electromagnetism - Does special relativity make magnetic fields irrelevant?

I've heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, how does this work?

Answer

Special relativity makes the existence of magnetic fields an inevitable consequence of the existence of electric fields. In the inertial system B moving relatively to the inertial system A, purely electric fields from A will look like a combination of electric and magnetic fields in B. According to relativity, both frames are equally fit to describe the phenomena and obey the same laws.

So special relativity removes the independence of the concepts (independence of assumptions about the existence) of electricity and magnetism. If one of the two fields exists, the other field exists, too. They may be unified into an antisymmetric tensor, $F_{\mu\nu}$.

However, what special relativity doesn't do is question the independence of values of the electric fields and magnetic fields. At each point of spacetime, there are 3 independent components of the electric field $\vec E$ and three independent components of the magnetic field $\vec B$: six independent components in total. That's true for relativistic electrodynamics much like the "pre-relativistic electrodynamics" because it is really the same theory!

Magnets are different objects than electrically charged objects. It was true before relativity and it's true with relativity, too.

It may be useful to notice that the situation of the electric and magnetic fields (and phenomena) is pretty much symmetrical. Special relativity doesn't really urge us to consider magnetic fields to be "less fundamental". Quite on the contrary, its Lorentz symmetry means that the electric and magnetic fields (and phenomena) are equally fundamental. That doesn't mean that we can't consider various formalisms and approximations that view magnetic fields – or all electromagnetic fields – as derived concepts, e.g. mere consequences of the motion of charged objects in spacetime. But such formalisms are not forced upon us by relativity.