TITLE: If gravity is a bend in Space-time then what is magnetism?
QUESTION [16 upvotes]: 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?

REPLY [6 votes]: 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).
{"set_name": "stack_exchange", "score": 16, "question_id": 30477}