Kaluza-Klein theory

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The Kaluza-Klein theory was one of the first attempts to unify the fundamental interactions between gravitation and electromagnetism .

In 1921 Theodor Kaluza expanded the four-dimensional space - time of the general theory of relativity (one time dimension and three space-like dimensions) by adding a further, fourth space-like dimension to a total of five dimensions. Interestingly, the resulting equations can be separated into Einstein's field equations and Maxwell's equations . In this way, the Minkowski space and Maxwell's equations can be embedded in a 5-dimensional Riemann curvature tensor in a vacuum . Einstein's General Theory of Relativity, in which an energy-momentum tensor of the source representing itself Kaluza equations also differ in that they swell los are.

Oskar Klein later expanded Kaluza's theory and argued that the fourth dimension of space is rolled up and therefore not observed. Stephen Hawking illustrates it this way: “It's like a straw. Its surface is two-dimensional, but one dimension is curled up into a small circle so that from a distance the straw looks like a one-dimensional line. ”With this compactification, Klein was also able to explain a quantization of the charge .

In general, however, the Kaluza-Klein theory could not (so far) be quantized, which is why interest in the Kaluza-Klein theory waned with the increasing success of quantum mechanics . The idea of ​​using compacted additional dimensions to standardize the basic forces, however, was later further developed in string theory and is referred to there as Kaluza-Klein compactification .

See also

literature

  • Thomas Appelquist: Modern Kaluza-Klein theories. Addison-Wesley, Redwood City 1987, ISBN 0-201-09829-6
  • Robert Coquereaux, Arkadiusz Jadcyzk: Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that ... World Scientific, Singapore 1988, ISBN 9971-5-0426-X
  • Paul S. Wesson: Five-dimensional physics - classical and quantum consequences of Kaluza-Klein cosmology. World Scientific, Singapore 2006, ISBN 978-981-256-661-4
  • Walter Thirring: Introduction to Kaluza-Klein Theory. in Selected papers by Walter E. Thirring . American Mathematical Soc., Providence 1998, ISBN 0-8218-0812-5 , pp. 633-663

Individual proof

  1. ↑ Stephen W. Hawking, Brief Answers to Big Questions . 19th edition. Klett-Cotta, Stuttgart 2019, ISBN 978-3-608-96376-2 , pp. 83 (252 pp.).

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