How would you go about (dis)proving the existence of magnetic monopoles?

Question

I mean either experimentally, by looking for one, or theoretically, or both.

Answer 1

You'd never be able to disprove its existence--you'd only be able to put lower limits on its mass (presumably we know the charge if you believe Dirac).  And I suspect that the limits you get from these soft approach are going to be much weaker than the hammer--just looking for their creation in accelerator experiments.

I mean look how subtle the Casimir effect is.  And that's a fluctuation of a massless field.  Nobody even talks about a similar effect with the electron field (although it theoretically exists).  Actually, I take that back.  The photon propagator does get touched up, and the EM coupling runs down from its "true" value, because of electron loops (Lamb shift).  But I don't think that anyone has detected a correction due to quark or mu loops.  And certainly not something big like a W.  And monopoles are apparently even heavier still if they exist at all.

Cosmologically, the absence of observed monopoles and other exotics is considered to be evidence (allbeit not the strongesst evidence) of inflation.  The temperatures may have been high enough to produce the exotics before inflation, but then the universe popped and spread them out so much that finding them would be like looking for needles in a very big haystack.

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Actually, I take that back about heavy particle loops.  I forgot about the crazy precision electroweak tests--the experimental value of the muon's g-2 is currently "suggesting" (a few sigma deviation from SM prediction) that there may be some heavy particle running in a triangle loop (along with a neutrino) in the muon's coupling to the photon.

This paper has apparently run all the known particles (even the heaviest) through the loops in the muon's coupling to the photon and accounted for them.

http://arxiv.org/abs/hep-ph/0611102

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I just bring the paper up because the precision electroweak measurements are probably the best way to detect the impact of particles we haven't seen yet.  They're so accurate that they can detect the contribution of even very massive particles running in a triangle loop around the muon/photon vertex.  If the theoretical results don't match the experimental results (and they're a few sigma off now), that suggests heavier particles out there we haven't found yet.  Magnetic monopoles aren't first on the list of candidates (superpartners are everyone's first guess), but they're a possibility since they couple to the photon like any charged particle (and would probably have their own version of the neutrino) so they could run in the triangle loop.

Answer 2

Put the presumed monopole inside a spherical mu-metal shield, and measure the magnetic field at points just outside the shield.  There should be a uniform outward field at all points on the surface of the shield.  You won't get this with any sort of a magnetic dipole.