One thing I've heard stated many times is that "most" or "many" physicists believe that, despite the fact that they have not been observed, there are such things as magnetic monopoles.
However, I've never really heard a good argument for why this should be the case. The explanations I've heard tend to limit themselves to saying that "it would create a beautiful symmetry within Maxwell's equations" or similar. But I don't see how the fact that "it would be beautiful" is any kind of reason for why they should exist! That doesn't sound like good science to me.
So obviously there must be at least another reason apart from this to believe in the existence of natural magnetic monopoles. (I'm aware that recent research has shown that metamaterials (or something similar) can emulate magnetic monopole behaviour, but that's surely not the same thing.) Can anyone provide me with some insight?
Answer
Aqwis, it would help in the future if you mentioned something about your background because it helps to know what level to aim at in the answer. I'll assume you know E&M at an undergraduate level. If you don't then some of this explanation probably won't make much sense.
Part one goes back to Dirac. In E&M we need to specify a vector potential $A_\mu$. Classically the electric and magnetic fields suffice, but when quantum mechanics is included you need $A_\mu$. The vector potential is only defined up to gauge transformations $A_\mu \rightarrow g(x)(A_\mu + \frac{i}{e} \partial_\mu ) g^{-1}(x)$ where $g(x)=\exp(i \alpha(x))$. The group involved in these gauge transformations is the real line (that is the space of possible values of $\alpha$) if electric charge is not quantized, but if charge is quantized, as all evidence points to experimentally, then the group is compact, that is it is topologically a circle, $S^1$. So to specify a gauge field we specify an element of $S^1$ at every point in spacetime. Now suppose we don't know for sure what goes on inside some region (because we don't know physics at short distances). Surround this region with a sphere. We can define our gauge transformation at every point outside this region, but now we have to specify it on two-spheres which cannot be contracted to a point. At a fixed radial distance the total space of angles plus the gauge transformation can be a simple product, $S^2 \times S^1$ but it turns out there are other possibilities. In particular you can make what is called a principal fibre bundle where the $S^1$ twists in a certain way as you move around the $S^2$. These are characterized by an integer $n$, and a short calculation which you can find various places in the literature shows that the integer $n$ is nothing but the magnetic monopole charge of the configuration you have defined. So charge quantization leads to the ability to define configurations which are magnetic monopoles. So far there is no guarantee that there are finite energy objects which correspond to these fields. To figure out if they are finite energy we need to know what goes on all the way down to the origin inside our region.
Part two is that in essentially all models that try to unify the Standard Model you find that there are in fact magnetic monopoles of finite energy. In grand unified theories this goes back to work of 't Hooft and Polyakov. It also turns out to be true in Kaluza-Klein theory and in string theory.
So there are three compelling reasons to expect that magnetic monopoles exist. The first is the beauty of a deep symmetry of Maxwell's equations called electric-magnetic duality, the second is that electric charge appears to be quantized experimentally and this allows you to define configurations with quantized magnetic monopole charge, and the third is that when you look into the interior of these objects in essentially all unified theories you find that the monopoles have finite energy.
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