Maxwell's Theory

In the theory of electromagnetism, we consider electric and magnetic fields, denoted by and . An electric charge induces an electric field. One might think that a magnetic field is induced, similarly, by a magnetic charge , but we have never discovered such things in nature–particles, or magnetic monopoles, containing an isolated unit of magnetic charge, a north pole, for instance, without a south pole. Dirac showed, however, that if magnetic monopoles do exist, then electric charge is necessarily quantized. Based on arguments from quantum formulation of gravity we expect that there are magnetic monopoles. Moreover, they would arise naturally in the context of the unification of electromagnetic forces with the other forces we discussed before.

Maxwell’s equations enjoy an interesting symmetry between the electric field and magnetic field: Of course, if there are no ’s, or if their masses are different for electrically charged states, then this is not a symmetry. However, even if magnetic monopoles do not exist, it does make sense in empty space where there are no charged particles. In this setting of empty space or a vacuum, Maxwell’s theory has an amazing symmetry: If you take Maxwell’s equations and replace the electric field with the magnetic field, and replace the magnetic field with the negative of the electric field (which is what the above arrows signify), the equations are unchanged. But remember, this remarkable symmetry only applies to empty space.