Kaluza–Klein theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-08

This is an audio version of the Wikipedia Article:
Kaluza–Klein theory


00:02:34 1 Kaluza hypothesis
00:08:06 2 Field equations from the Kaluza hypothesis
00:15:20 3 Equations of motion from the Kaluza hypothesis
00:21:56 4 Kaluza's hypothesis for the matter stress-energy tensor
00:34:20 5 Quantum interpretation of Klein
00:37:21 6 Quantum field theory interpretation
00:40:16 7 Group theory interpretation
00:40:26 8 Space–time–matter theory
00:45:54 9 Geometric interpretation
00:48:06 9.1 Einstein equations
00:48:30 9.2 Maxwell equations
00:50:15 9.3 Kaluza–Klein geometry
00:50:50 9.4 Generalizations
00:51:04 10 Empirical tests
00:56:43 11 See also
00:57:54 12 Notes
00:59:43 13 References



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SUMMARY
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In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory.
The five-dimensional theory developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921, which detailed a purely classical extension of general relativity to five dimensions and includes 15 components. Ten components are identified with the four-dimensional spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the "radion" or the "dilaton". Correspondingly, the five-dimensional Einstein equations yield the four-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the "cylinder condition" hypothesis, that no component of the five-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of five-dimensional relativity grow enormous in complexity. Standard four-dimensional physics seems to manifest the cylinder condition.
In 1926, Oskar Klein gave Kaluza's classical five-dimensional theory a quantum interpretation, to accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein suggested that the geometry of the extra fifth dimension could take the form of a circle, with the radius of 10−30 cm. Klein also calculated a scale for the fifth dimension based on the quantum of charge.In the 1940s the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups:
Thiry, 
working in France on his dissertation under Lichnerowicz;  Jordan, Ludwig, and Müller in Germany, with critical input from Pauli and Fierz; and Scherrer  working alone in Switzerland. Jordan's work led to the scalar-tensor theory of Brans–Dicke; Brans and Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews as well as the English translations of Thiry contain some errors. The complete Kaluza equations were evaluated using tensor algebra software in 2015.