The jury is still out on whether this is the case or not. Regardless, we can try to build a quantum field theory that is close enough to nature and exhibits the electromagnetic duality. Going back to our kitchen analogy, we can try to “cook up” new theories that possess dualities. We can change the ingredients and their quantities in recipes we know, get rid of some of them, throw in something extra, and so on. This kind of “experimental cuisine” may lead to variable results. We may not necessarily want to “eat” these imagined dishes. But edible or not, it may be worthwhile to study their properties in our dreamed-up kitchen – they may give us some clues about the dishes that are edible (that is to say, the models that could describe our universe).
This trial-and-error “model building” is a path along which progress has been made in quantum physics for decades (just as it was in the culinary art). And symmetry is a powerful guiding principle that has been used in creating these models. The more symmetrical a model is, the easier it is to analyze.
At this point, it is important to note that there are two kinds of elementary particles: fermions and bosons. The former are the building blocks of matter (electrons, quarks, etc.), and the latter are the particles that carry forces (such as photons). The elusive Higgs particle, discovered recently at the Large Hadron Collider under Geneva, is also a boson.
There is a fundamental difference between the two types of particles: two fermions cannot be in the same “state” simultaneously, whereas any number of bosons can. Because their behavior is so radically different, for a long time physicists assumed that any symmetry of a quantum field theory had to preserve a distinction between the fermionic and bosonic sectors – that nature forbids them to be mixed together. But in the mid-1970s several physicists suggested what looked like a crazy idea: that a new type of symmetry was possible that would exchange bosons with fermions. It was christened supersymmetry.
As Niels Bohr, one of the creators of quantum mechanics, famously said to Wolfgang Pauli, “We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.”
In the case of supersymmetry, we still don’t know whether it is realized in nature, but the idea has become popular. The reason is that many of the issues that plague conventional quantum field theories are eliminated when supersymmetry is introduced. Supersymmetric theories are generally more elegant and easier to analyze.
Quantum electromagnetism is not supersymmetric, but it has supersymmetric extensions. We throw in more particles, both bosons and fermions, so that the resulting theory exhibits supersymmetry.
In particular, physicists have studied the extension of the electromagnetism with the maximal possible amount of supersymmetry. And they showed that in this extended theory the electromagnetic duality is indeed realized.
To summarize, we don’t know whether a form of quantum electromagnetic duality exists in the real world. But we do know that in an idealized, supersymmetric, extension of the theory, the electromagnetic duality is manifest.
There is one important aspect of this duality that we haven’t yet discussed. The quantum field theory of electromagnetism has a parameter: the electric charge of the electron. It is negative, so we write it as -e, where e = 1.602 · 10-19 Coulombs. It is very small. The maximal supersymmetric extension of electromagnetism has a similar parameter, which we will also denote by e. If we perform the electromagnetic duality and exchange all things electric by all things magnetic, we will get a theory in which the charge of the electron will be not e, but its inverse, 1/e.