Physical · the question, drilled to the bottom

What Holds a Magnet Together

Ask how a magnet works and you'll be told opposite poles attract. That's true — and it explains nothing, the way "it falls because of gravity" explains nothing. So drill. Three times the floor gives way, and the third time the thing holding your fridge magnet up turns out not to be magnetism at all.

Drill 1 / 3A magnet is a crowd that agreed

Every iron atom is already a tiny magnet — its electrons carry spin, and spin is magnetic. A bar of iron contains some 10²³ of them. Whether the bar as a whole is a magnet comes down to one question: do the little magnets point the same way?

Heat fights order; the neighbours' pull for alignment fights heat. Below a sharp temperature the pull wins and patches of atoms lock into step — domains. Above it, heat wins and the directions scramble. Drag the temperature and watch a magnet switch on and off:

This is a real Ising model — the simplest honest cartoon of a ferromagnet. Its switch-over isn't a fudge: in two dimensions Lars Onsager solved it exactly in 1944, and the tipping point sits at T_c = 2/ln(1+√2) = 2.2692…, the marked line above. Heat past it and the alignment collapses to zero. This happens to real magnets: every ferromagnet has a Curie temperature where it simply stops being a magnet.

Representative values, Kittel, Introduction to Solid State Physics. Gadolinium's is near room temperature — it stops being a fridge magnet in your warm hand.

Drill 2 / 3The force that lines them up isn't magnetic

So neighbouring atomic magnets pull each other into alignment. The natural guess is that they pull magnetically — north-seeking each other, the way two compass needles do. Let's check that guess with a number, because it fails badly.

Two atomic dipoles a lattice-spacing apart in iron interact with an energy of about μ₀/4π · m²/r³. Put in iron's real numbers (r = 0.248 nm, moment 2.22 Bohr magnetons) and that energy is 2.8×10⁻²⁴ J — which, as a temperature, is 0.20 K. If magnetism were the glue, iron would scramble above a fifth of a degree above absolute zero. Instead it holds its alignment all the way to 1043 K — about 5,200× stronger than magnetism can account for.

The real glue is the exchange interaction, and it is a piece of sleight-of-hand by quantum mechanics. Electrons are identical fermions: the Pauli exclusion principle forbids two with the same spin from being in the same place. Same-spin electrons therefore stay further apart — which lowers their electrostatic (Coulomb) repulsion energy. In iron, aligning the spins is the cheaper arrangement, so the spins align.

Read that again, because it's the punchline of the second drill: the force that makes iron magnetic is the electric repulsion between electrons, refereed by a quantum rule about identity. No magnetic force enters anywhere. Magnetism, at the bottom, is held up by electricity.

Drill 3 / 3And the magnetic force itself is electricity

Fine — but a magnet still pushes a compass, still drags a paperclip. That force is magnetic, surely? Here is the strangest true thing on this page. The magnetic force is what the electric force looks like when you're moving. Einstein's 1905 relativity paper was titled On the Electrodynamics of Moving Bodies for exactly this reason.

Take a wire carrying a current: a fixed lattice of positive ions, and electrons drifting through it. The wire is electrically neutral — equal + and −, no net charge, no electric field. Now send a test charge gliding alongside it. In the lab it feels a sideways magnetic force. But ride along with the charge and switch frames:

In the charge's own frame the two rows move at different speeds, so relativistic length contraction packs them by different amounts. The − charges bunch up relative to the + charges (or the reverse) and the once-neutral wire now carries a net charge. A net charge makes an electric field, which pushes the (now stationary) test charge. Same push, different name. Work both stories out with real numbers and they agree to the last decimal place:

The bottomWhere the honest answer stops

So: a magnet is a crowd of spins that agreed; they agreed because of electric repulsion and a quantum rule, not magnetism; and the magnetic force you feel is electricity seen sideways. Keep drilling and you reach questions no analogy reduces — why does an electron have spin and a magnetic moment at all? Why does nature enforce Pauli exclusion? These bottom out in quantum field theory, in mathematics that doesn't translate into anything you've ever held. Richard Feynman, asked the plain question "why do magnets repel," refused to fake the floor:

That isn't a failure. It's the most truthful thing in the whole chain: an explanation that keeps going until it honestly runs out, and says so, instead of dressing the last gap in a word like "poles" and calling it understood. You now know more about a fridge magnet than almost any account online will tell you — and exactly where the knowing ends.