986), 6th ed., pp. 296-306; C. T. Walker and G. A. Slack, "Who named the-ON's?" Am. J. Phys. 38, 1380-1389 (1970), pp. 1384-1385.
77. See F. Seitz, The Modem Theory of Solids (McGraw-Hill, New York, 1940), Sec. 96; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986), 6th ed., pp. 296-306; C. T. Walker and G. A. Slack, "Who named the-ON's?" Am. J. Phys. 38, 1380-1389 (1970), pp. 1384-1385.
78. A. Pais, Ref. 7, pp. 73-74.
79. Y. Rocard and C. R. S. Manders, Ref. 4, p. 480, refer to the number of particles (actually the density) being held constant. Also see W. Greiner, L. Neise, and H. Stöcker, Ref. 4, p. 194.
80. Reference 6. The English translation is quoted from Ref. 16, p. 69.
81. For a commentary on Einstein's calculation, see B. H. Lavenda, Statistical Physics; A Probabilistic Approach (Wiley, New York, 1991), pp. 84-85; A. Pais, Ref. 7, pp. 69-70; Ref. 16, p. 69; Ref. 30, pp. 178-179.
82. For a commentary on Einstein's calculation, see B. H. Lavenda, Statistical Physics; A Probabilistic Approach (Wiley, New York, 1991), pp. 84-85; A. Pais, Ref. 7, pp. 69-70; Ref. 16, p. 69; Ref. 30, pp. 178-179.
83. Reference 6, p. 77 of the English translation.
84. Editorial Note in A. Einstein, The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years; Writings 1900-1909, edited by J. Stachel et al. (Princeton U.P., Princeton, 1989), p. 138.