electromagnetism - How Special Relativity causes magnetism

So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the basis of the article was that magnetism is just relativistic electricity, so I was wondering how a permanent magnet worked? It makes sense to me that a moving charged particle attracts unmoving particles of the opposite charge, but how do the orbits of electrons in a magnet cause it to have a magnetic field?

Answer

There are two phenomena in your question.

(1) Let us first understand how magnetic field can be considered to "arise" because of relativity. Imagine a frame of reference in which a charge $Q$ is at rest. If another charge $q$ is brought in its vicinity, it will experience only an electrostatic force. Now get on to another inertial frame of reference moving at a velocity $\vec{v}$ with respect to the first one. In this frame of reference, you will observe both the charges moving. The static charges of the old reference frame now appear as charges and currents. The electrostatic field of the previous frame now appears as an electrostatic field of different magnitude and a magnetic field. Since physics is the same in all inertial frames of reference, we are inclined to believe that $\vec{E}$ and $\vec{B}$ are manifestations of a single electromagnetic field.

This is a very "hand-waving" kind of an explanation. You may want to refer to Rober Resnick's "Special Theory of Relativity" or Melvin Schwartz's "Principles of Electrodynamics" for greater mathematical details.

(2) The first point tries to explain how magnetism due to a current can be considered to be a relativistic effect. Now let us consider magnetism due to electrons. Apart from charge and mass, electrons also have an intrinsic magnetic moment that can be explained only through relativistic quantum mechanics. Thus, magnetism of a bar magnet is also a relativistic effect. Please note that magnetism in a bar magnet is because of the electron's spin and not orbital motion.