Skip to main content
SpringerLink
Log in

Methods of Theoretical Physics

  • Chapter
  • First Online:
The Second Physicist

Part of the book series: Archimedes ((ARIM,volume 48))

  • 1245 Accesses

Abstract

We discussed methods of research in theoretical physics in a general way in the first chapter. In this chapter we look at specific examples of methods as they entered research: Boltzmann’s use of the molecular method in the mechanical theory of heat; Hertz’s use of the method of mathematical phenomenology in electrodynamics; Planck’s use of principles as a method in physical chemistry; and Helmholtz’s and Boltzmann’s use of the method of analogy in developing heat and electromagnetic theory. For theoretical physics as a field, teaching is as important as research, for without the regular renewal of trained researchers, the field would stagnate and eventually come to an end. In this chapter, we look at Neumann’s, Kirchhoff’s, and Helmholtz’s methods of presenting theoretical physics in lectures.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The extraordinary professorship for mathematical physics was created in 1863. Austrian Ministry of State, Section for Culture and Education, and Ministry of Finance reports, 10 July 1863, Öster. STA, 5 Phil, Physik. Hans Schobesberger, “Die Geschichte des Physikalischen Institutes der Universität Graz in den Jahren von 1850–1890” (manuscript), 16, Graz UA; Ministry of Culture and Education to Dean of the Philosophical Faculty, 15 April 1869; report by the Ministry to the Emperor, 28 June 1869; all in Öster. STA, 5 Phil. Physik; Theodor Des Coudres, “Ludwig Boltzmann,” Verh. Sächs. Ges. Wiss. 85 (1906): 615–27, on 623; Woldemar Voigt, “Ludwig Boltzmann,” Gött. Nachr.,1907, 69–82, on 72.

  2. 2.

    Ludwig Boltzmann, “Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten,” Sitzungsber. Wiener Akad. 58 (1868): 517–60, reprinted in Wiss. Abh., vol. 1, 49–96.

  3. 3.

    Ludwig Boltzmann, “Analytischer Beweis des zweiten Hauptsatzes der mechanischen Wärmetheorie aus den Sätzen über das Gleichgewicht der lebendigen Kraft,” Sitzungsber. Wiener Akad. 63 (1871): 712–32; repr. in Wiss. Abh., vol. 1, 288–308, on 308.

  4. 4.

    Boltzmann, “Weitere Studien”; Martin J. Klein, Paul Ehrenfest, The Making of a Theoretical Physicist. (Amsterdam and London: North-Holland, 1970), vol. 1, 100.

  5. 5.

    Boltzmann, “Über das Wärmegleichgewicht,” 254–55; Martin J. Klein, “Maxwell, His Demon, and the Second Law of Thermodynamics,” American Scientist 58 (1970): 84–97, on 92.

  6. 6.

    Boltzmann, “Weitere Studien,” 369–402, especially 393. The reasons for Boltzmann’s choice of the letter E, in this form of writing the second law, and of the sign reversal (the entropy increases while E decreases in the passage to equilibrium) together with Boltzmann’s 1872 paper in general are discussed in Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity 1894-1912 (New York: Oxford University Press, 1978), 42–46, 269n13.

  7. 7.

    For a time this statement was known as “Boltzmann’s minimum theory,” then as “Boltzmann’s H-theorem” (Stephen G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century, vol. 1, Physics and the Atomists [Amsterdam and New York: North-Holland, 1976], 238; see 235–38 for Brush’s discussion of Boltzmann’s 1872 paper).

  8. 8.

    Boltzmann, “Weitere Studien,” 345.

  9. 9.

    Klein, Ehrenfest, 102.

  10. 10.

    Ludwig Boltzmann, “Über das Wirkungsgesetz der Molekularkräfte,” Sitzungsber. Wiener Akad. 66 (1872): 213–219; repr. Wiss. Abh., vol. 1, 309–15.

  11. 11.

    Boltzmann, “Weitere Studien,” 368.

  12. 12.

    Ludwig Boltzmann, “Bemerkungen über einige Probleme der mechanischen Wärmetheorie,” Sitzungsber. Wiener Akad. 75 (1877): 62–100; repr. Wiss. Abh., vol. 2, 112–48, especially 116–22; Klein, Ehrenfest, 102–4. Loschmidt’s statement, which came to be called the “reversibility paradox,” had been discussed by William Thomson in 1874 (Brush, Motion We Call Heat, vol. 1, 238–39).

  13. 13.

    Ludwig Boltzmann, “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht,” Sitzungsber. Wiener Akad. 76 (1877): 373–435; repr. Wiss. Abh., vol. 2, 164–223, on 165–66.

  14. 14.

    Boltzmann, “Über die Beziehung,” 168, 175–76, 190–93. Boltzmann’s reasoning in his 1877 paper is analyzed in detail, for example, in René Dugas, La théorie physique au sens de Boltzmann et ses prolongements modernes (Neuchâtel-Suisse: Griffon, 1959), 192–99; Klein, Ehrenfest, 105–8; Kuhn, Black-Body Theory, 47–54; Salvo D’Agostino, A History of the Ideas of Theoretical Physics, Essays on Nineteenth and Twentieth Century Physics (Dordrecht: Kluwer Academic Publishers, 2000), 212–13.

  15. 15.

    Boltzmann, “Über die Beziehung,” 217–18, 223.

  16. 16.

    Max Planck, “Gedächtnissrede auf Heinrich Hertz,” Verh. phys. Ges. 13 (1894): 9–29; repr. in Physikalische Abhandlungen und Vorträge, 3 vols. (Braunschweig: F. Vieweg, 1958), vol. 3, 268–88, on 281–82.

  17. 17.

    Hertz abandoned his earlier approach to Maxwell’s theory, in 1884, which treated electrical waves in the air and the ether without a physical hypothesis about the ether. In its place, he adopted Helmholtz’s dielectric polarization, which was important for his course of experiments. He retained his belief that Maxwell’s theory was superior, but Helmholtz’s approach allowed him to prove it experimentally without presuming its truth (D’Agostino, History of the Ideas of Theoretical Physics, 138, 149, 177–78, 181–82; Olivier Darrigol, Electrodynamics from Ampère to Einstein [Oxford: Oxford University Press, 2000], 238).

  18. 18.

    Planck, “Hertz,” 282. In time, in agreement with Maxwell, Hertz recognized only one electric force, and he turned his attention from the electromagnetic effects of changing polarizations in material dielectrics to the free propagation of electric waves.

  19. 19.

    Hertz to his parents, 13 November and 23 December 1887, 1 January 1888, in Heinrich Hertz, Erinnerungen, Briefe, Tagebücher, ed. J. Hertz, 2nd rev. ed. M. Hertz and C. Süsskind (San Francisco: San Francisco Press, 1977), 236–48.

  20. 20.

    Heinrich Hertz, “Ueber die Einwirkung einer gradlinigen elektrischen Schwingung auf eine benachbarte Strombahn,” Ann. 34 (1888): 155–70, on 169.

  21. 21.

    Heinrich Hertz, “Ueber die Ausbreitungsgeschwindigkeit der elektrodynamischen Wirkungen,” Ann. 34 (1888): 551–69, on 568–69; “Ueber elektrodynamische Wellen im Luftraume und deren Reflexion,” Ann. 34 (1888): 610–23, on 610.

  22. 22.

    Heinrich Hertz, “Die Kräfte elektrischer Schwingungen behandelt nach der Maxwell’schen Theorie,” Ann. 36 (1888): 1–22, on 1.

  23. 23.

    Heinrich Hertz, “Ueber Strahlen elektrischer Kraft,” Ann. 36 (1889): 769–83, on 781.

  24. 24.

    Eugen Goldstein, “Aus vergangenen Tagen der Berliner Physikalischen Gesellschaft,” Naturwiss. 13 (1925): 39–45, on 44.

  25. 25.

    Helmholtz’s preface to Hertz, Gesammelte Werke, vol. 3, Die Prinzipien der Mechanik, in neuem Zusammenhange dargestellt, ed. P. Lenard (Leipzig, 1894); The Principles of Mechanics Presented in a New Form, ed. D. E. Jones and J. T. Walley (London, 1899; reprint New York: Dover, 1956).

  26. 26.

    D’Agostino, History of the Ideas of Theoretical Physics, 122–23.

  27. 27.

    Heinrich Hertz, Ueber die Beziehungen zwischen Licht und Elektricität (Bonn, 1889); in Ges. Werke, vol. 1, 339–54, on 339–40, 344, 352–53.

  28. 28.

    Heinrich Hertz, “On the Fundamental Equations of Electromagnetics for Bodies at Rest,” 1890, in Electric Waves, Being Researches on the Propagation of Electric Action with Finite Velocity through Space, trans. D. E. Jones (New York, 1893; repr. New York: Dover, 1962), 201.

  29. 29.

    Hertz, “Fundamental Equations … at Rest,” 201. These became a standard form of the equations of Maxwell’s theory; Hertz’s left-handed coordinate system determines the sign. Hertz’s introduction of these equations is analyzed in Tetu Hirosige, “Electrodynamics before the Theory of Relativity, 1890-1905,” Jap. Stud. Hist. Sci. 5 (1966), 1–49, on 2–6; and in P. M. Heimann, “Maxwell, Hertz and the Nature of Electricity,” Isis 62 (1970): 149–57.

  30. 30.

    Ludwig Boltzmann, “Über die Entwicklung der Methoden der theoretischen Physik in neuerer Zeit,” in Populäre Schriften (Leipzig: J. A. Barth, 1905), 198–227, on 221; Mach to Hertz, 25 September 1890, Ms. Coll., DM, 2976.

  31. 31.

    Hertz, Ueber die Beziehungen, 353–54.

  32. 32.

    Report by the Berlin U. Philosophical Faculty, 29 November 1888, DZA, Merseburg; quoted in Armin Hermann, Max Planck in Selbstzeugnissen und Bilddokumenten (Reinbek b. Hamburg: Rowohlt, 1973), 21–22.

  33. 33.

    Max Planck, “Ueber das Princip der Vermehrung der Entropie. Erste Abhandlung. Gesetze des Verlaufs von Reactionen, die nach constanten Gewichtsverhältnissen vor sich gehen,” Ann 30 (1887): 562–82; repr. in Phys. Abh., vol. 1, 196–216, on 196–200; Max Born, “Max Karl Ernst Ludwig Planck 1858-1947,” Obituary Notices of Fellows of the Royal Society 6 (1948): 161–88; repr. in Ausgewählte Abhandlungen, ed. Akademie der Wissenschaften in Göttingen (Göttingen: Vandenhoeck und Ruprecht, 1963), vol. 2, 626–46, on 629.

  34. 34.

    Einstein referred to the third paper of the series: Max Planck, “Ueber das Princip der Vermehrung der Entropie. Dritte Abhandlung. Gesetze des Eintritts beliebiger thermodynamischer and chemischer Reactionen,” Ann. 32 (1887): 462–503; repr. in Phys. Abh., vol.3, 232–73; Albert Einstein, “Max Planck als Forscher,” Naturwiss. 1 (1913): 1077–79, on 1077.

  35. 35.

    Max Planck, “Allgemeines zur neueren Entwicklung der Wärmetheorie,” Zs. f. phys. Chemie 8 (1891): 647–56; repr. Phys. Abh., vol. 1, 372–81, quotations on 380–81.

  36. 36.

    Proposal of Planck as ordinary member of the Prussian Academy of Sciences, signed by Helmholtz, Kundt, and Bezold. Document Nr. 23, in Physiker über Physiker, ed. Christa Kirsten, and Hans-Günther Körber (Berlin: Akademie-Verlag, 1975.), 125–26. The proposal is undated; Planck’s election was on 11 June 1894.

  37. 37.

    Maxwell was the first to work with general cyclic systems, applying them to electromagnetism. They were applied to heat by Maxwell, Rankine, and Helmholtz (Ludwig Boltzmann, Vorlesungen über die Prinzipe der Mechanik, vol. 2 [Leipzig: J. A. Barth, 1904], 166). The properties of monocyclic systems and Helmholtz’s reasons for studying them together with his conclusions are discussed in Martin J. Klein, “Mechanical Explanation at the End of the Nineteenth Century,” Centaurus 17 (1792): 58–82, on 63–67; Leo Königsberger, “The Investigations of Hermann von Helmholtz on the Fundamental Principles of Mathematics and Mechanics,” Annual Report of the … Smithsonian Institution … to July, 1896 (1898): 93–124, on 120–23; and, the main source of our discussion, Helmholtz’s Prussian Academy papers on the subject and his recapitulation of them in his Berlin lectures on the theory of heat: “Studien zur Statik monocyklischer Systeme,” Sitzungsber. preuss. Akad., 1884, 159–77, 311–18, 755–59, and Vorlesungen über theoretische Physik, vol. 6, Vorlesungen über die Theorie der Wärme, ed. Franz Richarz (Leipzig: J. A. Barth, 1903), 338–70. We acknowledge discussions with Stephen M. Winters, who has made a study of Helmholtz’s physics, including his monocyclic systems and least-action principle.

  38. 38.

    Ludwig Boltzmann, Vorlesungen über Maxwells Theorie der Elektricität und des Lichtes, vol. 2, Verhältniss zur Fernwirkungstheorie; specielle Fälle der Elektrostatik, stationären Strömung und Induction (Leipzig, 1893), 22, 50.

  39. 39.

    Arnold Sommerfeld, “Das Institut für Theoretische Physik,”in Die wissenschaftlichen Anstalten der Ludwig-Maximilians-Universität zu München, ed. Karl Alexander von Müller (Munich: R. Oldenbourg und Dr. C. Wolf, 1926), 290–91, on 290.

  40. 40.

    Ludwig Boltzmann, “Über die Methoden der theoretischen Physik” (1892), in Populäre Schriften, 1–10. Boltzmann approved of Maxwell’s expression “dynamical illustration” for mechanisms representing the electromagnetic field. He discussed this and related points in Ludwig Boltzmann, Vorlesungen über Maxwells Theorie der Elektricität und des Lichtes, vol. 1, Ableitung der Grundgleichungen für ruhende, homogene, isotrope Körper (Leipzig, 1891), 13, 35, and elsewhere in his lectures.

  41. 41.

    Ludwig Boltzmann, “Über ein Medium, dessen mechanische Eigenschaften auf die von Maxwell für den Electromagnetismus aufgestellten Gleichungen führen,” Sitzungsber. bay. Akad. 22 (1892): 279–301; repr. in Wiss. Abh., vol. 3, 406–27.

  42. 42.

    Ludwig Boltzmann, “Ueber die neueren Theorien der Elektrizität und des Magnetismus,” Verh. Ges. deutsch. Naturf. u. Ärzte 65 (1893): 34–35; repr. in Wiss. Abh., vol. 3, 502–3.

  43. 43.

    Hertz to Kőnig, 20 April 1889, Bonn (DM 3195).

  44. 44.

    In 1834–1839, 41 individuals attended Neumann’s private lectures, but only 18 attended his seminar. In 1840–1849, 56 individuals attended his private lectures, 11 his seminar. For 1850–1859, 52 attended his private lectures, 34 his seminar. After 1860, the seminar became stronger: in 1860–1869, 84 attended the private lectures, 61 his seminar.

  45. 45.

    Franz Neumann, Vorlesungen über mathematische Physik, gehalten an der Universität Königsberg. Einleitung in die theoretische Physik, ed. Carl Pape (Leipzig, 1883), vii, 1, 4, 78, 110, 117. The editor used lectures he took notes on in the winter 1858–1859, Paul Volkmann, Franz Neumann. 11. September 1798, 23. Mai 1895 [Leipzig, 1896], 38). Woldemar Voigt, “Zur Erinnerung an F. E. Neumann, gestorben am 23. Mai 1895 zu Königsberg i/Pr.,” Gött. Nachr., 1895, 248–65, on 256, 258; repr. “Gedächtnissrede auf Franz Neumann,” in Franz Neumanns Gesammelte Werke, edited by his students, 3 vols. (Leipzig: B. G. Teubner, 1906–28), vol. 1, 3–19; Review of Neumann’s Einleitung in die theoretische Physik in Die Fortschritte der Physik im Jahre 1883 39 (1883): 166–67.

  46. 46.

    Gustav Kirchhoff, Vorlesungen über mathematische Physik, vol. 1, Mechanik, 3rd ed. (Leipzig, 1883), quotation from the preface to the first edition in 1876. The volume is based on lectures Kirchhoff gave at Heidelberg just before moving to Berlin. The third edition is almost unchanged from the first. Ludwig Boltzmann, Gustav Robert Kirchhoff (Leipzig, 1888), 22. Robert Helmholtz, “A Memoir of Gustav Robert Kirchhoff,” trans. J. de Perott, in Annual Report of the … Smithsonian Institution … to July, 1889, 1890, 527–40, on 531.

  47. 47.

    Kirchhoff’s preface to Vorlesungen über Mechanik.

  48. 48.

    Kirchhoff, Vorlesungen über Mechanik, chapter 1.

  49. 49.

    Gustav Kirchhoff, Vorlesungen über mathematische Physik, vol. 2, Vorlesungen über mathematische Optik, ed. K. Hensel (Leipzig, 1891). This volume is based on lectures he gave at Berlin in 1876–77 and 1885–86.

  50. 50.

    Gustav Kirchhoff, Vorlesungen über Electricität und Magnetismus, ed. M. Planck (Leipzig, 1891).

  51. 51.

    Gustav Kirchhoff, Vorlesungen über mathematische Physik, vol. 4, Vorlesungen über die Theorie der Wärme, ed. Max Planck (Leipzig, 1894), 1–5. This volume is based on lectures he gave at Berlin in 1876, 1878, 1880, 1882, and 1884.

  52. 52.

    Ibid., 5, 10, 12, 57.

  53. 53.

    Ibid., 51, 60–61, 69, 97, 102, 134–36.

  54. 54.

    Kirchhoff, Theorie der Wärme, 2nd and 3rd lectures.

  55. 55.

    Kirchhoff, Electricität und Magnetismus, 11.

  56. 56.

    Boltzmann, Kirchhoff, 25.

  57. 57.

    Planck’s foreword to Gustav Kirchhoff, Vorlesungen über mathematische Physik, vol. 3, Vorlesungen über Elektrictät und Magnetismus, ed. M. Planck (Leipzig, 1891).

  58. 58.

    Hermann von Helmholtz, Vorlesungen über theoretische Physik, vol. 1, Einleitung zu den Vorlesungen Über theoretische Physik, ed. A. König and C. Runge (Leipzig: J. A. Barth, 1903), pt. 1, 1, 7, 10–11, 14–16. Helmholtz’s introductory lectures were given at Berlin in 1893.

  59. 59.

    Helmholtz, Einleitung, 21.

  60. 60.

    Hermann von Helmholtz, Vorlesungen über theoretische Physik, vol. 2, Vorlesungen über die Dynamik continuirlich verbreiteter Massen, ed. Otto Krigar-Menzel (Leipzig: J. A. Barth, 1902), 1–2. The volumes of Helmholtz's lectures on the mechanics of mass points and of continuously distributed masses were based on lectures he gave at Berlin in 1893–94.

  61. 61.

    Ibid., 2–3.

  62. 62.

    Ibid., 7–8.

  63. 63.

    Hermann von Helmholtz, Vorlesungen über theoretische Physik, vol 6, Vorlesungen über die Theorie der Wärme, ed. Franz Richarz (Leipzig: J. A. Barth, 1903), 256–58. This volume was compiled from his notebooks for the summer semester of 1890, from stenographic notes taken of his lectures in the summer semester of 1893, and from notes taken by the editor of the volume in the early 1880s.

  64. 64.

    Helmholtz, Dynamik discreter Masseenpunkte, 231.

  65. 65.

    Hermann von Helmholtz, Vorlesungen über theoretische Physik, vol. 5, Vorlesungen über die elektromagnetische Theorie des Lichtes, ed. Arthur König and Carl Runge (Hamburg and Leipzig, 1897), 14–16.

  66. 66.

    Hermann von Helmholtz, Vorlesungen über theoretische Physik, vol. 4, Vorlesungen über Elektrodynamik und Theorie des Magnetismus, ed. O. Krigar-Menzel and M. Laue (Leipzig: J. A. Barth, 1907). Acknowledged by Emil Bose, in Phys. Zs. 9 (1908): 141.

  67. 67.

    Wilhelm Wien, “Helmholtz als Physiker.” Naturwiss. 9 (1921): 694–99, on 697.

  68. 68.

    Max von Laue, “Über Hermann von Helmholtz,” in Forschen und Wirken. Festschrift zur 150-Jahr-Feier der Humboldt-Universität zu Berlin 1810-1960, vol. 1 (Berlin: VEB Deutscher Verlag der Wissenschaften, 1960), 359–66, on 360. In Wilhelm Ostwald’s division of scientists into two temperamental types, “Classical” and “Romantic,” Helmholtz was classical.

  69. 69.

    This is not just a play on words. Lewis Pyenson suggests that Boltzmann’s and Mach’s use of the word “classical” to describe traditional mechanics around 1890 would have been recognized at the time as having an affinity with the word appearing in “classical” philology, referring to the languages of ancient cultures, greatly admired in educated circles. This appears in Pyenson’s discussion of neo-humanism and mathematics in German education in the late nineteenth century (The Young Einstein: The Advent of Relativity [Bristol and Boston: Adam Hilger, 1985], 175).

  70. 70.

    Karl Böhm, “H. von Helmholtz, Einleitung zu den Vorlesungen über theoretische Physik,” Phys. Zs. 5 (1904): 140–43.

  71. 71.

    Wien, “Helmholtz als Physiker,” 699.

  72. 72.

    The association of the classical-modern distinction with the Solvay Congress has been proposed by Richard Staley. He points out that if it is meant to imply that physicists before 1900 were working in classical physics and physicists after 1900 were working in modern physics, it is a myth. There is a loose connection with the same terms, “classical” and “modern,” appearing in other parts of culture, such as art, at the same time (Einstein’s Generation: The Origins of the Relativity Revolution [Chicago and London: University of Chicago Press, 2008], 348–49, 353, 355, 422).

  73. 73.

    Peter M. Harman, Energy, Force, and Matter: The Conceptual Development of Nineteenth-Century Physics (Cambridge: Cambridge University Press, 1982), 9–10.

Author information

Authors and Affiliations

  1. Eugene, Oregon, USA

    Christa Jungnickel & Russell McCormmach

Authors
  1. Christa Jungnickel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Russell McCormmach
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Jungnickel, C., McCormmach, R. (2017). Methods of Theoretical Physics. In: The Second Physicist. Archimedes, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-49565-1_12

Download citation

Publish with us

Policies and ethics

Search

Navigation