Advertisement

Ludvig Lorenz and His Non-Maxwellian Electrical Theory of Light

  1. 1.Niels Bohr ArchiveNiels Bohr InstituteCopenhagenDenmark
Article
First Online:

Abstract

Maxwell’s celebrated electromagnetic theory of light dates from 1865. Two years later, without appealing to the ether as a carrier of light waves, the Danish physicist Ludvig Lorenz (1829–1891) independently published another electrical theory of light based on optical equations and the novel idea of retarded potentials. In spite of resting on a very different conceptual foundation, Lorenz’s theory led to almost the same results as Maxwell’s. But whereas Maxwell’s field theory heralded a revolution in physics, Lorenz’s alternative was largely forgotten and soon relegated to a footnote in the history of physics. In part based on archival material and other sources in Danish, this paper offers a detailed contextual account of Lorentz’s theory and its reception in the physics community. Moreover, it includes a brief introduction to other of Lorenz’s scientific contributions and discusses the reasons why his electrical theory of light failed to attract serious interest.

Keywords

Ludvig Lorenz electromagnetism optics James Clerk Maxwell retarded potentials ether 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Albert Einstein, “Maxwell’s Influence on the Evolution of the Idea of Physical Reality,” in Ideas and Opinions (New York: Three Rivers Press, 1982), 269.Google Scholar
  2. 2.
    Geoffrey Cantor and Michael Hodge, eds., Conceptions of Ether: Studies in the History of Ether Theories 1740–1900 (Cambridge: Cambridge University Press, 1981); Peter M. Harman, Energy, Force, and Matter: The Conceptual Development of Nineteenth-Century Physics (Cambridge: Cambridge University Press, 1982); John J. Roche, ed., Physicists Look Back: Studies in the History of Physics (Bristol: Adam Hilger, 1990); Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford: Oxford University Press, 2000).Google Scholar
  3. 3.
    Mogens Pihl, “Lorenz, Ludwig Valentin,” in Dictionary of Scientific Biography, ed. Charles Gillispie (New York: Charles Scribner’s Sons, 1972), 8:501–2; Helge Kragh, “Ludvig Lorenz and Nineteenth Century Optical Theory: The Work of a Great Danish Scientist,” Applied Optics 30 (1991), 4688–95.Google Scholar
  4. 4.
    Ludvig Lorenz, “Ueber die Reflexion des Lichts an der Gränzfläche zweier isotropen, durchsichtigen Mittel,” Annalen der Physik und Chemie 111 (1860), 460–73.Google Scholar
  5. 5.
    Ludvig Lorenz, ”Ueber die Refractionsconstante,” Annalen der Physik und Chemie 11 (1880), 70–103; Hendrik A. Lorentz, ”Ueber die Beziehung zwischen der Fortplanzungsgeschwindigkeit des Lichtes und der Körperdichte,” Annalen der Physik und Chemie 9 (1880), 641–65.Google Scholar
  6. 6.
    Ludvig Lorenz, “Ueber das Leitungsvermögen der Metalle für Wärme und Electricität,” Annalen der Physik und Chemie 13 (1881), 422–47, 582–606.Google Scholar
  7. 7.
    Ludvig Lorenz, “Sur la Lumière Réfleché et Réfractée par une Surface Transparente,” in Oeuvres Scientifiques de L. Lorenz, vol. 1, ed. Herman Valentiner, 403–502 (Copenhagen: Carlsberg Foundation, 1898–1904).Google Scholar
  8. 8.
    Nelson A. Logan, “Survey of Some Early Studies of the Scattering of Plane Waves by a Sphere,” Proceedings of the IEEE 53 (1965), 773–85.Google Scholar
  9. 9.
    Ole Keller, “Optical Works of L. V. Lorenz,” in Progress in Optics, vol. 43, ed. Emil Wolf, 195–294 (Amsterdam: Elsevier Science, 2002); Thomas Wriedt, “Mie Theory: A Review,” in The Mie Theory, ed. Wolfram Hergert and Thomas Wriedt (Berlin: Springer-Verlag, 2012), 53–71.Google Scholar
  10. 10.
    Gabriel Lamé, Leçons sur la Théorie Mathématique de l’Élasticité des Corps Solides (Paris: Gauthiers-Villar, 1852), 325–27. In 1859 Lorenz followed Lamé’s lecture course on the theory of elasticity.Google Scholar
  11. 11.
    Ludvig Lorenz, “On the Theory of Light, II,” Philosophical Magazine 28 (1864), 409–25, on 412.Google Scholar
  12. 12.
    Ludvig Lorenz, “Om Lyset,” Tidsskrift for Physik og Chemi 6 (1867), 1–9. For an English translation of this paper, see Helge Kragh, “Ludvig Lorenz (1867) on Light and Electricity,” ArXiv, March 16, 2018, http://arxiv.org/abs/1803.06371.
  13. 13.
    William D. Niven, ed., The Scientific Papers of James Clerk Maxwell (New York: Dover Publications, 1965), pt. 1, 528.Google Scholar
  14. 14.
    Ludvig Lorenz, “On the Identity of the Vibrations of Light with Electrical Currents,” Philosophical Magazine 34 (1867), 287–301. The German version appeared in Annalen der Physik und Chemie 131 (1867), 243–63.Google Scholar
  15. 15.
    Notebooks on philosophical and other issues, ca. 1845–1854. Lorenz Papers, Niels Bohr Archive, Copenhagen.Google Scholar
  16. 16.
    Karen Jelved, Andrew D. Jackson, and Ole Knudsen, eds., Selected Scientific Works of Hans Christian Ørsted (Princeton: Princeton University Press, 1998), 398–99.Google Scholar
  17. 17.
    Lorenz, “Om Lyset” (ref. 12).Google Scholar
  18. 18.
    Lorenz, “On the Identity” (ref. 14), which is also the source of the following quotations if not otherwise mentioned.Google Scholar
  19. 19.
    Olivier Darrigol, “James MacCullagh’s Ether: An Optical Route to Maxwell’s Equations?,” European Physical Journal 35 (2010), 133–72.Google Scholar
  20. 20.
    G. Robert Kirchhoff, “Über die Bewegung der Elektricität in Drähten,” Annalen der Physik und Chemie 100 (1857), 193–217; “Über die Bewegung der Elektricität in Leitern,” Annalen der Physik und Chemie 102 (1857), 529–44; Vorlesungen über Electricität und Magnetismus, ed. Max Planck, 183–201 (Leipzig: B. G. Teubner, 1891).Google Scholar
  21. 21.
    Wilhelm Weber and Rudolf Kohlrausch, “Ueber die Elektricitätsmenge, welche bei galvanischen Strömen durch den Querschnitt der Kette fliesst,” Annalen der Physik und Chemie 99 (1856), 10–25. For details and context, see Andre K. T. Assis, “On the First Electromagnetic Measurements of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch,” in Volta and the History of Electricity, ed. Fabio Bevilacqua and Enrico Giannetto, 267–86 (Milan: Hoepli, 2003), which includes an English translation of the Weber-Kohlrausch paper.Google Scholar
  22. 22.
    Quoted in Darrigol, Electrodynamics (ref. 2), 73.Google Scholar
  23. 23.
    Lorenz, “On the Identity” (ref. 14), who used the symbol c for Weber’s c w and a for the velocity of the electrical waves in free space.Google Scholar
  24. 24.
    Niven, Scientific Papers (ref. 13), pt. 1, 500. The French physicist Hippolyte Fizeau determined in 1849 the speed of light in air to c = 313,300 km s−1.Google Scholar
  25. 25.
    Lorenz, “Om Lyset” (ref. 12).Google Scholar
  26. 26.
    Arthur O. Lovelock, The Great Chain of Being (Cambridge, MA: Harvard University Press, 1976); R. H. Kane, “Nature, Plenitude and Sufficient Reason,” American Philosophical Quarterly 13 (1976), 23–31.Google Scholar
  27. 27.
    Lorenz, “Om Lyset” (ref. 12).Google Scholar
  28. 28.
    Ludvig Lorenz, “On the Theory of Light, I,” Philosophical Magazine 26 (1863), 81–93.Google Scholar
  29. 29.
    Ludvig Lorenz, “Mémoire sur la Théorie de l’Élasticité des Corps Homogène a Élasticité Constante,” Journal für die reine und angewandte Mathematik 58 (1861), 329–51.Google Scholar
  30. 30.
    Lorenz, “On the Identity” (ref. 14), 289. In the Danish original and in the translation in Annalen, the “inducing action of the variable intensities” was ascribed to Weber’s law, but for some reason the reference to Weber was left out in the English version.Google Scholar
  31. 31.
    Edmund Whittaker, A History of the Theories of Aether and Electricity (London: Thomas Nelson and Sons, 1958), 270; John J. Roche, “A Critical Study of the Vector Potential,” in Physicists Look Back (ref. 2), 144–68.Google Scholar
  32. 32.
    J. David Jackson and Lev B. Okun, “Historical Roots of Gauge Invariance,” Reviews of Modern Physics 73 (2001), 663–80.Google Scholar
  33. 33.
    Robert K. Merton, “The Matthew Effect in Science,” Science 159 (1968), 56–63; Stephen M. Stigler, “Stigler’s Law of Eponymy,” in Science and Social Structure, ed. Thomas F. Gieryn (New York: New York Academy of Sciences, 1980), 147–58; J. David Jackson, “Examples of the Zeroth Theorem of the History of Science,” American Journal of Physics 76 (2008), 704–19.Google Scholar
  34. 34.
    Niven, Scientific Papers (ref. 13), pt. 1, 476. Maxwell used different names for A and only settled on “vector potential” in his Treatise of 1873. See Alfred M. Bork, “Maxwell and the Vector Potential,” Isis 58 (1967), 210–22.Google Scholar
  35. 35.
    O. L. Brill and B. Goodman, “Causality in the Coulomb Gauge,” American Journal of Physics 35 (1967), 832–37.Google Scholar
  36. 36.
    James C. Maxwell, A Treatise on Electricity and Magnetism, vol. 2 (New York: Dover Publications, 1954), 434. See the comments in Bruce J. Hunt, The Maxwellians (Ithaca, NY: Cornell University Press, 1991), 117, and Jed Z. Buchwald, From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century (Chicago: University of Chicago Press, 1985), 277.Google Scholar
  37. 37.
    Hunt, Maxwellians (ref. 36), 117–18.Google Scholar
  38. 38.
    Bernhard Riemann, Schwere, Electricität und Magnetismus, ed. Karl Hattendorff (Hannover: Carl Rümpler, 1875), 330. See also M. Norton Wise, “German Concepts of Force, Energy, and the Electromagnetic Ether: 1845–1880,” in Cantor and Hodge, Conceptions of Ether (ref. 2), 269–308.Google Scholar
  39. 39.
    Carl Friedrich Gauss, Werke, vol. 5 (Göttingen: Kön. Gesellschaft der Wissenschaften zu Göttingen, 1877), 627–29.Google Scholar
  40. 40.
    Léon Rosenfeld, “The Velocity of Light and the Evolution of Electrodynamics,” Nuovo Cimento, Supplement 4 (1956), 1630–69; Hubert Goenner, “Some Remarks on ‘A Contribution to Electrodynamics’ by Bernhard Riemann,” in From Riemann to Differential Geometry, ed. Lizhen Ji, Athanase Papadopoulos and Sumio Yamada (Berlin: Springer, 2017).Google Scholar
  41. 41.
    Bernhard Riemann, “Ein Beitrag zur Elektrodynamik,” Annalen der Physik und Chemie 131 (1867), 239–42; Walter Kaiser, “Die zeitliche Ausbreitung von Potentialen in der Elektrodynamik,” Gesnerus 35 (1978), 297–317.Google Scholar
  42. 42.
    For references, see Kaiser, “Ausbreitung von Potentialen” (ref. 41), Thomas Archibald, “Carl Neumann versus Rudolf Clausius on the Propagation of Electrodynamic Potentials,” American Journal of Physics 54 (1986), 786–90, and Karl-Heinz Schlote, “Carl Neumann’s Contributions to Electrodynamics,” Physics in Perspective 6 (2004), 252–70.Google Scholar
  43. 43.
    Peter M. Harman, ed., The Scientific Letters and Papers of James Clerk Maxwell, vol. 2 (Cambridge: Cambridge University Press, 1995), 500.Google Scholar
  44. 44.
    Rudolf Clausius, “Ueber die von Gauss angeregte neue Auffassung der elektrodynamischen Erscheinungen,” Annalen der Physik und Chemie 135 (1868), 606–21.Google Scholar
  45. 45.
    Parry Moon and Domina E. Spencer, “Electromagnetism without Magnetism: An Historical Sketch,” American Journal of Physics 22 (1954), 120–24; Germain Rosseaux, “Lorenz or Coulomb in Galilean Electromagnetism?” Europhysics Letters 71 (2005), 15–20.Google Scholar
  46. 46.
    Alfred Liénard, “Champ Électrique et Magnétique Produit par une Charge Électrique Concentrée en un Point et Animée d’un Movement Quelconque,” L’Éclairage Électrique 16 (1898), 5–14, 53–59, 106–12; Emil Wiechert, “Elektrodynamische Elementargesetze,” Annalen der Physik 4 (1901), 667–89.Google Scholar
  47. 47.
    C. Neumann to L. Lorenz, 4 September 1868, Lorenz Papers, Danish Museum of Science and Technology.Google Scholar
  48. 48.
    Hermann von Helmholtz, “Über die Bewegungsgleichungen der Elektricität für ruhende leitende Körper,” Journal für die reine und angewandte Mathematik 72 (1870), 57–129; Walter Kaiser, “Helmholtz’s Instrumental Role in the Formation of Classical Electrodynamics,” in Hermann von Helmholtz and the Foundations of Nineteenth-Century Science, ed. David Cahan, 374–402 (Berkeley: University of California Press, 1993).Google Scholar
  49. 49.
    Keller, “Optical Works” (ref. 9), 273.Google Scholar
  50. 50.
    Fortschritte der Physik 23 (1870), 197–200. The italics and the exclamation mark are Radicke’s.Google Scholar
  51. 51.
    James C. Maxwell, “On a Method of Making a Direct Comparison of Electrostatic with Electromagnetic Force; with a Note on the Electromagnetic Theory of Light,” Philosophical Transactions of the Royal Society 158 (1868), 643–57. Maxwell referred to Lorenz’s paper in Annalen and not to the version in Philosophical Magazine.Google Scholar
  52. 52.
    Harman, Scientific Letters and Papers, vol. 2 (ref. 43), 353–55. According to Jackson and Okun, “Historical Roots” (ref. 32), Maxwell’s criticism is unjustified because it ignores the electromagnetic momentum. See also Alfred O’Rahilly, Electromagnetic Theory: A Critical Examination of Fundamentals (New York: Dover Publications, 1965), 182–85, and Kirk T. McDonald, “Maxwell’s Objection to Lorenz’s Retarded Potentials” (2016), http://www.physics.princeton.edu/~mcdonald/examples/maxwell.pdf.
  53. 53.
    Niven, Scientific Papers (ref. 13), pt. 2, 228.Google Scholar
  54. 54.
    Wolfgang Pietsch, “Hidden Underdetermination: A Case Study in Classical Electrodynamics,” International Studies in the Philosophy of Science 26 (2012), 125–51.Google Scholar
  55. 55.
    Maxwell, Treatise (ref. 36), 450.Google Scholar
  56. 56.
    Hendrik A. Lorentz, H. A. Lorentz: Collected Papers, vol. 1 (The Hague: Martinus Nijhoff, 1936), 193–383.Google Scholar
  57. 57.
    Erik Edlund, “On the Nature of Electricity,” Philosophical Magazine 44 (1872), 81–100, 174–188.Google Scholar
  58. 58.
    Hendrik A. Lorentz, “Nobel Lecture: The Theory of Electrons and the Propagation of Light,” Nobelprize.org, https://www.nobelprize.org/nobel_prizes/physics/laureates/1902/lorentz-lecture.html.
  59. 59.
    Ole Knudsen, “The Influence of Gibbs’s European Studies on his Later Work,” in From Ancient Omens to Statistical Mechanics, ed. J. L. Berggren and Bernard R. Goldstein, 271–80 (Copenhagen: University Library, 1987).Google Scholar
  60. 60.
    Joseph J. Thomson, “Report on Electrical Theories,” in Report of the Fifty-Fifth Meeting of the British Association for the Advancement of Science Held at Aberdeen in September 1885, 97–155 (London: John Murray, 1886).Google Scholar
  61. 61.
    Ludvig Lorenz, “Der elektrische Leitungswiderstand des Quecksilbers in absolutem Maasse,” Annalen der Physik und Chemie 149 (1873), 251–69; “Sur les Méthodes à Employer pour la Détermination de l’Ohm,” Journal de Physique 1 (1882), 477–83.Google Scholar
  62. 62.
    Max Abraham, Theorie der Elektrizität, vol. 2 (Leipzig: B. G. Teubner, 1905), 59. For other erroneous statements concerning the priority of retarded potentials, see O’Rahilly, Electromagnetic Theory (ref. 52), 184.Google Scholar
  63. 63.
    Oliver Heaviside, Electromagnetic Theory, vol. 3 (London: The Electrician, 1912), 452.Google Scholar
  64. 64.
    FitzGerald to Larmor, November 21, 1897. FitzGerald’s Δ2 is the Laplace operator usually written as Δ or ∇2. In a letter to Lodge of 1901, FitzGerald said of Lorenz’s functions that they were “essentially the same as I have been always using.” Both quoted in Hunt, The Maxwellians (ref. 36), 42.Google Scholar
  65. 65.
    Oliver J. Lodge, “George Francis FitzGerald,” The Electrician 46 (1901), 701–2.Google Scholar
  66. 66.
    Pierre Duhem, The Electric Theories of J. Clerk Maxwell: A Historical and Critical Study, trans. A. Aversa (Heidelberg: Springer, 2015), 150–55.Google Scholar
  67. 67.
    J. C. Friedrich Zöllner, Erklärung der universellen Gravitation aus den statischen Wirkungen der Elektrizität und die allgemeine Bedeutung des Weberschen Gesetzes (Leipzig: L. Staackmann, 1882).Google Scholar
  68. 68.
    J. C. Friedrich Zöllner, Über die physikalischen Beziehungen zwischen hydrodynamischen und elektrodynamischen Erscheinungen, Berichten d. Königl. Sächs. Gesellschaft der Wissenschaften zu Leipzig (1876), 166. Available at https://books.google.co.uk/books?id=J0oVi23zMzAC.
  69. 69.
    Éleuthère Mascart and Jules Joubert, Leçons sur l’Électricité et le Magnétisme, vol. 1 (Paris: G. Masson, 1882), 688.Google Scholar
  70. 70.
    Albrecht Fölsing, ed., Heinrich Hertz: Die Constitution der Materie, Eine Vorlesung über die Grundlagen der Physik aus dem Jahre 1884 (Berlin: Springer, 1999), 88.Google Scholar
  71. 71.
    Heinrich Hertz, “Über die Beziehungen zwischen den Maxwell’schen elektrodynamischen Grundgleichungen und den Grundgleichungen der gegnerischen Elektrodynamik,” Annalen der Physik und Chemie 23 (1884), 84–103.Google Scholar
  72. 72.
    Darrigol, Electrodynamics (ref. 2), 258–62; Olivier Darrigol, “The Electrodynamic Revolution in Germany as Documented by Early German Expositions of ‘Maxwell’s Theory,’” Archive for History of Exact Sciences 45 (1993), 189–280.Google Scholar
  73. 73.
    Paul Drude, Physik des Aethers auf elektromagnetischer Grundlage (Stuttgart: F. Enke, 1894), 9.Google Scholar
  74. 74.
    Paul Volkmann, Vorlesungen über die Theorie des Lichtes (Leipzig: B. G. Teubner, 1891), 5.Google Scholar
  75. 75.
    Viktor von Lang, Einleitung in die theoretische Physik (Braunschweig: Vieweg und Sohn, 1891), 478–80.Google Scholar
  76. 76.
    Ludvig Lorenz, “Über die Fortpflanzung der Electricität,” Annalen der Physik und Chemie 7 (1879), 161–93.Google Scholar
  77. 77.
    Rosenfeld, “Velocity of Light” (ref. 40).Google Scholar
  78. 78.
    Niven, Scientific Papers (ref. 13), pt. 1, 535.Google Scholar
  79. 79.
    Manuscript in Danish on “The Motion of Electricity in a System of Conducting Elements Separated by Empty Space,” Lorenz Papers, Royal Danish Academy of Sciences and Letters, dated June 1, 1887.Google Scholar
  80. 80.
    Whittaker, Theories of Aether and Electricity (ref. 31), 270. Whittaker also stated that Lorenz “was unable to derive from his equations any explanation of the existence of refractive indices.” As mentioned, although Lorenz did not publish his derivation, he actually provided such an explanation.Google Scholar
  81. 81.
    Wilhelm Wien “Elektromagnetische Lichttheorie,” in Encyclopädie der mathematischen Wissenschaften, vol. 5.3, ed. Arnold Sommerfeld, 95–198 (Leipzig: B. G. Teubner, 1909), 104.Google Scholar
  82. 82.
    O’Rahilly, Electromagnetic Theory (ref. 52), 189. The original title of the 1938 book was Electromagnetics.Google Scholar
  83. 83.
    Mogens Pihl, Der Physiker L. V. Lorenz: Eine kritische Untersuchung (Copenhagen: Munksgaard, 1939), 52; “The Scientific Achievements of L. V. Lorenz,” Centaurus 17 (1972), 83–94.Google Scholar
  84. 84.
    Ronold King, review of Pihl, Der Physiker L. V. Lorenz (ref. 83), in Isis 40 (1949), 64–66.Google Scholar
  85. 85.
    Autobiographical note on the occasion of receiving an honorary doctorate from the University of Uppsala, Lorenz Papers, Danish Museum of Science and Technology.Google Scholar
  86. 86.
    Wise, “German Concepts” (ref. 38); Darrigol, Electrodynamics (ref. 2), 213.Google Scholar
  87. 87.
    Edlund, “Nature of Electricity” (ref. 57). For other examples, see Helge Kragh, “The Aether in Late Nineteenth Century Chemistry,” Ambix 36 (1989), 49–65.Google Scholar
  88. 88.
    Ludvig Lorenz, ”Eksperimentale og Theoretiske Undersøgelser af Legemernes Brydningsforhold,” Det Kongelige Danske Videnskabernes Selskab Skrifter 8 (1869), 205–48.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Personalised recommendations

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners in accordance with our Privacy Statement. You can manage your preferences in Manage Cookies.

Close
OK
Manage Cookies