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So in analogy to Einstein's general relativity which states that the curvature of space-time causes different bodies to act on each other through distance, how does electromagnetic force act through space? I don't think this can be explained in any way by the curvature of space-time, so what is it? I tried to search for an answer for this, and came across Theodor Kaluza's hypothetical fifth dimension applied to general relativity which can explain Maxwell's equations. I'm actually surprised by how little information I could obtain on the subject, since nobody seems to ask the question how does the electromagnetic force work, the same way people used to believe Newton's gravity is all there is. Or am I missing something that's out there, or is the subject too deep to be solved right now and need another 100 year until a great mind very much like Einstein's could come up with a revolutionary idea that will reshape our thinking about just everything?

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  • $\begingroup$ By creating a field, which is just intuitively a means of propagating information from the source to all space,where the field exists. $\endgroup$ – Lelouch Nov 20 '16 at 5:54
  • $\begingroup$ Take a look at this answer (possible duplicate) physics.stackexchange.com/questions/192360/… $\endgroup$ – Prof. Legolasov Nov 20 '16 at 9:07
  • $\begingroup$ Hi. Quoting from arxiv.org/abs/gr-qc/9805018v1 . "In Minkowski’s time, there had already been experimental phenomena (namely, electromagnetic ones) whose invariance with respect to Lorentz trans formations could be interpreted as four-dimensional coordinate invariance. No such observations pointed to a fifth dimension. Nordstr ̈m and Kaluza thereofore avoided the question and simply demanded that all derivatives with re spect to x4 vanish. Continue... $\endgroup$ – Constantine Black Nov 20 '16 at 9:45
  • $\begingroup$ cont : In other words, physics was to take place — for as-yet unknown reasons — on a four-dimensional hypersurface in a five-dimensional universe (Kaluza’s “cylinder condition”) ... Electrodynamics, for example, could be “derived” by imposing local U(1) gauge-invariance on a free-particle Lagrangian. From the gauge-invariant point of view, Kaluza’s feat in extracting electromagnetism from five-dimensional gravity was no longer so surprising: continue $\endgroup$ – Constantine Black Nov 20 '16 at 9:46
  • $\begingroup$ cont : it worked, in effect, because U(1) gauge-invariance had been “added onto” Einstein’s equations in the guise of invariance with respect to coordinate transformations along the fifth dimension. In other words, gauge symmetry had been “explained” as a geometric symmetry of spacetime. The electromagnetic field then appeared as a vector “gauge field” in four dimensions." See also en.wikipedia.org/wiki/… $\endgroup$ – Constantine Black Nov 20 '16 at 9:47

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