We now know one electron's magnetism is relativistic. But why do billions of them in an iron bar line up — when the force aligning them is not magnetic at all? The finale: exchange interaction, the Ising model, and the symmetry breaking that links a fridge magnet to the origin of mass.
Part 2 conjured spin by switching on a field. But spin is intrinsic — it should be written into how the electron transforms when we rotate space itself. Part 3: the group theory of SU(2), SO(3), and the Lorentz group, and why the electron has no choice but to be a spinor.
Demand a wave equation that is first order in time and respects relativity, and the electron is forced to grow four components, an internal axis, and a magnetic moment out of thin air. Part 2: how spin — and magnetism — fall out of Dirac's equation.
A magnet pulls a nail across the table — surely the simplest demonstration in physics. Yet the magnetic force does no work, and classical physics turns out to forbid magnetism outright. Part 1 of a series: setting up the paradox.