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Preludes to dark energy: zero-point energy and vacuum speculations

Abstract

According to modern physics and cosmology, the universe expands at an increasing rate as the result of a “dark energy” that characterizes empty space. Although dark energy is a modern concept, some elements in it can be traced back to the early part of the twentieth century. I examine the origin of the idea of zero-point energy, and in particular how it appeared in a cosmological context in a hypothesis proposed by Walther Nernst in 1916. The hypothesis of a zero-point vacuum energy attracted some attention in the 1920s, but without attempts to relate it to the cosmological constant that was discussed by Georges Lemaître in particular. Only in the late 1960s, was it recognized that there is a connection between the cosmological constant and the quantum vacuum. As seen in retrospect, many of the steps that eventually led to the insight of a kind of dark energy occurred isolated and uncoordinated.

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References

  • Assis A.K.T., Neves M.C.D. (1995) The redshift revisited. Astrophysics and Space Science 227: 13–24

    Article  Google Scholar 

  • Barkan Diana K (1999) Walther Nernst and the transition to modern physical science. Cambridge University Press, Cambridge

    Google Scholar 

  • Barker E.F. (1923) Molecular spectra and half-quanta. Astrophysical Journal 58: 201–207

    Article  Google Scholar 

  • Barone M. (2004) The vacuum as ether in the last century. Foundations of Physics 34: 1973–1982

    Article  Google Scholar 

  • Bartel, Hans-Georg, and Rudolf P. Huebener. 2007. Walther Nernst: Pioneer of physics and of chemistry. Singapore: World Scientific.

  • Bennewitz Kurt, Franz Simon (1923) Zur Frage der Nullpunktsenergie. Zeitschrift für Physik 16: 183–199

    Article  Google Scholar 

  • Blome Hans-Joachim, Wofgang Priester (1984) Vacuum energy in a Friedmann-Lemaître universe. Die Naturwissenschaften 71: 528–531

    Article  Google Scholar 

  • Blome Hans-Joachim, Wofgang Priester (1985) Vacuum energy in cosmic dynamics. Astrophysics and Space Science 117: 327–335

    Article  Google Scholar 

  • Bohr, Niels. 1913. On the constitution of atoms and molecules. Philosophical Magazine 26: 1–25, 476–502, 851–875.

  • Bohr Niels (1922) The theory of spectra and atomic constitution. Cambridge University Press, Cambridge

    Google Scholar 

  • Bohr, Niels. 1932. Atomic stability and conservation laws. In Atti del Convegno di Fisica Nucleare, 119–130. Rome: Reale Accademia d’Italia. Reprinted in Niels Bohr collected works, ed. Rudolf Peierls, vol. 9 (North-Holland, Amsterdam, 1986).

  • Bohr, Niels. 1981. Niels Bohr collected works, vol. 2. Ed. Ulrich Hoyer. Amsterdam: North-Holland.

  • Bohr, Niels. 1984. Niels Bohr collected works, vol. 5. Ed. Klaus Stoltzenburg. Amsterdam: North-Holland.

  • Born Max, Werner Heisenberg, Pascual Jordan (1926) Zur Quantenmechanik II. Zeitschrift für Physik 35: 557–615

    Article  Google Scholar 

  • Boyer Timothy H (1969) Derivation of the blackbody radiation spectrum without quantum assumptions. Physical Review 182: 1374–1383

    Article  Google Scholar 

  • Bromberg Joan (1976) The concept of particle creation before and after quantum mechanics. Historical Studies in the Physical Sciences 7: 161–182

    Google Scholar 

  • Bronstein Matvei (1933) On the expanding universe. Physikalische Zeitschrift der Sowjetunion 3: 73–82

    MATH  Google Scholar 

  • Browne P.F. (1995) The cosmological views of Nernst: An appraisal. Apeiron 2: 72–78

    Google Scholar 

  • Calder Lucy, Ofer Lahav (2008) Dark energy: Back to Newton?. Astronomy & Geophysics 49: 1.13–1.18

    Article  Google Scholar 

  • Carazza Bruno, Guidetti G.P. (1986) The Casimir electron model. Archive for History of Exact Sciences 35: 273–279

    MathSciNet  Article  Google Scholar 

  • Cassidy David C. (1978) Heisenberg’s first paper. Physics Today 31: 23–28

    Article  Google Scholar 

  • Cassidy David C. (1979) Heisenberg’s first core model of the atom: The formation of a professional style. Historical Studies in the Physical Sciences 10: 187–224

    Google Scholar 

  • Condon Edward U., Julian E. Mack (1930) A cosmological conjecture. Nature 125: 455

    Article  Google Scholar 

  • Darrigol Olivier (1988) Statistics and combinatorics in early quantum theory. Historical Studies in the Physical Sciences 19: 17–80

    Google Scholar 

  • Davies Paul (1982) Something for nothing. New Scientist 94: 580–582

    Google Scholar 

  • Debye Peter (1913) Über den Einfluss der Wärmebewegung auf die Interferenzerscheinungen bei Röntgenstrahlungen. Verhandlungen der Deutschen Physikalischen Gesellschaft 15: 678–689

    Google Scholar 

  • Debye Peter (1914) Interferenz von Röntgenstrahlungen und Wärmebewegung. Annalen der Physik 43: 49–95

    Google Scholar 

  • Debye, Peter. 1915. Die Konstitution des Wasserstoff-Moleküls. Sitzungsberichte, Bayerischen Akademie der Wissenschaften München: 1–26.

  • De Sitter Willem (1931) The expanding universe. Scientia 49: 1–10

    Google Scholar 

  • Earman John (2001) Lambda: The constant that refuses to die. Archive for History of Exact Sciences 55: 189–220

    MathSciNet  Article  Google Scholar 

  • Eddington Arthur S. (1920) The internal constitution of the stars. Nature 106: 14–20

    Article  Google Scholar 

  • Eddington Arthur S (1926) The internal constitution of the stars. Cambridge University Press, Cambridge

    Google Scholar 

  • Eddington Arthur S. (1936) Relativity theory of protons and electrons. Cambridge University Press., Cambridge

    Google Scholar 

  • Ehrenfest Paul (1913) Bemerkung betreffs der spezifischen Wärme zweiatoniger Gase. Verhandlungen der Deutschen Physikalischen Gesellschaft 15: 451–457

    Google Scholar 

  • Einstein Albert (1915) Experimenteller Nachweis der Ampèreschen Molekularströme. Die Naturwissenschaften 3: 237–238

    Article  Google Scholar 

  • Einstein, Albert. 1919. Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle? Sitzungsberichte, Preussische Akademie der Wissenschaften (Berlin): 349–356.

  • Einstein Albert (1920) Äther und Relativitätstheorie. Springer, Berlin

    MATH  Google Scholar 

  • Einstein Albert (1945) The meaning of relativity. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Einstein Albert (1983) Sidelights on relativity. Dover Publications, New York

    Google Scholar 

  • Einstein, Albert. 1993. The collected papers of Albert Einstein, vol. 5. Ed. Martin J. Klein, A.J. Kox, and Robert Schulmann. Princeton: Princeton University Press.

  • Einstein, Albert. 1995. The collected papers of Albert Einstein, vol. 4. Ed. Martin J. Klein et al. Princeton: Princeton University Press.

  • Einstein, Albert. 1998. The collected papers of Albert Einstein, vol. 8A. Ed. Robert Schulmann et al. Princeton: Princeton University Press.

  • Einstein, Albert. 2009. The Collected Papers of Albert Einstein, vol. 12. Ed. Diana K. Buchwald et al. Princeton: Princeton University Press

  • Einstein Albert, Otto Stern (1913) Einige Argumente für die Annahme einer molekularen Agitation beim absoluten Nullpunkt. Annalen der Physik 40: 551–560

    MATH  Article  Google Scholar 

  • Einstein Albert et al (1952) The principle of relativity. Dover Publications, New York

    MATH  Google Scholar 

  • Enz, Charles P. 1974. Is the zero-point energy real? In Physical reality and mathematical description, ed. C.P. Enz and J. Mehra, 124–132. Dordrecht: Reidel.

  • Enz Charles P (2002) No time to be brief: A scientific biography of Wolfgang Pauli. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Enz, Charles P. 2009. Of matter and spirit: Selected essays by Charles P. Enz. Singapore: World Scientific.

  • Enz Charles P., Armin Thellung (1960) Nullpunktsenergie und Anordnung nicht vertauschbarer Faktoren im Hamiltonoperator. Helvetica Physica Acta 33: 839–848

    MathSciNet  Google Scholar 

  • Eucken, Arnold. 1912. Die Molekularwärme des Wasserstoffs bei tiefen Temperaturen. Sitzungsberichte, Preussische Akademie der Wissenschaften (Berlin): 141–151.

  • Forman, Paul. 1971. Weimar culture, causality, and quantum theory, 1918–1927: Adaption of German physicists and mathematicians to a hostile intellectual environment. Historical Studies in the Physical Sciences 3: 1–115.

  • Gearhart Clayton A. (2010) “Astonishing successes” and “bitter disappointment”: The specific heat of hydrogen in quantum theory. Archive for History of Exact Sciences 64: 113–202

    Article  Google Scholar 

  • Gliner Erast (1966) Algebraic properties of the energy-momentum tensor and vacuum-like states of matter. Soviet Physics JETP 22: 378–382

    Google Scholar 

  • Gorelik Gennady E., Victor Ya Frenkel (1994) Matvei Petrovich Bronstein and Soviet theoretical physics in the thirties. Birkhäuser, Basel

    MATH  Book  Google Scholar 

  • Günther Paul (1924) Die kosmologische Betrachtungen von Nernst. Zeitschrift für Angewandte Chemie 37: 454–457

    Article  Google Scholar 

  • Haas Arthur E (1912) Ist die Welt in Raum und Zeit unendlich?. Archiv für Systematische Philosophie 18: 167–184

    Google Scholar 

  • Heilbron John L., Thomas S. Kuhn (1969) The genesis of the Bohr atom. Historical Studies in the Physical Sciences 1: 211–290

    Google Scholar 

  • Heisenberg, Werner. 1925. Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33: 879–893.

    Google Scholar 

  • Hirosige, Tetu, and Sigeo Nisio. 1964. Formation of Bohr’s theory of atomic constitution. Japanese Studies in History of Science 3: 6–28.

    Google Scholar 

  • Huber Peter, Toivo Jaakkola (1995) The static universe of Walther Nernst. Apeiron 2: 53–57

    Google Scholar 

  • Huterer Dragan, Michael S. Turner (1999) Prospects for probing the dark energy via supernova distance measurements. Physical Review D 60: 081301

    Article  Google Scholar 

  • Illy József (1981) Revolutions in a revolution. Studies in History and Philosophy of Science 12: 173–210

    MathSciNet  Article  Google Scholar 

  • Imes Elmer S. (1919) Measurement in the near infrared absorption of some diatomic gases. Astrophysical Journal 50: 251–276

    Article  Google Scholar 

  • Jammer Max (1966) The conceptual development of quantum mechanics. McGraw-Hill, New York

    Google Scholar 

  • Jauncey George, Albert Hughes L. (1926) Radiation and the disintegration and aggregation of atoms. Proceedings of the National Academy of Sciences 12: 169–173

    MATH  Article  Google Scholar 

  • Jordan, Pascual. 1927. Über die thermodynamische Gleichgewichtskonzentration der kosmischen Materie. Zeitschrift für Physik 41: 711–717.

    Google Scholar 

  • Jordan Pascual (1928) Die Lichtquantenhypothese. Ergebnisse der Exacten Naturwissenschaften 7: 158–208

    Article  Google Scholar 

  • Jordan Pascual, Wolfgang Pauli (1928) Zur Quantenelektrodynamik ladungsfreier Felder. Zeitschrift für Physik 47: 151–173

    Article  Google Scholar 

  • Keesom, Willem H. 1913. On the equation of state of an ideal monatomic gas according to the quantum-theory. Communications from the Physical Laboratory of the University of Leiden 30b.

  • Kerzberg, Pierre. 1989. The invented universe: The Einstein–De Sitter Controversy (1916–1917) and the rise of relativistic cosmology. Oxford: Clarendon Press.

  • Klein, Martin J. 1970. Paul Ehrenfest, vol. 1: The making of a theoretical physicist. Amsterdam: North-Holland.

  • Kostro Ludwik (2000) Einstein and the ether. Montreal, Apeiron

    Google Scholar 

  • Kragh Helge (1990) Dirac: A scientific biography. Cambridge University Press, Cambridge

    Google Scholar 

  • Kragh Helge (1995) Cosmology between the wars: The Nernst–MacMillan alternative. Journal for the History of Astronomy 26: 93–115

    MathSciNet  Google Scholar 

  • Kragh, Helge. 1999. Steady-state cosmology and general relativity: Reconciliation or conflict? In The expanding worlds of general relativity, ed. Hubert Goenner et al., 377–402. Boston: Birkhäuser.

  • Kragh Helge (2002) The vortex atom: A victorian theory of everything. Centaurus 44: 32–115

    MathSciNet  Article  Google Scholar 

  • Kragh Helge (2007) Cosmic radioactivity and the age of the universe. Journal for the History of Astronomy 38: 393–412

    Google Scholar 

  • Kragh Helge (2008) Entropic creation: Religious contexts of thermodynamics and cosmology. Aldershot, Ashgate

    Google Scholar 

  • Kragh Helge (2009) Continual fascination: The oscillating universe in modern cosmology. Science in Context 22: 587–612

    Article  Google Scholar 

  • Kramers Hendrik A., Helge Holst (1925) Das Atom und die Bohrsche Theorie seines Baues. Springer, Berlin

    Book  Google Scholar 

  • Kramers Hendrik A., Wolfgang Pauli (1923) Zur Theorie der Bandenspektren. Zeitschrift für Physik 13: 351–367

    Article  Google Scholar 

  • Kratzer Adolf (1923) Die Feinstruktur einer Klasse von Bandenspektren. Annalen der Physik 71: 72–103

    Article  Google Scholar 

  • Kuhn, Thomas S. 1978. Black-body theory and the quantum discontinuity, 1894–1912. Oxford: Clarendon Press.

  • Langevin, Paul, and Maurice de Broglie, eds. 1912. La Théorie du Rayonnement et les Quanta: Rapports et Discussions de la Réunion Tenue à Bruxelles, du 30 Octobre au 3 Novembre 1911. Paris: Gauthier-Villars.

  • LeBon Gustave (1905) The evolution of matter. Charles Scribner’s Sons, New York

    Google Scholar 

  • Lemaître Georges (1934a) Evolution of the expanding universe. Proceedings of the National Academy of Sciences 20: 12–17

    Article  Google Scholar 

  • Lemaître Georges (1934b) Evolution in the expanding universe. Nature 133: 654

    MATH  Google Scholar 

  • Lemaître Georges (1949) Cosmological applications of relativity. Reviews of Modern Physics 21: 357–366

    MathSciNet  MATH  Article  Google Scholar 

  • Lemaître, Georges. 1958. The primeval atom hypothesis and the problem of the clusters of galaxies. In La Structure et l’Évolution de l’Univers, ed. R. Stoops, 1–32. Brussels: Coudenberg.

  • Lenz Wilhelm (1926) Das Gleichgewicht von Materie und Strahlung in Einsteins geschlossener Welt. Physikalische Zeitschrift 27: 642–645

    Google Scholar 

  • Lindemann Fredrick (1919) Note on the vapour pressure and affinity of isotopes. Philosophical Magazine 38: 173–181

    Google Scholar 

  • Lodge Oliver (1907) The density of the æther. Philosophical Magazine 13: 488–506

    Google Scholar 

  • Lodge Oliver (1920) Note on a possible structure for the ether. Philosophical Magazine 39: 170–174

    Google Scholar 

  • Lorentz Hendrik A (1909) The theory of electrons. Leipzig, Teubner

    Google Scholar 

  • Luminet, Jean-Pierre. 2007. The rise of big bang models, from myth to theory and observations. ArXiv:0704.3579v (astro-ph).

  • Maneff, G. 1932. Über das kosmologische Problem der Relativitätstheorie. Zeitschrift für Astrophysik 4: 231–240.

    Google Scholar 

  • McCrea William H (1951) Relativity theory and the creation of matter. Proceedings of the Royal Society A 206: 562–575

    Article  Google Scholar 

  • McCrea William H (1986) Time, vacuum and cosmos. Quarterly Journal of the Royal Astronomical Society 27: 137–152

    Google Scholar 

  • Mehra, Jagdish. 2001. The golden age of theoretical physics, vol. 1. Singapore: World Scientific.

  • Mehra, Jagdish, and Helmut Rechenberg. 1982–2000. The historical development of quantum theory, 6 vols. New York: Springer.

  • Mehra, Jagdish, and Helmut Rechenberg. 1999. Planck’s half-quanta: A history of the concept of zero-point energy. Foundations of Physics 29: 91–132.

    Google Scholar 

  • Miller Arthur I (1973) A study of Henri Poincaré’s “Sur la dynamique de l’électron”. Archive for History of Exact Sciences 10: 207–328

    MathSciNet  Article  Google Scholar 

  • Millikan Robert A (1913) Atomic theories of radiation. Science 37: 119–133

    Article  Google Scholar 

  • Milloni P.W., Shih M.-L. (1991) Zero-point energy in early quantum theory. American Journal of Physics 59: 684–697

    Article  Google Scholar 

  • Mulliken Robert S (1924) The band spectrum of boron monoxide. Nature 114: 349–350

    Article  Google Scholar 

  • Mulliken Robert S (1925) The isotope effect in band spectra, II: The spectrum of boron monoxide. Physical Review 25: 259–294

    Article  Google Scholar 

  • Navarro, Luis, and Enric Pérez. 2006. Paul Ehrenfest: The genesis of the adiabatic hypothesis, 1911–1914. Archive for History of Exact Sciences 60: 209–267.

    Google Scholar 

  • Needell, Allan A. 1980. Irreversibility and the failure of classical dynamics: Max Planck’s work on the quantum theory 1900–1915, vol. 3058. Ann Arbor: University Microfilms.

  • Nernst Walther (1907) Theoretische Chemie. Ferdinand Enke, Stuttgart

    Google Scholar 

  • Nernst, Walther. 1911. Zur Theorie der spezifischen Wärme und über die Anwendung der Lehre von den Energiequanten auf physikalisch-chemische Fragen überhaupt. Zeitschrift für Electrochemie 17: 265–275.

  • Nernst, Walther. 1912. Zur neueren Entwicklung der Thermodynamik. Verhandlungen der Gesellschaft Deutscher Naturforscher und Ärtzte 1: 100–116.

  • Nernst, Walther. 1916. Über einen Versuch, von quantentheoretischen Betrachtungen zur Annahme stetiger Energieänderungen zurückzukehren. Verhandlungen der Deutschen Physikalischen Gesellschaft 18: 83–116.

  • Nernst Walther (1921) Das Weltgebäude im Lichte der Neueren Forschung. Julius Springer, Berlin

    MATH  Book  Google Scholar 

  • Nernst Walther (1922) Zum Gültigkeitsbereich der Naturgesetze. Naturwissenschaften 10: 489–495

    Article  Google Scholar 

  • Nernst Walther (1928) Physico-chemical considerations in astrophysics. Journal of the Franklin Institute 206: 135–142

    Article  Google Scholar 

  • Nernst Walther (1938) Die Strahlungstemperatur des Universums. Annalen der Physik 32: 44–48

    Article  Google Scholar 

  • Overduin, James, Hans-Joachim Blome, and Josef Hoell. 2007. Wolfgang Priester: From the big bounce to the Λ-dominated universe. Die Naturwissenschaften 94: 417–429.

    Google Scholar 

  • Pachner Jaroslav (1965) An oscillating isotropic universe without singularity. Monthly Notices of the Royal Astronomical Society 131: 173–176

    Google Scholar 

  • Partington, James R. 1953. The Nernst memorial lecture: Hermann Walther Nernst. Journal of the American Chemical Society, 2853–2872.

  • Pauli, Wolfgang. 1933. Die allgemeinen Prinzipien der Wellenmechanik. In Handbuch der Physik, vol. 24, part 1, ed. H. Geiger and K. Scheel, 83–272. Berlin: Springer.

  • Pauli, Wolfgang. 1979. Wolfgang Pauli. Wissenschaftlicher Briefwechsel, vol. 1. Ed. Armin Hermann et al. New York: Springer.

  • Peebles P., James E (1993) Principles of physical cosmology. Princeton University Press, Princeton

    Google Scholar 

  • Peebles, P. James E., and Bharat Ratra. 2003. The cosmological constant and dark energy. Reviews of Modern Physics 75: 559–606.

    Google Scholar 

  • Planck, Max. 1911. Eine neue Strahlungshypothese. Verhandlungen der Deutschen Physikalischen Gesellschaft 13: 138–148. Reprinted in Max Planck, ed. Physikalische Abhandlungen und Vorträge, vol. 2, 249–259 (Braunschweig: Vieweg & Sohn, 1958).

  • Planck, Max. 1912a. Über die Begründung das Gesetzes des schwarzen Strahlung. Annalen der Physik 37: 642–656. Reprinted in Max Planck, ed. Physikalische Abhandlungen und Vorträge, vol. 2, 287–301 (Braunschweig: Vieweg & Sohn, 1958).

  • Planck, Max. 1912b. La loi du rayonnement noir et l’hypothèse des quantités élémentaires d’action. In La Théorie du Rayonnement et les Quanta, ed. Paul Langevin and Maurice de Broglie, pp. 93–114. Paris: Gauthier-Villars. German translation in Max Planck, ed. Physikalische Abhandlungen und Vorträge, vol. 2, 269–286 (Braunschweig: Vieweg & Sohn, 1958).

  • Planck, Max. 1913. Vorlesungen über die Theorie der Wärmestrahlung. Leipzig: J. A. Barth.

  • Planck Max (1923) Die Bohrsche Atomtheorie. Die Naturwissenschaften 11: 535–537

    Article  Google Scholar 

  • Planck, Max. 1958. Physikalische Abhandlungen und Vorträge, vol. 2. Braunschweig: Vieweg & Sohn.

  • Planck, Max et al. 1914. Vorträge über die Kinetische Theorie der Materie und der Elektrizität. Leipzig: B. G. Teubner.

  • Priester, Wolfgang. 1984. Urknall und Evolution des Kosmos – Fortschritte in der Kosmologie. Opladen: Westdeutscher Verlag.

  • Reiche Fritz (1918) Die Quantentheorie: Ihr Ursprung ind ihre Entwicklung. Die Naturwissenschaften 6: 213–230

    Article  Google Scholar 

  • Reiche Fritz (1920) Zur Theorie der Rotationsspektren. Zeitschrift für Physik 1: 283–293

    Article  Google Scholar 

  • Reiche Fritz (1921) Die Quantentheorie: Ihr Ursprung und ihre Entwicklung. Julius Springer, Berlin

    MATH  Google Scholar 

  • Rowlands Peter (1990) Oliver Lodge and the Liverpool Physical Society. Liverpool University Press, Liverpool

    Google Scholar 

  • Rugh, Svend E., Henrik Zinkernagel, and Tian Yu Cao. 1999. The Casimir effect and the interpretation oft he vacuum. Studies in History and Philosophy of Modern Physics 30: 111–139.

  • Rugh, Svend E., and Henrik Zinkernagel. 2002. The quantum vacuum and the cosmological constant problem. Studies in History and Philosophy of Modern Physics 33: 663–705.

    Google Scholar 

  • Schnippenkötter, Josef. 1920. Das Entropiegesetz: Seine Physikalische Entwicklung und seine Philosophische und Apologetische Bedeutung. Essen: Fredebeul & Koenen.

  • Schrödinger Erwin (1918) Über ein Lösungssystem der allgemein kovarianten Gravitationsgleichungen. Physikalische Zeitschrift 19: 20–22

    Google Scholar 

  • Schrödinger Erwin (1926) Quantisierung als Eigenwertproblem. Zweite Mitteilung. Annalen der Physik 79: 489–527

    MATH  Article  Google Scholar 

  • Schweber, Silvan S. 1994. QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton: Princeton University Press.

  • Sciama Dennis W (1978) The ether transmogrified. New Scientist 77: 298–300

    Google Scholar 

  • Sciama, Dennis W. 1991. The physical significance of the vacuum state of a quantum field. In The Philosophy of Vacuum, ed. Simon Saunders and Harvey R. Brown, pp. 137–158. Oxford: Clarendon Press.

  • Simon, Francis. 1956 The third law of thermodynamics: An historical survey. Yearbook of the Physical Society: 1–22.

  • Smeenk, Chris. 2005. False vacuum: Early universe cosmology and the development of inflation. In The Universe of General Relativity, ed. A.J. Kox and Jean Eisenstaedt, pp. 223–257. Boston: Birkhäuser.

  • Stern Otto (1913) Zur kinetischen Theorie des Dampdrucks einatomiger freier Stoffe und über die Entropiekonstante einatomiger Gase. Physikalische Zeitschrift 14: 629–632

    Google Scholar 

  • Stern Otto (1919) Zusammenfassender Bericht über die Molekulartheorie des Dampfdruckes fester Stoffe und ihre Bedeutung für die Berechnung chemischer Konstanten. Zeitschrift für Electrochemie 25: 66–80

    Google Scholar 

  • Stern, Otto. 1925. Über das Gleichgewicht zwischen Materie und Strahlung. Zeitschrift für Electrochemie und Angewandte Physikalische Chemie 31:448–449.

  • Stern, Otto. 1926a. Über die Umwandlung von Atomen in Strahlung. Zeitschrift für Physikalische Chemie 120: 60–62.

  • Stern Otto (1926b) Transformation of atoms into radiation. Transactions of the Faraday Society 21: 477–478

    Article  Google Scholar 

  • Straumann Norbert (2009) Wolfgang Pauli and modern physics. Space Science Reviews 148: 25–36

    Article  Google Scholar 

  • Sutherland William (1899) Cathode, Lenard and Röntgen rays. Philosophical Magazine 47: 269–284

    Google Scholar 

  • Tolman Richard C (1920) The entropy of gases. Journal of the American Chemical Society 42: 1185–1193

    Article  Google Scholar 

  • Tolman, Richard C. 1928. On the equilibrium between radiation and matter in Einstein’s closed universe. Proceedings of the National Academy of Sciences 14:353–356.

    Google Scholar 

  • Tolman Richard C (1934) Relativity, thermodynamics and cosmology. Oxford University Press, Oxford

    Google Scholar 

  • Valentiner, Siegfried. 1919. Die Grundlagen der Quantentheorie in Elementarer Darstellung. Braunschweig: Vieweg & Sohn.

  • Van Delft, Dirk. 2007. Freezing Physics: Heike Kamerlingh Onnes and the Quest for Cold. Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen.

  • Van Delft Dirk (2008) Zero-point energy: The case of the Leiden low-temperature laboratory of Heike Kamerlingh Onnes. Annals of Science 65: 339–362

    Article  Google Scholar 

  • Van der Waerden, Bartel L., ed. 1967. Sources of quantum mechanics. New York: Dover Publications.

  • Wheaton, Bruce R. 1983. The tiger and the shark: Empirical roots of wave-particle dualism. Cambridge: Cambridge University Press.

  • Whitaker M.A.B. (1985) Planck’s first and second theories and the correspondence principle. European Journal of Physics 6: 266–270

    Article  Google Scholar 

  • Wiechert, Emil. 1921a. Der Äther im Weltbild der Physik. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zur Göttingen, Math.-Phys. Klasse 1: 29–70.

  • Wiechert Emil (1921) Anmerkungen zur Theorie der Gravitation und über das Schicksal der Gestirne. Vierteljahrschrift der Astronomische Gesellschaft 56: 171–191

    Google Scholar 

  • Wilczek, Frank. 1998. The persistence of the ether. Physics Today 52(January): 11–12.

    Google Scholar 

  • Zaycoff G. Raschco (1932) Zur relativistichen Kosmogonie. Zeitschrift für Astrophysik 6: 128–197

    Google Scholar 

  • Zel’dovich Yakov B. (1968) The cosmological constant and the theory of elementary particles. Sovjet Physics Uspekhi 11: 381–393

    Article  Google Scholar 

  • Zwicky Fritz (1928) On the thermodynamic equilibrium in the universe. Proceedings of the National Academy of Sciences 14: 592–597

    MATH  Article  Google Scholar 

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Kragh, H. Preludes to dark energy: zero-point energy and vacuum speculations. Arch. Hist. Exact Sci. 66, 199–240 (2012). https://doi.org/10.1007/s00407-011-0092-3

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Keywords

  • Dark Energy
  • Quantum Theory
  • Cosmological Constant
  • Vacuum Energy
  • Correspondence Principle