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• Kaluza–Klein_theory abstract "In physics, Kaluza–Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time. It is considered to be an important precursor to string theory.The five-dimensional theory was developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The 5-dimensional metric has 15 components. Ten components are identified with the 4-dimensional spacetime metric, 4 components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the "radion" or the "dilaton". Correspondingly, the 5-dimensional Einstein equations yield the 4-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the hypothesis known as the "cylinder condition", that no component of the 5-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of 5-dimensional relativity are enormously more complex. Standard 4-dimensional physics seems to manifest the cylinder condition. Kaluza also set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.In 1926, Oskar Klein gave Kaluza's classical 5-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 also calculated a scale for the fifth dimension based on the quantum of charge.It wasn't until the 1940s that 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 recently evaluated using tensor algebra software.".
• Kaluza–Klein_theory wikiPageExternalLink sitzungsberichte1921preussi.
• Kaluza–Klein_theory wikiPageExternalLink 1401.8048.
• Kaluza–Klein_theory wikiPageExternalLink 1401.8048.pdf.
• Kaluza–Klein_theory wikiPageExternalLink ihplec.pdf.
• Kaluza–Klein_theory wikiPageExternalLink acta.
• Kaluza–Klein_theory wikiPageExternalLink 0002255.
• Kaluza–Klein_theory wikiPageExternalLink kkgrav.html.
• Kaluza–Klein_theory wikiPageExternalLink extradim.htm.
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• Kaluza–Klein_theory wikiPageWikiLink 2-form.
• Kaluza–Klein_theory wikiPageWikiLink Action_(physics).
• Kaluza–Klein_theory wikiPageWikiLink Alternatives_to_general_relativity.
• Kaluza–Klein_theory wikiPageWikiLink Astrophysics.
• Kaluza–Klein_theory wikiPageWikiLink Brans-Dicke_theory.
• Kaluza–Klein_theory wikiPageWikiLink Brans–Dicke_theory.
• Kaluza–Klein_theory wikiPageWikiLink Category:Particle_physics.
• Kaluza–Klein_theory wikiPageWikiLink Category:Physical_cosmology.
• Kaluza–Klein_theory wikiPageWikiLink Category:Physics_beyond_the_Standard_Model.
• Kaluza–Klein_theory wikiPageWikiLink Category:String_theory.
• Kaluza–Klein_theory wikiPageWikiLink Category:Theories_of_gravitation.
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• Kaluza–Klein_theory wikiPageWikiLink Compactification_(physics).
• Kaluza–Klein_theory wikiPageWikiLink Cosmic_inflation.
• Kaluza–Klein_theory wikiPageWikiLink Cosmological_model.
• Kaluza–Klein_theory wikiPageWikiLink DGP_model.
• Kaluza–Klein_theory wikiPageWikiLink De_Rham_cohomology.
• Kaluza–Klein_theory wikiPageWikiLink Einstein_equation.
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• Kaluza–Klein_theory wikiPageWikiLink Einsteins_equation.
• Kaluza–Klein_theory wikiPageWikiLink Electromagnetic_field.
• Kaluza–Klein_theory wikiPageWikiLink Electromagnetic_stress-energy_tensor.
• Kaluza–Klein_theory wikiPageWikiLink Electromagnetic_stress–energy_tensor.
• Kaluza–Klein_theory wikiPageWikiLink Electromagnetism.
• Kaluza–Klein_theory wikiPageWikiLink Electroweak.
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• Kaluza–Klein_theory wikiPageWikiLink Feynman_diagram.
• Kaluza–Klein_theory wikiPageWikiLink Fiber_bundle.
• Kaluza–Klein_theory wikiPageWikiLink Fifth_dimension_(geometry).
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• Kaluza–Klein_theory wikiPageWikiLink Free_space.
• Kaluza–Klein_theory wikiPageWikiLink Friedmann–Lemaître–Robertson–Walker_metric.
• Kaluza–Klein_theory wikiPageWikiLink Fubinis_theorem.
• Kaluza–Klein_theory wikiPageWikiLink Gauge_group.
• Kaluza–Klein_theory wikiPageWikiLink Gauge_theory.
• Kaluza–Klein_theory wikiPageWikiLink General_relativity.
• Kaluza–Klein_theory wikiPageWikiLink Geodesic.
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• Kaluza–Klein_theory wikiPageWikiLink Geodesics_in_general_relativity.
• Kaluza–Klein_theory wikiPageWikiLink Graviscalar.
• Kaluza–Klein_theory wikiPageWikiLink Gravitation.
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• Kaluza–Klein_theory wikiPageWikiLink Gunnar_Nordström.
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• Kaluza–Klein_theory wikiPageWikiLink Hodge_dual.
• Kaluza–Klein_theory wikiPageWikiLink Hodge_star.
• Kaluza–Klein_theory wikiPageWikiLink Hodge_theory.
• Kaluza–Klein_theory wikiPageWikiLink Homology_(mathematics).
• Kaluza–Klein_theory wikiPageWikiLink Horizontal_bundle.
• Kaluza–Klein_theory wikiPageWikiLink Hyperspace_(book).
• Kaluza–Klein_theory wikiPageWikiLink Inflation_(cosmology).
• Kaluza–Klein_theory wikiPageWikiLink Integer.
• Kaluza–Klein_theory wikiPageWikiLink K-theory.
• Kaluza–Klein_theory wikiPageWikiLink K_theory.
• Kaluza–Klein_theory wikiPageWikiLink Large_Hadron_Collider.
• Kaluza–Klein_theory wikiPageWikiLink Large_extra_dimension.
• Kaluza–Klein_theory wikiPageWikiLink Large_extra_dimensions.
• Kaluza–Klein_theory wikiPageWikiLink Lie_group.
• Kaluza–Klein_theory wikiPageWikiLink Lorentz_force.
• Kaluza–Klein_theory wikiPageWikiLink Lorentz_force_law.
• Kaluza–Klein_theory wikiPageWikiLink Mass.
• Kaluza–Klein_theory wikiPageWikiLink Matsubara_frequency.
• Kaluza–Klein_theory wikiPageWikiLink Maxwell_equation.
• Kaluza–Klein_theory wikiPageWikiLink Maxwell_equations.
• Kaluza–Klein_theory wikiPageWikiLink Maxwell_stress_tensor.
• Kaluza–Klein_theory wikiPageWikiLink Maxwells_equations.
• Kaluza–Klein_theory wikiPageWikiLink Metric_(mathematics).
• Kaluza–Klein_theory wikiPageWikiLink Noncommutative_geometry.
• Kaluza–Klein_theory wikiPageWikiLink Noncommutative_space.
• Kaluza–Klein_theory wikiPageWikiLink Nordstrxc3xb6ms_theory_of_gravitation.
• Kaluza–Klein_theory wikiPageWikiLink Nuclear_Physics_(journal).
• Kaluza–Klein_theory wikiPageWikiLink Nuclear_Physics_B.
• Kaluza–Klein_theory wikiPageWikiLink Orbifold.
• Kaluza–Klein_theory wikiPageWikiLink Oskar_Klein.

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