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Pascual Jordan, Varying Gravity, and the Expanding Earth


In the 1950s, surprising links were proposed between cosmological theory and the geological and paleontological sciences. These links were mainly provided by Paul Dirac’s hypothesis of 1937 that the gravitational constant G decreases with cosmic time. Pascual Jordan, famous for his pioneering contributions to quantum theory, took up Dirac’s hypothesis; after the end of World War II, Jordan developed its geophysical consequences, concluding that the Earth is expanding. Much of Jordan’s later scientific work focused on the expanding Earth and other aspects of the earth sciences relating to the varying-G hypothesis. This chapter in the history of science has received almost no attention from either scientists or historians. The article analyzes Jordan’s cosmo-geological work in relation to the somewhat similar efforts of other “expansionists” in the period that led to the plate tectonic revolution in the earth sciences.

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  1. Dirac’s value of 7 × 108 yr, or T H = 2.1 × 109 yr, is a little puzzling since it corresponds to a Hubble constant H 0 = 465 km s−1 Mpc−1. In 1938, the accepted value, as determined by Edwin Hubble, was H 0 = 540 km s−1 Mpc−1, or T H = 1.8 × 109 yr. No astronomical measurements indicated a value less than 500 km s−1 Mpc−1. Dirac gave no source for his value.

  2. The correspondence between the research interests of Jordan and Dirac is remarkable. Not only did they develop much of quantum electrodynamics and quantum field theory in parallel, but Jordan (collaborating with Wigner) also came close to the relativistic wave equation of the electron that Dirac published in 1928. They both accepted Lemaître’s model of the universe at an early time. When Dirac proposed the existence of magnetic monopoles in 1931, Jordan was the only physicist to take up the theory and develop it further. The same kind of interaction at a distance occurred in the case of Dirac’s G(t) cosmology.

  3. The hypsographic (or hypsometric) curve shows the proportion of land area at various elevations by plotting relative area against relative height.

  4. Sima, an older name derived from silicon and magnesium, denotes the lower layer of the Earth’s crust composed of basaltic rock. It lies below the granitic shell that forms the foundation of the continental masses and is known as sial (from silicon and aluminium).


  1. Jürgen Ehlers and Engelbert Schücking, “‘Aber Jordan war der erste’: Zur Erinnerung an Pascual Jordan (1902–1980),” Physik Journal 1 (2002), 71–74.

  2. Jordan’s contributions to quantum mechanics are amply documented in the rich historical literature on the subject. See, for example, Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, vol. 6, part 1 (New York: Springer-Verlag, 2000) and Bert Schroer, “Pascual Jordan, Biographical Notes, his Contributions to Quantum Mechanics and his Role as a Protagonist of Quantum Field Theory,” in Pascual Jordan (19021980). Mainzer Symposium zum 100. Geburtstag, preprint no. 329 (Berlin: Max Planck Institute for the History of Science, 2007), 47–68. Available online from, accessed December 5, 2014.

  3. Silvan S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga (Princeton: Princeton University Press, 1994), 5–11.

  4. For a full biography of Jordan’s writings, see Wolf D. Beiglböck, “Pascual Jordan: Schriftenverzeichnis,” in Pascual Jordan (ref. 2), 175–206.

  5. Richard H. Beyler, “Targeting the Organism: The Scientific and Cultural Context of Pascual Jordan’s Quantum Biology, 1932–1947,” Isis 87 (1996), 248–273.

  6. Alan D. Beyerchen, Scientists under Hitler: Politics and the Physics Community in the Third Reich (New Haven: Yale University Press, 1977).

  7. M. Norton Wise, “Pascual Jordan: Quantum Mechanics, Psychology, National Socialism,” in Monika Renneberg and Mark Walker, eds., Science, Technology and National Socialism (Cambridge: Cambridge University Press, 1994), 224–254.

  8. Engelbert L. Schucking, “Jordan, Pauli, Politics, Brecht, and a Variable Gravitational Constant,” Physics Today 52 (October 1999), 26–31.

  9. On Jordan’s philosophy of science and general world view, see Pascual Jordan, Der Naturwissenschaftler vor der Religiösen Frage: Abbruch einer Mauer (Oldenburg: Gerhard Stalling Verlag, 1963). See also Richard H. Beyler, “Ernst Pascual Jordan: Freedom vs. Materialism,” in Nicolaas A. Rupke, ed., Eminent Lives in Twentieth-Century Science & Religion (Frankfurt am Main: Peter Lang, 2009), 233–252.

  10. Paul Dirac, “The Cosmological Constants,” Nature 139 (1937), 323. On Dirac’s cosmological theory, see Helge Kragh, “Cosmo-Physics in the Thirties: Towards a History of Dirac Cosmology,” Historical Studies in the Physical Sciences 13 (1982), 69–108; Kragh, Dirac: A Scientific Biography (Cambridge: Cambridge University Press, 1990), 223–246; and John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986), esp. 231–243.

  11. Paul Dirac, “The Relation between Mathematics and Physics,” Proceedings of the Royal Society of Edinburgh 59 (1939), 122–139, on 139. See also Kragh, Dirac (ref. 10), 275–278 and Helge Kragh, “Mathematics and Physics: The Idea of a Pre-Established Harmony,” Science & Education (2014), doi: 10.1007/s11191-014-9724-8. [AU: please give citation to print version if possible] [HK: has not yet appeared with page numbers].

  12. Paul Dirac, “A New Basis for Cosmology,” Proceedings of the Royal Society A 165 (1938), 199–208, on 204.

  13. George Gamow, “History of the Universe,” Science 158 (1967), 766–769, on 767. On January 2, 1937, Dirac married Margit Wigner Balasz, the sister of the Hungarian-American physicist Eugene Wigner.

  14. Herbert Dingle, “Modern Aristotelianism,” Nature 139 (1937), 784–786; Kragh, “Cosmo-Physics” (ref. 10); George Gale and Niall Shanks, “Methodology and the Birth of Modern Cosmological Inquiry,” Studies in History and Philosophy of Modern Physics 27 (1996), 279–296.

  15. Arthur S. Eddington, “The Cosmological Controversy,” Science Progress 34 (1939), 225–236.

  16. Subrahmanyan Chandrasekhar, “The Cosmological Constants,” Nature 139 (1937), 757–758; Daulat S. Kothari, “Cosmological and Atomic Constants,” Nature 142 (1938), 354–355.

  17. Fritz Zwicky, “On the Theory and Observation of Highly Collapsed Stars,” Physical Review 55 (1939), 726–743, on 733; Walter Baade and Fritz Zwicky, “On Super-Novae,” Proceedings of the National Academy of Sciences 20 (1934), 254–259.

  18. Pascual Jordan, Schwerkraft und Weltall: Grundlagen der theoretischen Kosmologie, 2nd rev. ed. (Braunschweig: Vieweg & Sohn, 1955), 137. On Jordan’s cosmological theories, see John North, The Measure of the Universe: A History of Modern Cosmology (Oxford: Oxford University Press, 1965), 205–208; Jagjit Singh, Great Ideas and Theories of Modern Cosmology (New York: Dover Publications, 1970), 229–235; and Helge Kragh, Matter and Spirit in the Universe: Scientific and Religious Preludes to Modern Cosmology (London: Imperial College Press, 2004), 175–185.

  19. Pascual Jordan, Die Physik des 20. Jahrhhunderts (Braunschweig: Vieweg, 1936), 152. English translation: Jordan, Physics of the 20th Century, trans. Eleanor Oshry (New York: Philosophical Library, 1944).

  20. Pascual Jordan, “Die physikalischen Weltkonstanten,” Die Naturwissenschaften 25 (1937), 513–517; Jordan, “Bemerkungen zur Kosmologie,” Annalen der Physik 32 (1939), 64–70; Jordan, “Über die Entstehung der Sterne,” Physikalische Zeitschrift 45 (1944), 183–190, 233–244.

  21. Pascual Jordan, Der Herkunft die Sterne (Stuttgart: Hirzel, 1947); Jordan, “Formation of the Stars and Development of the Universe,” Nature 164 (1949), 637–640.

  22. Hermann Bondi, Cosmology (Cambridge: Cambridge University Press), 164.

  23. Jordan, “Entstehung der Sterne” (ref. 20), 190.

  24. Paul Couderc, The Expansion of the Universe (London: Faber and Faber, 1952), 225.

  25. Arthur E. Haas, “An Attempt to a Purely Theoretical Derivation of the Mass of the Universe,” Phys. Rev. 49 (1936), 411–412.

  26. Jordan, “Bemerkungen” (ref. 20), 66; Jordan, “Formation of the Stars” (ref. 21), 638. The Haas-Jordan idea of a zero-energy universe was independently reintroduced by several later cosmologists and is today often ascribed to Edward Tryon, “Is the Universe a Quantum Fluctuation?” Nature 246 (1973), 396–397.

  27. Wolfgang Pauli, “Raum, Zeit und Kausalität in der modernen Physik,” Scientia 59 (1936), 65–76, on 76; Pascual Jordan, “Zur empirischen Kosmologie,” Die Naturwissenschaften 26 (1938), 417–421.

  28. Fritz G. Houtermans and Pascual Jordan, “Über die Annahme der zeitlichen Veränderlichkeit des β-Zerfalls und die Möglichkeiten ihrer experimentellen Prüfung,” Zeitschrift für Naturforschung 1 (1946), 125–130. Specifically, they assumed that \(\frac{dN}{dt} = - \lambda^{*} N\left( t \right)\frac{1}{\sqrt t } \;{\text{or}}\;N\left( t \right) = N_{0} \exp \left( { - 2\lambda^{*} \sqrt t } \right)\).

  29. Helmut Hönl, “Zwei Bemerkungen zum kosmologischen Problem,” Ann. Phys. (Berlin) 6 (1949), 169–176. See also Richard Dehm, “Geologisches Erdalter und astrophysikalisches Weltalter,” Die Naturwissenschaften 36 (1949), 166–171.

  30. Hubert Goenner, “Some Remarks on the Genesis of Scalar-Tensor Theories,” General Relativity and Gravitation 44 (2012), 2077–2097; Carl H. Brans and Robert H. Dicke, “Mach’s Principle and a Relativistic Theory of Gravitation,” Phys. Rev. 124 (1961), 925–935; Carl H. Brans, “Varying Newton’s Constant: A Personal History of Scalar-Tensor Theories,” Einstein Online 4 (2010), 1002,, accessed December 5, 2014. On the importance of the Brans-Dicke theory, see David Kaiser, “Is ψ just a ψ? Pedagogy, Practice, and the Reconstitution of General Relativity, 1942–1975,” Stud. Hist. Phil. Mod. Phys. 29 (1998), 321–338.

  31. Engelbert L. Schücking, “Jürgen Ehlers,” in Bernd G. Schmidt, ed., Einstein’s Field Equations and their Physical Implications (Berlin: Springer-Verlag), v–vi, on vi.

  32. Joshua N. Goldberg, “US Air Force Support of General Relativity, 1956–1972,” in Jean Eisenstaedt and A. J. Kox, eds., Studies in the History of General Relativity (Boston: Birkhäuser, 1992), 89–102.

  33. Pascual Jordan, “Fünfdimensionale Kosmologie,” Astronomische Nachrichten 276 (1948), 193–208.

  34. Peter G. Bergmann, “Unified Field Theory with Fifteen Field Variables,” Annals of Mathematics 49 (1948), 255–264.

  35. Pascual Jordan, “Zum gegenwärtigen Stand der Diracschen kosmologischen Hypothesen,” Zeitschrift für Physik 157 (1959), 112–121. See also Dieter R. Brill, “Review of Jordan’s Extended Theory of Gravitation,” in Christian Møller, ed., Evidence for Gravitational Theories (New York: Academic Press, 1962), 50–68.

  36. Helmut Hönl and Heinz Dehnen, “Erlaubt die 3° Kelvin-Strahlung Rückschlüsse auf eine konstante oder veränderliche Gravitationszahl?” Zeitschrift für Astrophysik 68 (1968), 181–189.

  37. Pascual Jordan,”Bemerkungen zu der Arbeit von H. Hönl und H. Dehnen,” Z. Astrophys. 68 (1968), 201–203; Jordan, The Expanding Earth: Some Consequences of Dirac’s Gravitation Hypothesis (Oxford: Pergamon Press, 1971), xv.

  38. Jordan, Schwerkraft (ref. 18), vi.

  39. Ibid., 223.

  40. Pascual Jordan, “Four Lectures about Problems of Cosmology,” in António Giáo, ed., Cosmological Models (Lisbon: Instituto Gulbenkian de Ciêcia, 1964), 101–136, on 111.

  41. Jordan, Expanding Earth (ref. 37), x.

  42. Ibid., xi.

  43. Ibid., 10.

  44. Pascual Jordan, “The Expanding Earth,” in Jagdish Mehra, ed., The Physicist’s Conception of Nature (Dordrecht: Reidel, 1973), 60–70, on 61.

  45. Wolfgang Pauli to Pascual Jordan, October 1, 1952, in Karl von Meyenn, ed., Wolfgang Pauli: Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a., vol. 4, part 1 (Berlin: Springer, 1996), 737.

  46. Pascual Jordan to Wolfgang Pauli, December 17, 1952, in Meyenn, Wolfgang Pauli (ref. 45), 800.

  47. Pascual Jordan, “Zum Problem der Erdexpansion,” Die Naturwissenschaften 48 (1961), 417–425, on 417.

  48. Obituaries in Alpina Americana Journal 15 (1966), 115–116 and Alpine Journal 71 (1966), 190. Online: and

  49. Some of Fisher’s publications and abstracts are listed in Ruth King et al., eds., Bibliography of North American Geology, 19501959 (Washington D.C.: United States Government Printing Office, 1965). The bibliography includes an abstract by Fisher with the title “Arguments for a Solid Core of the Earth at 0° K.”

  50. On GRF and its history, see, accessed December 5, 2014. Among the prize winners of the 1950s and 1960s were notables such as John Wheeler, Hermann Bondi, Roger Penrose, Stephen Hawking, and Dennis Sciama.

  51. See, accessed December 5, 2014.

  52. Pascual Jordan, “The Theory of a Variable ‘Constant’ of Gravitation” (1954),, accessed December 5, 2014.

  53. Pascual Jordan, “Empirical Tests of Dirac’s Hypothesis about Gravitation” (1967),, accessed December 5, 2014.

  54. Pascual Jordan, “On the Possibility of Avoiding Ramsey’s Hypothesis in Formulating a Theory of Earth Expansion,” in Stanley K. Runcorn, ed., The Application of Modern Physics to the Earth and Planetary Interiors (London: Wiley Interscience, 1969), 55–62, on 55.

  55. Alfred Wegener, The Origin of Continents and Oceans (New York: Dover Publications, 1966), 35–40. Originally published as Wegener, Die Entstehung der Kontinente und Ozeane (Braunschweig: Vieweg, 1915).

  56. Hans C. Joksch, “Statistische Analyse der hypsometrischen Kurve der Erde,” Zeitschrift für Geophysik 21 (1955), 109–112.

  57. Pascual Jordan, “Empirical Confirmation of Dirac’s Hypothesis of Diminishing Gravitation,” in Recent Developments in General Relativity (Oxford: Pergamon Press, 1962), 283–288, on 286.

  58. Pascual Jordan, “Geophysical Consequences of Dirac’s Hypothesis,” Reviews of Modern Physics 34 (1962), 596–600, on 599.

  59. Jordan, Schwerkraft (ref. 18), 228.

  60. Jordan, Expanding Earth (ref. 37), 47.

  61. Horst Gerstenkorn, “Veränderungen der Erde-Monde-System durch Gezeitenreibung in der Vergangenheit bei zeitabhängiger Gravitationskonstante,” Z. Astrophys. 42 (1957), 137–155. On Gerstenkorn and lunar theory, see Stephen G. Brush, A History of Modern Planetary Science (Cambridge: Cambridge University Press, 1996), 3:200–202.

  62. Pascual Jordan, Jürgen Ehlers, and Wolfgang Kundt, “Quantitatives zur Diracschen Schwerkraft-Hypothese,” Z. Phys. 178 (1964), 501–518, on 513.

  63. Edward Teller, “On the Change of Physical Constants,” Phys. Rev. 73 (1948), 801–802. See also Helge Kragh, “Cosmonumerology and Empiricism: The Dirac-Gamow Dialogue,” Astronomy Quarterly 8 (1991), 109–126.

  64. Jordan, Schwerkraft (ref. 18), 235.

  65. Jordan, Expanding Earth (ref. 37), 158; Jordan, “Über die Wolkenhülle der Venus,” Akademie der Wissenschaften und der Literatur in Mainz, Mathematisch-Naturwissenschaftlichen Klasse (1967), 43–53.

  66. Jordan, “Four Lectures” (ref. 40), 115.

  67. Hans-Jost Binge, “Vulkanismus und Intrusionen als Folge der Zeitabhängigkeit von κ in der Jordanschen Kosmologie,” Z. Naturforsch. A 10 (1955), 900; Jordan, Schwerkraft (ref. 18), 233; Jordan, “Expanding Earth” (ref. 37), 68–69.

  68. Hans-Jost Binge, Folgerungen der Diracschen Hypothese für die Physik des Erdkörpers, unpublished dissertation, Hamburg University, 1962; Jordan, Expanding Earth (ref. 37), 118–121.

  69. Jordan, Expanding Earth (ref. 37), 123.

  70. Richard Nunan, “Expanding Earth Theories,” in Gregory A. Good, ed., Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena, vol. 2 (New York: Garland Publishing, 1998), 243–250; Henry R. Frankel, The Continental Drift Controversy: Volume II: Paleomagnetism and Confirmation of Drift (Cambridge: Cambridge University Press, 2012), 278–354.

  71. S. Warren Carey, “The Expanding Earth—an Essay Review,” Earth Science Reviews 11 (1975), 105–143, on 134; Carey, The Expanding Earth (Amsterdam: Elsevier, 1976), 446.

  72. Jordan, Expanding Earth (ref. 37), 49, 66.

  73. László Egyed, “On the Origin and Constitution of the Upper Part of the Earth’s Mantle,” Geologische Rundschau 50 (1960), 251–258; Egyed, “The Expanding Earth?” Nature 197 (1963), 1059–1060; Egyed, Physik der Festen Erde (Leipzig: Teubner, 1969).

  74. Arthur Holmes, Principles of Physical Geology (New York: Ronald Press, 1965), 983–987.

  75. Pascual Jordan, Die Expansion der Erde: Folgerungen aus der Diracschen Gravitationshypothese (Braunschweig: Vieweg & Sohn, 1966), 80–83; Jordan, Ehlers, and Kundt, “Quantitatives” (ref. 62), 507.

  76. Robert H. Dicke, “Principle of Equivalence and the Weak Interactions,” Rev. Mod. Phys. 29 (1957), 355–362; Dicke, “Dirac’s Cosmology and the Dating of Meteorites,” Nature 183 (1959), 170–171; Dicke, “The Earth and Cosmology,” Science 138 (1962), 653–664. Interviews with Dicke conducted by the American Institute of Physics between 1975 and 1988,, accessed December 5, 2014. See also Helge Kragh, “Gravitation and the Earth Sciences: The Contributions of Robert Dicke,” arxiv:1501.04293 [physics. Hist-ph], 2015.

  77. Dicke, “Earth and Cosmology” (ref. 76).

  78. Ibid., 660. See also Charles T. Murphy and Robert H. Dicke, “The Effects of a Decreasing Gravitational Constant in the Interior of the Earth,” Proceedings of the American Philosophical Society 108 (1964), 224–246.

  79. Paolo Sudiro, “The Earth Expansion Theory and its Transition from Scientific Hypothesis to Pseudoscientific Belief,” History of Geo- and Space Sciences 5 (2014), 135–148.

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  80. Pascual Jordan, “Die Bedeutung der Diracschen Hypothese für die Geophysik,” Akademie der Wissenschaften und der Literatur in Mainz, Mathematisch-Naturwissenschaftlichen Klasse (1959), 771–795, on 795.

  81. Jordan, “Geophysical Consequences” (ref. 58), 600.

  82. Wolfgang Kundt, “Jordan’s ‘Excursion’ into Geophysics,” in Pascual Jordan (ref. 2), 123–132. Jordan and Kundt wrote in 1961 an important paper on general relativity theory, which has recently been republished in English translation. See General Relativity and Gravitation 46 (2014), 1659.

  83. Pascual Jordan, “Über den positivischen Begriff der Wirklichkeit,” Die Naturwissenschaften 22 (1934), 485–490; Richard H. Beyler, “From Positivism to Organicism: Pascual Jordan’s Interpretations of Modern Physics in Cultural Context,” PhD diss., Harvard University, 1996; Beyler, “Ernst Pascual Jordan” (ref. 9).

  84. Jordan, “Physikalischen Weltkonstanten” (ref. 20), 515.

  85. Jordan, Expanding Earth (ref. 37), 19.

  86. Goenner, “Some Remarks” (ref. 30).

  87. Homer E. Le Grand, Drifting Continents and Shifting Theories (Cambridge: Cambridge University Press, 1988), 227.

  88. Jordan’s work on the expanding Earth is not mentioned in Frankel, Continental Drift Controversy (ref. 70), Nunan, “Expanding Earth Theories” (ref. 70), Beyler, Positivism to Organicism (ref. 83), or Richard Nunan, “The Theory of an Expanding Earth and the Acceptability of Guiding Assumptions,” in Arthur Donovan, Larry Laudan, and Rachel Laudan, eds., Scrutinizing Science: Empirical Studies of Scientific Change (Dordrecht: Kluwer Academic, 1988), 289–313.

  89. Jürgen Müller and Liliane Biskukep, “Variations of the Gravitational Constant from Lunar Laser Ranging Data,” Classical and Quantum Gravity 24 (2007), 4533–4538.

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Correspondence to Helge Kragh.

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Helge Kragh is emeritus professor at the Niels Bohr Institute, Copenhagen University, Denmark.

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Kragh, H. Pascual Jordan, Varying Gravity, and the Expanding Earth. Phys. Perspect. 17, 107–134 (2015).

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