Editing Unified field theory (section)

=== Classic theory ===
The first successful [[Classical unified field theories|classical unified field theory]] was developed by [[James Clerk Maxwell]].  In 1820, [[Hans Christian Ørsted]] discovered that [[electric current]]s exerted forces on [[magnet]]s, while in 1831, [[Michael Faraday]] made the observation that time-varying [[magnetic field]]s could induce electric currents. Until then, electricity and magnetism had been thought of as unrelated phenomena. In 1864, Maxwell published his famous paper on [[A Dynamical Theory of the Electromagnetic Field|a dynamical theory of the electromagnetic field]]. This was the first example of a theory that was able to encompass previously separate field theories (namely electricity and magnetism) to provide a unifying theory of electromagnetism. By 1905, [[Albert Einstein]] had used the constancy of the [[speed-of-light]] in Maxwell's theory to unify our notions of space and time into an entity we now call [[spacetime]]. In 1915, he expanded this theory of [[special relativity]] to a description of gravity, [[general relativity]], using a field to describe the curving geometry of four-dimensional (4D) spacetime.

In the years following the creation of the general theory, a large number of physicists and mathematicians enthusiastically participated in the attempt to unify the then-known fundamental interactions.<ref>See [[Catherine Goldstein]] & Jim Ritter (2003) "The varieties of unity: sounding unified theories 1920-1930" in A. Ashtekar, et al. (eds.), ''Revisiting the Foundations of Relativistic Physics'', Dordrecht, Kluwer, p. 93-149; Vladimir Vizgin (1994), ''Unified Field Theories in the First Third of the 20th Century'', Basel, Birkhäuser; Hubert Goenner [http://relativity.livingreviews.org/Articles/lrr-2004-2/ On the History of Unified Field Theories] {{webarchive|url=https://web.archive.org/web/20110805194546/http://relativity.livingreviews.org/Articles/lrr-2004-2/ |date=2011-08-05 }}.</ref> Given later developments in this domain, of particular interest are the theories of [[Hermann Weyl]] of 1919, who introduced the concept of an (electromagnetic) [[gauge theory|gauge field]] in a classical field theory<ref>Erhard Scholtz (ed) (2001), ''Hermann Weyl's'' Raum - Zeit- Materie ''and a General Introduction to His Scientific Work'', Basel, Birkhäuser.</ref> and, two years later, that of [[Theodor Kaluza]], who extended General Relativity to [[Five-dimensional space|five dimensions]].<ref>Daniela Wuensch (2003), "The fifth dimension: Theodor Kaluza's ground-breaking idea", ''Annalen der Physik'', vol. 12, p. 519–542.</ref> Continuing in this latter direction, Oscar Klein proposed in 1926 that the fourth spatial dimension be [[compactification (physics)|curled up]] into a small, unobserved circle. In [[Kaluza–Klein theory]], the gravitational curvature of the extra spatial direction behaves as an additional force similar to electromagnetism. These and other models of electromagnetism and gravity were pursued by Albert Einstein in his attempts at a [[classical unified field theories|classical unified field theory]]. By 1930 Einstein had already considered the Einstein-Maxwell–Dirac System [Dongen]. This system is  (heuristically) the super-classical [Varadarajan] limit of (the not mathematically well-defined) [[quantum electrodynamics]]. One can extend this system to include the weak and strong nuclear forces to get the Einstein–Yang-Mills–Dirac System. The French physicist [[Marie-Antoinette Tonnelat]] published a paper in the early 1940s on the standard commutation relations for the quantized spin-2 field. She continued this work in collaboration with [[Erwin Schrödinger]] after [[World War II]]. In the 1960s [[Mendel Sachs]] proposed a generally covariant field theory that did not require recourse to renormalization or perturbation theory. In 1965, Tonnelat published a book on the state of research on unified field theories.