Fucking Magnets

My first question comes via d10, from the rpg.net forums:

How do magnets work? 

Observers of the physical world have long noticed the tendency of certain bits of matter to attract or repel each other. These tendencies are called the fundamental forces, and there are four of them. Why do they exist? Why are there four? Could things have been some other way? These are questions of fundamental ontology, and way beyond my ability to answer. I think Stephen Hawking may be working on it, but even if he comes up with a good explanation, it's going to be something that only a few people will be able to understand.

In the meantime, you'll have to be satisfied with the anthropic principle - the reason we find these questions interesting is the fact that we're able to ask them. Presumably, there are alternate hypothetical universes of undifferentiated goo or trans-galactic superbrains where they ask why there are zero or 27 fundamental forces, respectively.

But back to magnets. Of the four fundamental forces, we can safely ignore three of them and focus on electromagnetism. Electromagnetism is an extremely influential force, responsible as it is for most of what we call "reality." For example, have you ever noticed how you can't walk through walls? Electromagnetism is to blame.

As far as electromagnetism is concerned, we can divide everything up into two categories - charged particles and uncharged particles. Uncharged particles, we're not interested in. They are basically invisible to electromagnetism, and are instead influenced by those other forces I told you I was going to ignore.

Charged particles come in two varieties, Positive and Negative, although these names are pretty arbitrary, and they could easily have been the other way around. The important thing about charged particles is that opposites attract and like charges repel. So, a positive will stick to a negative, but two negatives will bounce off each other.

The reason this is important is that atoms are made up of charged particles (and also some uncharged particles that we're not interested in.) The creamy center of an atom (the nucleus) is positively charged, and the creamy exterior (the electrons) is negatively charged (quantum physics in general is pretty creamy). That, incidentally, is the reason you can't walk through walls. If you tried, your electrons would bounce off the wall's electrons (actually, it's even more complicated than that, but one thing at a time).

When it comes to magnets, the electrons are the important thing. Electrons are attracted to the nucleus of an atom, but - hoo boy, this is where I just want to say "fuck it, it's a miracle" - they've got too much energy to just touch, so instead, they orbit, except not really. An electron is more like a smear, where you can say it is probably in some general area, and this smear can be described, with very precise mathematics, as a wave (that's not something I'm going to attempt to do, but it can be done).

And here's where it gets weird - only certain waves are valid, (specifically, those with a wavelength that is an integer multiple of the space available, which doesn't really sound all that weird, but trust me, if you know anything about waves, it's kind of batshit) and since electrons repel each other that means that any given nucleus can only have a very specific number of electrons orbiting it. One way to think of it is that atoms have "equipment slots" and those slots can be, but don't have to be, filled with electrons.

Take a look at the periodic table of elements: http://www.ptable.com/ The shape of the table is not arbitrary. An element's location on the table can tell you about its electrons. All the elements in the same row have the same number of slots. All the ones in the same column have the same number of electrons in their outermost ring of slots (okay, it's more complicated than that, but I really don't want to get into it).

Where this becomes relevant to your original question is in the answer to the question you probably should have asked: "why isn't everything a magnet?" And that has to do with the way that atoms interact with each other. Basically, the universe is lazy, and generally prefers for things to be as unenergetic as possible. So, if two or more atoms get close to each other, and one atom has an open slot at a lower energy level, that atom will "steal" an electron from the other. Sometimes, this will result in two charged atoms that then go their separate ways, but other times, if the relative energy levels are right, the two atoms will share the electron instead.

This is kind of like having a crush on someone who's really popular, but only likes you as a friend. With enough of a push, they'll leave you behind, but all other things being equal, they'll drag you along to parties with a whole new clique. Your friends (ie the first atom's electrons) won't really mix with the new clique (ie the second atom's electrons) and you really don't like the one person in the clique who is also clearly crushing on your friend (ie the second atom's nucleus) so you spend most of the party trying to stay as far apart as possible while the popular person mingles with both cliques.

If you then add a third atom, two things happen. First, the metaphor becomes really strained, and second, the nuclei of all three atoms will try and stay as far apart as possible. So, your friends are avoiding their friend, you are avoiding them, and you are trying to stay as close to your friends as possible. Yet, maybe this third group is less objectionable than the second, so you'd be willing to stand a little closer just to put more distance between yourself and group 2.

The net result of this is that groups of atoms have different shapes, depending on the particular configuration of electron energy levels and the relative size of the nuclei. One of those shapes, present naturally only in certain metals (iron, nickel, and cobalt to be exact), is a line. When the atoms line up in this way, there is a stable difference in charge between one end of the line and the other, and this charge difference creates potential energy. When you add new atoms of the appropriate type into the mix, that potential energy will allow the larger group to bully the newcomers into lining up too, and this is experienced as either an attraction or a repulsion, depending on the orientation of the magnets involved.

Incidentally, if the magnetic field becomes strong enough, it becomes capable of forcing just about any sort of atom to play along: http://www.youtube.com/watch?v=A1vyB-O5i6E

I hope that answers your question, and I really hope that any physicists reading this forgive me for how much I left out and/or oversimplified.