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==ფარდობითობის სპეციალური თეორია==
მაქსველის განტოლებებს ახლო კავშირი აქვთ [[ფარდობითობის სპეციალური თეორია|ფარდობითობის სპეციალურ თეორიასთან]]: ერთის მხრივ ისტორიულად მაქსველის განტოლებებმა უმნიშვნელოვანესი როლი შეასრულეს ამ თეორიის განვითარებაში, ხოლო მერეს მხრივ ფარდობითობის თეორია მაქსველის განტოლებების მათემატიკურად კომპაქტურად ჩაწერის საშუალებას იძლევა (კოვარიანტული [[ტენზორი|ტენზორების]] მეშვეობით).
===Historical developments===
Maxwell's electromagnetic wave equation only applied in what he believed to be the rest frame of the luminiferous medium because he didn't use the '''v'''×'''B''' term of his equation (D) when he derived it. Maxwell's idea of the luminiferous medium was that it consisted of aethereal vortices aligned solenoidally along their rotation axes.
The American scientist [[Albert Abraham Michelson|A.A. Michelson]] set out to determine the velocity of the earth through the luminiferous medium aether using a light wave interferometer that he had invented. When the [[Michelson-Morley experiment]] was conducted by [[Edward Morley]] and [[Albert Abraham Michelson]] in 1887, it produced a [[null result]] for the change of the velocity of light due to the Earth's motion through the hypothesized aether. This null result was in line with the theory that was proposed in 1845 by [[Sir George Stokes, 1st Baronet|George Stokes]] which suggested that the aether was entrained with the Earth's orbital motion.
[[Hendrik Lorentz]] objected to Stokes' aether drag model and along with [[George FitzGerald]] and [[Joseph Larmor]], he suggested another approach. Both Larmor (1897) and Lorentz (1899, 1904) derived the [[Lorentz transformation]] (so named by [[Henri Poincaré]]) as one under which Maxwell's equations were invariant. Poincaré (1900) analyzed the coordination of moving clocks by exchanging light signals. He also established mathematically the group property of the Lorentz transformation (Poincaré 1905).
This culminated in [[Albert Einstein|Albert Einstein's]] theory of [[special relativity]], which postulated the absence of any absolute rest frame, dismissed the aether as unnecessary (a bold idea, which did not come to Lorentz nor to Poincaré), and established the invariance of Maxwell's equations in all inertial frames of reference, in contrast to the famous Newtonian equations for [[classical mechanics]]. But the transformations between two different inertial frames had to correspond to Lorentz' equations and not - as formerly believed - to those of [[Galileo]] (called [[Galilean transformation]]s).<ref>U. Krey, A. Owen, ''Basic Theoretical Physics - A Concise Overview'', Springer, Berlin and elsewhere, 2007, ISBN 978-3-540-36804-5</ref> Indeed, Maxwell's equations played a key role in Einstein's famous paper on special relativity; for example, in the opening paragraph of the paper, he motivated his theory by noting that a description of a [[Moving magnet and conductor problem|conductor moving with respect to a magnet]] must generate a consistent set of fields irrespective of whether the force is calculated in the rest frame of the magnet or that of the conductor.<ref>
{{cite web
|url=http://www.fourmilab.ch/etexts/einstein/specrel/www/
|title=On the Electrodynamics of Moving Bodies
|publisher=Fourmilab.ch
|date=
|accessdate=2008-10-19
}}</ref>
''General'' relativity has also had a close relationship with Maxwell's equations. For example, [[Kaluza-Klein theory|Kaluza and Klein]] showed in the 1920s that Maxwell's equations can be derived by extending [[general relativity]] into five dimensions. This strategy of using higher dimensions to unify different forces continues to be an active area of research in [[particle physics]].
===მაქსველის განტოლებების კოვარიანტული ფორმა===
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