From the Oxford English Dictionary:
noun 1 A rapid turning or whirling motion
1.4 Physics The intrinsic angular momentum of a subatomic particle.
noun 3 [in singular] The presentation of information in a particular way; a slant, especially a favourable one
I was going to write something about covering groups, which I've been reading about today, but one of the applications of covering groups in theoretical physics is in linking quantum spin to rotations. Spin is fascinating and weird. I got sidetracked.
I suspect that spin is not really all that weird, if one thinks about it properly. But in the process of discovering what exactly holds the world together, one doesn't always come across ideas in contexts that make it easy to think about them properly. Such is the case with (quantum) spin, which, despite the name, does not involve any rapid twirling or whirling motions. In fact, all the talk about twirling and whirling could probably be classified as spin in the third sense "presentation of information in a particular way; a slant, especially a favourable one" (but not necessarily an accurate one).
Spin is just a property of a particle (I'll disagree with the OED on its technically needing to be a subatomic particle, but admittedly that's overwhelmingly the context where we talk about spin.) It's easy enough to imagine a particle having a position. It can have a mass, which we tend to think about in terms of how much it weighs -- although the ideas aren't quite the same. We're happy to think about a particle having a speed. Other things are harder to imagine.
We know that there's a thing called electric charge. It's what makes lightbulbs shine and computers compute. It's the reason you can rub a plastic ruler on your head and use it to pick up scraps of paper; and the cause of thunder and lightning. It certainly seems to exist. But what exactly is it? Well, it's electric charge. If we describe it as being like something easier to imagine then we're describing it as being something different from itself.
There's another thing called spin. People sometimes try to describe it as whirling and twirling, because that's easy to imagine and the context in which it was first noticed. In fact, it can be linked very closely -- but not identically -- to the idea of rotations using the mathematics of covering groups. However, spin is not about twirling and whirling, so we end up describing it as something other than itself when we take that route. It tends not to end well.
|There are two yellow lines in the sodium spectrum, not just one.|
Spin is a thing that means splitting the light from a sodium lamp with a prism produces two yellow lines, instead of just one. There's a yellow line for each kind of spin. Spin is the thing that means if you fire a stream of particles into a magnetic field, some will go up and some will go down. It means electron energies are arranged twice as efficiently as you might expect. Like electric charge, spin has noticeable effects. Even if we can't exactly imagine it, it makes sense to talk about it.
That's where the maths comes in handy, of course -- it gives us a way to talk about things like spin, even when we don't have a convenient way to imagine what they 'actually' are.
Savo 'lass a lalaith.