### Magnetic Monopoles

OK, perhaps the title is a bit misleading. However, a Science paper published today (DOI: 10.1126/science.1167747) describes a method by which images of magnetic monopoles can be induced and measured, in full compliance with E&M. The trick? By taking advantage of the quantum Hall Effect, you can construct a system such that the boundary conditions can be constructed to break temporal (T) symmetry, allowing quantum mechanical topological effects.

By doing this around an insulating surface, and bringing a charged particle near it, a magnetic monopole image is induced as a mirror to the electric charge. Whew. The idea of this is a nice mathematical trick that can make solutions far simpler than they would normally be, if you reduce a system to a set of "image charges" that represent a more complex field.

Perhaps someone has noted that this appears to break Maxwell's equations. Namely , the divergence of **B** = 0 (∂_{μ}F_{νλ}=0) according to Maxwell's Equations is maintained by the following:

As we started with the Maxwell's equation, which includes [del] · B = 0, the magnetic flux integrated over a closed surface must vanish. We can check that this is the case by considering a closed surface—for example, a sphere with radius a—that encloses a topological insulator. The detailed calculation is presented in the supporting online material (17). Inside the closed surface, there is not only a image magnetic monopole charge, but also a line of magnetic charge density whose integral exactly cancels the point image magnetic monopole.

And thus everything ends up working out. Trippy. Even more to the point, this could be measured by a magnetic force microscope, with mathematical proof to show its contribution could be distinguished from other, more trivial considerations. Perhaps not the most pertinent discovery every, but still quite interesting to move the idea of a magnetic monopole out of pure speculation into something detectable.

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