My dear friend Jacob has a YouTube Channel, where he’s decided to start answering people’s questions. This week, he addressed that age-old memetic question: How do magnets work? Not bad, Jacob. But, as a physics major, I can’t really let it stand without comment.
There are a few points that ought to be clarified, but let’s take a step back for a moment. The question at hand here is, basically, the structure of matter. Jacob speaks about negatively charged electrons repelling each other, and correctly notes that this is what makes an object “solid” despite being mostly empty space. His mistake comes when he asserts that magnetism essentially works on the same principle. To which I can only say, “Eh…not really…” Those are electrostatic properties, produced by
charges at rest. Magnetism is…weirder.
Again, the problem is the structure of matter. Jacob claims the electrons orb it the nucleus like a planet orbits a star, which is a very classical viewpoint. By “classical” I mean “wrong.” You see, we’ve known for some time that this doesn’t make any sense. If electrons are being pulled towards the nucleus then they would fall in unless they were moving. So they must be moving, and if they’re at a stable point then they must be moving in an orbit. Fine. But because they’re in an orbit, they are constantly changing their direction of motion—that is, constantly accelerating (experiencing a change in velocity). And that is extremely bad news.
See, we know that moving electrical charges or changing electric fields produce magnetic fields. We also know that changing magnetic fields produce electric fields. (We would like to find magnetic “charges” to make that a more symmetrical statement buuuuuut it’s looking like they don’t exist.) So, in Jacob’s atomic model, we have moving electrons which constantly change direction, therefore constantly change magnetic field, so that will produce an electric field that’s constantly changing, so that will produce…and we have an electromagnetic wave radiating out of our orbiting electron. The trouble comes because that wave carries energy, and if that wave carries energy, the electron loses energy—and slows down, crashing into the nucleus. Notice the problem? The solar-system model of matter is unstable. If it were true, there wouldn’t be any atoms at all.
I don’t blame Jacob for this. The “it’s like a solar system” model is still taught in schools, after all. It’s inaccurate in lots of other ways, of course—electrons are not really tiny balls, and they can only occupy discrete orbits. We, as a civilization, need to sit down and think of a better metaphor to teach our children. In reality, electrons don’t move in orbits because they aren’t really moving. They have a certain amount of energy that causes them to assume a certain distance from the nucleus, and then they occupy a particular shape of orbital, which don’t look like planetary orbits at all, in general.
Each suborbital fits two electrons, which posed quite a problem in the early 20th century. You see, it was known that no two electrons could occupy the same quantum state, as then they’d be the same electron. So to have two electrons in one orbital, there was another “quantum number”, which has a value of plus or minus one-half. It was eventually discovered that this corresponded to what is known as “spin.” Now, since electrons are totally featureless, it doesn’t make any sense for one to spin the way you spin a basketball. But it shares many properties with rotational momentum, so we have spin-up and spin-down electrons nonetheless.
Which brings us, finally, to magnetism. Spin-up and spin-down electrons react differently to magnetic fields—spray them into a magnetic field oriented correctly and you can separate them into those categories. Most atoms are spin-neutral, as each spin-up has a corresponding spin-down in its suborbital. Sometimes, though, due to an odd number of electrons or the way in which the orbitals fill up, unpaired electrons are left over, giving the atom a net magnetic moment. Even so, in most materials, these moments are pointed in all different directions, resulting in, again, no magnetic susceptibility. But apply a magnetic field to these materials, and the spins of electrons and directions of atoms are aligned with it, and when the magnetic field is removed, this net magnetism remains. Hence, a paperclip, once stuck to a magnet, still retains some magnetism.
Jacob’s statement that magnetism is caused by “all the electrons moving in the same direction” could be argued to be essentially correct, after all, didn’t I just say that all the electrons were spinning in the same direction? I did, but it’s important to note what models we’re talking about. To speak about this subject correctly, we have to note that electrons can’t actually spin, rather, they have an attached number that behaves like a spin. We also have to note that the electrons themselves aren’t actually moving, they’re just left unpaired in their atoms. Jacob’s explanation is very classical, very rooted in the idea of electrons as tiny billiard balls rotating about central particles. That makes it easier to understand, yes, but in the process he loses much of the subtlety and much of the beauty of how the universe works on subatomic scales—where it is truly, fantastically, beautifully weird, and worthy of close inspection.
One more thing! He promised he’d include Richard Feynman but he missed this absolutely perfect clip of Richard Feynman talking about talking about magnets. Rectified below.
