Zero-Point Energy: The Case of the Leiden Low-Temperature Laboratory of Heike Kamerlingh Onnes

Summary

In this paper we examine the reaction of the Leiden low-temperature laboratory of Heike Kamerlingh Onnes to new ideas in quantum theory. Especially the contributions of Albert Einstein (1906) and Peter Debye (1912) to the theory of specific heat, and the concept of zero-point energy formulated by Max Planck in 1911, gave a boost to solid state research to test these theories. In the case of specific heat measurements, Kamerlingh Onnes's laboratory faced stiff competition from Walter Nernst's Institute of Physical Chemistry in Berlin. In fact, Berlin got the better of it because Leiden lacked focus. After the liquefaction of helium in 1908, Kamerlingh Onnes transformed his laboratory into an international facility for low temperature research, and for this reason it was impossible to make headway with the specific heat measurements. In the case of zero-point energy, Leiden developed a magnetic research programme to test the concept. Initially the balance of evidence seemed to be tipping in favour of zero-point energy. After 1914, however, Leiden would desert the theory in fovour, of a concept from calssical physics. A curious move that illustrates Kamerlingh Onnes's discomfort with the new quantum theory.

Notes

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⁹Heike Kamerlingh Onnes to Julius, 19 October 1914, Universiteitsmuseum Utrecht, Julius archives, map vacature Debye.

¹⁰J.M. Burgers’ interview of T.S. Kuhn and Martin Klein, 9 June 1962, as part of the project ‘Sources for the History of Quantum Physics’, Burgers archives, Delft University of Technology.

¹¹Heike Kamerlingh Onnes to Dekhuyzen, 22 July 1916, Noord-Hollands Archief, Keesom archives, inv. no. 17.

¹²Albert van Helden, ‘Willem Hendrik Keesom 1876–1956’, in A History of Science in the Netherlands, edited by K. van Berkel, A. van Helden and L. Palm (Leiden, 1999), 498–500.

¹³The other one was Wander Johannes de Haas, also a pupil of Kamerlingh Onnes.

¹⁴Heike Kamerlingh Onnes to Julius, 19 October 1914, Universiteitsmuseum Utrecht, Julius archives, map vacature Debye.

¹⁵Pierre Marage and Grégoire Wallenborn (ed.), The Solvay Councils and the Birth of Modern Physics (Basel, 1999).

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¹⁹Kurt Mendelssohn, The Quest for Absolute Zero (London, 1966), 128–29.

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²¹A.T. Petit and P.L. Dulong, Annales de Chimie et Physique, 10 (1819), 395.

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³³Dirk van Delft, Freezing Physics.

³⁴Heike Kamerlingh Onnes to Crommelin, 4 November 1911, Huygens Laboratory, archives of Heike Kamerlingh Onnes.

³⁵Pierre Marage and Grégoire Wallenborn (ed.), The Solvay Councils and the Birth of Modern Physics (Basel, 1999).

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³⁷H. Kamerlingh Onnes, ‘Rapport sur les Résistances Électriques’, La théorie du royonnement et les quantas, edited by P. Langevin and M. de Broglie (Parijs, 1912), 304–12. Communications from the Physical Laboratory of the University of Leiden, Supplement 29.

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³⁹P. Langevin and M. de Broglie (ed.), La théorie du royonnement et les quantas (Paris 1912). Two years later, a German edition (incorporating more recent results) was published by Eucken.

⁴⁰In 1885 Kamerlingh Onnes started his own journal: Communications from the Physical Laboratory of the University of Leiden.

⁴¹H. Kamerlingh Onnes, ‘Further experiments with liquid helium, A. Isotherms of monatomic gases etc.’ KNAW, Proceedings, 1911, 1093–1113. Comm., 119.

⁴²H. Kamerlingh Onnes, ‘Further experiments with liquid helium. E. A helium cryostat. Remarks on the preceeding communications (with a plate). Comm., 123.

⁴³H. Kamerlingh Onnes and G. Holst, ‘Further experiments with liquid helium. M. Priliminary determination of the specific heat and of the thermal conductivity of mercury at temperatures, obtainable with liquid helium, besides some measurements of thermo-electric forces and resistances for the purpose of these investigations’. Comm., 142c.

⁴⁴W.H. Keesom, ‘De verdampingswarmte van waterstof’, Handelingen van het 13 ^de Nederlandsch Natuur- en Geneeskundig Congres (Haarlem, 1911), 45–52. Comm., 137e.

⁴⁵See note 24.

⁴⁶Keesom, Comm., 137e.

⁴⁷See note 29 and 30.

⁴⁸W.H. Keesom and H. Kamerlingh Onnes, ‘The specific heat at low temperatures. I. Measurements on the specific heat of lead between 14° and 80°K and of copper between 15° and 22°K. Comm. 143.

⁴⁹Heike Kamerlingh Onnes to Julius, 21 October 1914, Utrechts Universiteitsmuseum, Julius archives, map vacature Debye.

⁵⁰ Theorie du Rayonnement et les Quanta, 301.

⁵¹A. Eucken, ‘Die Molekularwärme des Wasserstofs bei tiefen Temperaturen’, Sitzungsberichte der Königlich Preussische Akademie der Wissenschaften, 1 February 1912, 141–51.

⁵²H. Kamerlingh Onnes and W.H. Keesom, ‘Die Zustandsgleichung’, Enzyklopädie der mathematischen Wissenschaften 5 (Leipzig 1903–1921), 615–945. Comm., Supplement 23.

⁵³W.H. Keesom, ‘On the second virial coefficient for monatomic gases, and for hydrogen below the Boyle-point’, KNAW, Proceedings, 15 I, 1912, pp. 643–49. Comm., Supplement 26.

⁵⁴Because of a bad health, Onnes was represented at the Congress by his Leiden colleague J.P. Kuenen.

⁵⁵H. Kamerlingh Onnes, ‘Report on researches made in the Leiden cryogenic laboratory between the Second and Third International Congress of Refrigeration’, Comm., 34a (September 1913), 10.

⁵⁶Heike Kamerlingh Onnes to Julius, 21 October 1914, Utrechts Universiteitsmuseum, Julius archives, map vacature Debye.

⁵⁷Peter Debye, ‘Zur Theorie der spezifischen Wärmen’, Annalen der Physik 39 (1912), 789–839.

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⁵⁹W.H. Keesom and H. Kamerlingh Onnes, ‘The specific heat at low temperatures. I. Measurements on the specific heat of lead between 14° and 80°K. and of copper between 15° and 22°K’, in KNAW, Proceedings, 17 II, 1914–1915, Amsterdam, 1915, pp. 894–914. Comm., 143.

⁶⁰W.H. Keesom and H. Kamerlingh Onnes, ‘The specific heat at low temperatures. II. Measurements on the specific heat of copper between 14 and 90°K’, in KNAW, Proceedings, 18 I, 1915, Amsterdam, 1915, pp. 484–93. Comm., 147a.

⁶¹W.H. Keesom and H. Kamerlingh Onnes, ‘The specific heat at low temperatures. III. Measurements of the specific heat of solid nitrogen between 14°K. and the triple point and of liquid nitrogen between the triple point and the boiling point’, in KNAW, Proceedings, 18 II, 1916, Amsterdam, 1916, pp. 1247–1255. Comm., 149a.

⁶²W. Nernst, The New Heat Theorem, Dover edition (New York, 1969), 52.

⁶³W.H. Keesom, ‘The specific heat at low temperatures. IV. Measurements of the specific heat of liquid hydrogen. Preliminary results on the specific heat of solid hydrogen and on the heat of fusion of hydrogen’, in KNAW, Proceedings, 20 II, 1918, Amsterdam, 1918, pp. 1000–1004. Comm., 153a.

⁶⁴The experiments were performed by the Harvard postdoc Leo Dana.

⁶⁵Heike Kamerlingh Onnes to Julius, 14 September 1914, Utrechts Universiteitsmuseum, Julius archives, map vacature Debye.

⁶⁶Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory I (New York, 1982), 113–36.

⁶⁷A. Einstein and O. Stern, ‘Einige Argumente für die Annahme einer molekularen Agitation beim absoluten Nullpunkt’, Annalen der Physik 40 (1913), 551–60.

⁶⁸Arnold Eucken, ‘Die Molekularwärme des Wasserstoffs bei tiefen Temperaturen’, Sitzungsberichte der Königlich Preussische Akademie der Wissenschaften (1912), 141–51.

⁶⁹P. Ehrenfest, ‘Bemerkung betreffs der spezifischen Wärme zweiatomiger Gase’, Verhandlungen der Deutsche Physikalische Gesellschaft, 15 (1913), 451.

⁷⁰Martin J. Klein, A.J. Kox, Jürgen Renn and Robert Schulmann (ed.), ‘Einstein and Stern on Zero-Point Energy’, The Collected Papers of Albert Einstein, vol. 4 (Princeton, NJ, 1995), 270–73.

⁷¹Einstein to Ehrenfest, November 1913, in Martin J. Klein, A.J. Kox and Robert Schulmann (ed.), The Collected Papers of Albert Einstein, vol. 5 (Princeton, NJ, 1993), 563–64.

⁷² Vorträge über die kinetische Theorie der Materie und der Elektrizität (Leipzig 1914).

⁷³ Vorträge über die kinetische Theorie der Materie und der Elektrizität (Leipzig 1914)., H. Kamerlingh Onnes and W.H. Keesom, ‘Über die Translationsenergie in einatomigen Gasen beim absoluten Nullpunkt’, 193–94.W.H. Keesom, ‘On the equation of state of an ideal monatomic gas according to the quantum theory’, in KNAW, Proceedings, 16 I, 1913, Amsterdam, 1913, pp. 227–36. Comm. Supplement 30a.

⁷⁴H.B.G. Casimir, ‘Hugo Tetrode (1895–1931): Een geniale outsider’. In Mens en kosmos (Amsterdam 1993), 180–89.

⁷⁵H. Tetrode, ‘Die chemische Konstante der Gase und das elementare Wirkungsquantum’, Annalen der Physik, 38 (1912), 434–42; H. Tetrode. ‘Bemerkungen über den Energieinhalt einatomiger Gase und über die Quantentheorie für Flüssigkeiten’, Physikalische Zeitschrift, 14 (1913), 212–15.

⁷⁶Museum Boerhaave, archives of Heike Kamerlingh Onnes, inv. no. 72.

⁷⁷Heike Kamerlingh Onnes to Julius, 19 October 1914, Universiteitsmuseum Utrecht, Julius archives, map vacature Debye.

⁷⁸Gavroglu and Goudaroulis, Through Measurement to Knowledge, lxxx–lxxxvii.

⁷⁹For an overview, see Pierre Weiss, ‘Les recherches magnétiques au Laboratoire cryogène de Leyde’. Het Natuurkundig Laboratorium 1904–1922, 233–74.

⁸⁰E. Oosterhuis, ‘Magnetic researches IX. The deviations from Curie's law in connection with the zero point energy’, in KNAW, Proceedings, 16 I, 1913, Amsterdam, 1913, pp. 432–40. Comm. Supplement 31.

⁸¹W.H. Keesom, ‘Over het arbeidsvermogen van de draaiende beweging der moleculen’, Handelingen van het XVIIe Vlaamsch Natuur- en Geneeskundig Congres (Ghent 1913), 68–73.

⁸²W.H. Keesom, ‘On the magnetization of ferromagnetic substances considered in connection with the assumption of a zero-point energy. II. On the susceptibility in the excited ferromagnetic state’, in KNAW, Proceedings, 16 I, 1913, Amsterdam, 1913, pp. 468–76. Comm. Supplement 32b.

⁸³W.H. Keesom, ‘On the manner in which the susceptibility of paramagnetic substances depends on the density’, in KNAW, Proceedings, 17 I, 1914, Amsterdam, 1914, pp. 110–22. Comm. Supplement 36c.

⁸⁴Albert Perrier and H. Kamerlingh Onnes, ‘Magnetic researches XIII. The susceptibility of liquid mixtures of oxygen and nitrogen and the influence of the mutual distance of the molecules upon paramagnetism’, in KNAW, Proceedings, 16 II, 1913–1914, Amsterdam, 1914, pp. 901–16. Comm. 139d.

⁸⁵Keesom to Lorentz, 12 March 1914, Noord-Hollands Archief, Lorentz archives, inv. 40.

⁸⁶Heike Kamerlingh Onnes to Julius, 19 October 1914, Universiteitsmuseum Utrecht, Julius archives, map vacature Debye.

⁸⁷Jean Becquerel and H. Kamerlingh Onnes, ‘The absorption spectra of the compounds of the rare earths at the temperatures obtainable with liquid hydrogen, and their change by the magnetic field. (With five plates). Comm. 103.

⁸⁸Museum Boerhaave, archives of Heike Kamerlingh Onnes, inv. no. 72.

⁸⁹Keesom to Lorentz, 29 April 1913, Noord-Hollands Archief, Lorentz archives, inv. 40.

⁹⁰Lorentz to Keesom, 1 May 1913, Museum Boerhaave, Keesom archives, box 1.

⁹¹Wien to Keesom, 9 May 1913, Museum Boerhaave, Keesom archives, box 1.

⁹²Lorentz to Julius, 14 October 1914, Utrechts Universiteitsmuseum, Julius archives, map vacature Debye.

⁹³Planck to Heike Kamerlingh Onnes, 10 March 1915, Museum Boerhaave, archives of Heike Kamerlingh Onnes, inv. no. 306.

⁹⁴Dirk van Delft, ‘Albert Einstein in Leiden’, Physics Today, April 2006, 57–62.

⁹⁵H. Kamerlingh Onnes, ‘Paramagnétisme aux basses températures’, Atomes et electrons (Paris 1923), 131–64. Comm., supplement 44a.

⁹⁶W.H. Keesom, ‘Over de afwijkingen, die vloeibare zuurstof vertoont van de wet van Curie’, Verslagen 29 (February 1921), 1155–65. Comm., Supplement 44c.

⁹⁷P.W. Milonni and M.-L. Shih, ‘Zero-point energy in early quantum theory’, American Journal of Physics 59 (August 1991), 684–98.

⁹⁸Heike Kamerlingh Onnes to Vissering, 1 December 1919, Gemeentearchief Leiden, LUF, inv. no. 204.

⁹⁹Museum Boerhaave, Heike Kamerlingh Onnes to Einstein, 8 February 1920.

¹⁰⁰Dirk van Delft, ‘Albert Einstein in Leiden’, Physics Today, April 2006, pp 57–62.

¹⁰¹Museum Boerhaave, Heike Kamerlingh Onnes to Einstein, 13 August 1921.

¹⁰²Einstein to Heike Kamerlingh Onnes, 4 November 1924, Museum Boerhaave, archives of Heike Kamerlingh Onnes.

¹⁰³Museum Boerhaave, Heike Kamerlingh Onnes to Einstein, 13 November 1924.

¹⁰⁴L.I. Dana and H. Kamerlingh Onnes, ‘Further experiments with liquid helium. BA. Priliminary determinations of the latent heat of vaporization of liquid helium’, 1926, Comm., 179c.

¹⁰⁵L.I. Dana and H. Kamerlingh Onnes, ‘Further experiments with liquid helium. BB. Priliminary determinations of the specific heat of liquid helium’, 1926, Comm., 179d.

¹⁰⁶Einstein to Maria Rooseboom, 27 February 1953, Albert Einstein & Museum Boerhaave (Leiden, 1993), 40–41.