Kaluza—Klein Theory

  • Daniela Wuensch

Theodor Kaluza (1885–1954) set forth his idea of unifying gravitation and electromagnetism within five-dimensional space-time in a paper from the beginning of 1919. It was presented by Albert Einstein (1879–1955) to the Berlin Academy of Science and published in its Sitzungsberichte in 1921 under the title “Zum Unitätsproblem der Physik” [4]. Having received the manuscript from the author in April 1919, Einstein was so impressed with the idea of unifying the basic forces in a five-dimensional space that he used it himself up to the mid-1940s in eight of his own papers.

Kaluza's idea of unifying gravitation and electromagnetism goes back to David Hilbert's (1862–1943) unification program and to the pioneering work of two of his pupils: Hilbert sought unification within a four-dimensional space by having electromagnetism come from gravitation in 1915 [2]. His pupil Gunnar Nordström (1881–1923) explored unification within a five-dimensional unwarped (Minkowskian) space in the foregoing year [7]. The unification attempt by Hermann Weyl (1885–1955) in 1918, finally, was to apply a gauge transformation within a four-dimensional space with a generalized non-Riemannian metric [10]. Although Nordström was the first to introduce a five-dimensional space, it was Kaluza's theory from 1919 that proposed a realistic unification of the two interactions. Nordström's theory predated the general theory of relativity (1915) so the gravitation was derived from electromagnetism within a space described by a Minkowskian flat metric. As a consequence, it could not explain phenomena like light deflection and was therefore condemned as a prerelativistic theory.


Gauge Transformation Hide Variable Natural Force Basic Force Klein Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Primary Literature

  1. 1.
    B. S. DeWitt: Dynamical Theory of Groups and Fields. Relativity, Groups and Topology, C. DeWitt and B.S. DeWitt (Eds.) 725, (Gordon & Breach: New York and London 1964)Google Scholar
  2. 2.
    D. Hilbert: Die Grundlagen der Physik. Erste Mitteilung am 20. November 1915 Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, 395–407 (1915)Google Scholar
  3. 3.
    B. Hoffmann and O. Veblen: Projective Relativity. The Physical Review 36, 810–822 (1930)CrossRefADSGoogle Scholar
  4. 4.
    T. Kaluza: Zum Unitätsproblem der Physik. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin 966–972 (1921)Google Scholar
  5. 5.
    O. Klein: Quantentheorie und fünfdimensionale Relativitätstheorie. Zeitschrift für Physik 37, 895–906 (1926a)CrossRefADSGoogle Scholar
  6. 6.
    O. Klein: The Atomicity of Electricity as a Quantum Theory Law. Nature 118, 516 (1926b)CrossRefADSGoogle Scholar
  7. 7.
    G. Nordström: Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu vereinigen. Physikalische Zeitschrift 15, 504–506 (1914)Google Scholar
  8. 8.
    L. Randall: Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. (Ecco: New York 2005)Google Scholar
  9. 9.
    O. Veblen: Projektive Relativitätstheorie. (Springer: Berlin 1933)Google Scholar
  10. 10.
    H. Weyl: Gravitation und Elektrizitä t. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin 465–478 (1918)Google Scholar
  11. 11.
    E. Witten: Search for a Realistic Kaluza–Klein Theory. Nuclear Physics B 186, 412–428 (1981)ADSMathSciNetGoogle Scholar

Secondary Literature

  1. 12.
    D. Wuensch and H. Goenner: Kaluza's and Klein's Contributions to Kaluza-Klein theory. Proceedings of the Tenth Marcel Grossmann Meeting July 20 to 26, 2003, Rio de Janeiro, Brasil, 2041–2047 (World Scientific: Singapore, 2005)Google Scholar
  2. 13.
    D. Wuensch: Der Erfinder der fünften Dimension. Theodor Kaluza, Leben und Werk. (Termessos: Göttingen 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniela Wuensch

There are no affiliations available

Personalised recommendations