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There are four known forces in the universe. Two of these forces are the force of gravity and the force of electromagnetism. The first is the result of the mass of the object that has the gravity. The second is the result of charge in both the affected particle as well as the particles that generated the electrical and magnetic fields. Since both forces operate over spacetime why isn't there a model that common to both?

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marked as duplicate by John Rennie, Kyle Kanos, ACuriousMind, Qmechanic Apr 3 '15 at 19:28

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This question is based on the wrong assumption that there isn't a geometric formulation of EM.

There is - gauge theory, and just as the Riemann tensor is the curvature of the Levi-Civita connection on the tangent bundle of spacetime, the electromagnetic field strength is the curvature of the gauge principal connection on a $\mathrm{U}(1)$-principal bundle over spacetime.

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  • $\begingroup$ Are you saying EM warps spacetime like gravity? If so, how can it selectively warp for opposing charged particles and not for uncharged ones (for example)? $\endgroup$ – Jiminion Apr 3 '15 at 15:23
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    $\begingroup$ @Jiminion: No, I am not saying that electromagnetism warps spacetime. I'm just presenting the "common model" the question asks about, in which all forces arise from bundles with connections. Gravity is connected to what is commonly called the warping of spacetime (which is a "distortion" of the metric) because the Levi-Civita connection is determined by the metric, while the principal connections don't care for the metric at all. $\endgroup$ – ACuriousMind Apr 3 '15 at 15:30
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    $\begingroup$ There is also the Kaluza-Klein model which treats EM as actual spacetime curvature in a higher spatial dimension (assumed to be 'compact')--apparently it's a precursor to elements of string theory but I don't know the details. $\endgroup$ – Hypnosifl Apr 3 '15 at 15:32
  • $\begingroup$ @Hypnosifl: Correct, but Kaluza-Klein is more than a reformulation of EM and GR, because it predicts massive excitations in the compactified dimension, the so-called Kaluza-Klein tower, which are absent in usual EM and GR. $\endgroup$ – ACuriousMind Apr 3 '15 at 15:35
  • $\begingroup$ See Baez: "in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial". Then see Einstein talking about inhomogeneous space, google on electromagnetic geometry, and see this. I think of electromagnetism as curved space, and gravity as inhomogeneous space. $\endgroup$ – John Duffield Apr 3 '15 at 15:37

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