# If gravity is a bend in Space-time then what is magnetism?

Einstein postulated that gravity bends the geometry of space-time then what does magnetism do in to the geometry of space-time, or is there even a correlation between space-time geometry and magnetism?

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I am not sure how exactly to interpret your question, the current two answers assume you ask whether the electromagnetic (EM) field curves space-time. But if your question is more "can the EM field be understood geometrically like gravity"?. Then yes. While gravity is curvature of space-time, electromagnetism turns out to be curvature of a so-called $U(1)$ principle bundle. This provides a analogy to gravity. See en.wikipedia.org/wiki/… –  Heidar Jun 21 '12 at 4:43
@Heidar - You should elaborate that as an answer, it'll be a really interesting one. –  Kitchi Mar 5 '13 at 16:22

That's a very complicated question. Electromagnetic energy does contribute to space-time curvature, just like any other form of energy (e.g. 'mass'), and the curvature of space-time also affects the geometry of fields and their propagation. An example is the trajectory of a photon (a particle of 'light')---which has been observed to be deflected by gravity exactly as general relativity predicts.

Note, however, there is no generally accepted theory which explains both gravity and electromagnetism (i.e. a 'unified theory'), so we don't entirely know how they interact / work-together. Our current framework ('quantum electrodynamics') describes electricity and magnetism as fields on top of a (possibly curved) space-time. I.e. the space-time is treated differently from the electromagnetism.

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there is no generally accepted theory which explains both gravity and electromagnetism Not true. GR explains both. We don't have a theory that explains both and includes quantum mechanics, but there was nothing quantum-mechanical about the question. –  Ben Crowell Oct 28 '14 at 20:02

Einstein postulated that gravity bends the geometry of space-time

In the context of GTR, gravity is the curvature of spacetime, not the cause of it. The curvature of spacetime is related to the density and flux of energy and momentum. So, it is said, "matter tells spacetime how to curve, spacetime tells matter how to move".

It's not quite clear what you mean by "magnetism" however it is the case that the classical electromagnetic field transports energy and momentum and thus contributes to the curvature of spacetime.

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I want to expand a bit on Heidar's comment as I suspect this may be what you're really asking. Have a look at ALL "forces" as manifestations of properties of space-time as my answer to this covers similar ground.

Einstein postulated that gravity bends the geometry of space-time

isn't true. Einstein's theory describes gravity as a curvature in spacetime. Gravity doesn't bend spacetime; we see the curvature as gravity. Describing gravity in this way makes it very different to the other forces, however you can also describe gravity not as curvature in spacetime, but as curvature in a mathematical object called the connection. See http://en.wikipedia.org/wiki/Curvature_form for details of this approach, though I'm afraid that article isn't intended for non-nerds.

The point of describing gravity using a curved connection is that the other forces, strong and weak as well as electromagnetism, can be described in the same way. If you use this approach then magnetism is due to curvature just like gravity is.

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There is a big difference though between the nature of the connections! A connection on real space should probably be pointed out to not be the same as one on a fibre bundle of space + "internal dimensions". Although what you're saying isn't wrong. –  tachyonicbrane Jun 21 '12 at 15:31

If you want to think about Electromagnetism geometrically then the curvature of the "U(1) bundle" would be the electromagnetic field F. In this way F (the Faraday tensor) plays the role that the Riemann Curvature tensor "R" plays in general relativity. The analog of the Christoffel symbol would be the photon field A. The big difference is the gauge group for EM is U(1) and the "gauge group" for Gravity is the group of diffeomorphisms (essentially coordinate changes) of space-time. But note that U(1) is related to not a real dimension of space but a phase in the wave function (symmetry under phase shifts), this is related to the fact that electric charge isn't literally momentum in a 5th circular dimension (as would be the case if Kaluza-Klein theory were true).

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## protected by Qmechanic♦Mar 5 '13 at 15:49

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