International Journal of Theoretical Physics

, Volume 45, Issue 3, pp 576–588 | Cite as

Kaluza–Klein 5D Ideas Made Fully Geometric

  • Scott A. Starks
  • Olga Kosheleva
  • Vladik Kreinovich


After the 1916 success of general relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂ g ij /∂ x 5 = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approach is that while the model itself is geometric, conditions like cylindricity are not geometric. This problem was partly solved by Einstein and Bergman who proposed, in their 1938 paper, that the 5th dimension is compactified into a small circle S 1 so that in the resulting cylindric 5D space-time R 4× S 1 the dependence on x 5 is not macroscopically noticeable. We show that if, in all definitions of vectors, tensors, etc., we replace R 4 with R 4× S 1, then conditions like cylindricity automatically follow – i.e., these conditions become fully geometric.

Key Words

5D geometry Kaluza–Klein theory compactification of extra dimensions Einstein-Bergman approach to 5D models 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Scott A. Starks
    • 1
  • Olga Kosheleva
    • 1
  • Vladik Kreinovich
    • 1
  1. 1.NASA Pan-American Center for Earth and Environmental Studies (PACES)University of Texas at El PasoEl PasoUSA

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