Theme Thursday: Sport?

Boogie at the UCT Ballroom and Latin Dancing Society

Cari at Clan Donaldson runs the Theme Thursday linkup, and since she says there are no rules, I will persist in joining in erratically, even when I'm not really in the target audience. Also I will post-process the heck out of mediocre pictures until I can convince myself that they're arty. And claim that the social dancing when Ballroom lessons are cancelled for the holiday is a sport. (Actually, looking at what other people have linked, this last might be on-trend.)

Straight off the camera cellphone

 If I go to black and white, I can convert the motion blur to graininess (yay, unsharp mask) and call it a feature, yes? It was fun to play with, at any rate; and a fun evening to remember. So perhaps I can file this under "further perks of [still] being a student". It fits somewhere below "Science is cooool" and above "No, actually, I don't get to take the university holiday off. I need to learn everything about everything before my funding runs out."

 
Savo 'lass a lalaith.

Of spin and other nonsense

From the Oxford English Dictionary:

spin:

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.

I should be debugging

, but the server's down and sometimes it's good to step off the hamster wheel. I think. Maybe. It's okay to step off the hamster wheel, right? Are we allowed to admit that there is a hamster wheel?

I'm not complaining, mind you. I love my work. Really, laugh-out-loud, love theoretical physics and seeing how ridiculously, beautifully abstract mathematics can describe the real world and how things actually happen. I love C++ debugging somewhat less, but I can accept that it's part of the package. Which isn't to say it's not a bit of a hamster wheel.

On Saturday at a workshop on science communication I told an auditoriumful of people that I was infatuated with Grassman algebras. That isn't a hamster wheel. It's something to remember and savour. It's a reason to get on the hamster wheel when the wheel needs to be turned, even if I don't seem to be going anywhere.

Grassman algebras are very neat. See, ordinary numbers commute. That means you get equations like

ab - ba = 0

which is to say

ab = ba.

Five times three is the same as three times five, and for most of the things we want to use maths for, that's awfully convenient. If I switch the length and breadth of a room, I don't want the area to change! But sometimes switching things around does change things. Putting on my shoes and then my socks is not the same as putting on my socks and then my shoes.

It turns out that in particle physics there's a family of particles -- called fermions -- that behave like this. If fermion the first and fermion the second are identical (for instance, they might both be electrons), it still matters which order I put them in. No, that's not intuitive, but it does seem to be the way nature works. If I switch fermion one and fermion two, so that instead I'm looking at fermion two and fermion one, the mathematics I'm using needs to have a minus sign attached. And that's where Grassman numbers (the things you use in Grassman algebras) come in. Grassman numbers don't commute, they anticommute:

ab + ba = 0 

which is to say

ab = -ba.

In fact, Grassman numbers behave just the way fermions seem to. That means that while I might describe the length and breadth of a room using ordinary ("real") numbers, it's more convenient to describe fermions using Grassman numbers. I have to modify the rules of maths slightly to make sure that they anticommute, but otherwise I can carry on just as before. The kind of number I'm using does most of the work and I don't have to keep accounting for the odd behaviour of fermions. The fact that they do strange things when you swap them around is built in.

 I think that's pretty. Just about pretty enough that I might muster the willpower to go and ask C++ why it insists that the solution to my equation is infinity. (The solution is not infinity. Unless I've given it the wrong equation. Or the wrong method for solving the equation. Or I accidentally typed +∞ before printing the answer. Maybe I'll go check that last one.)
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Savo 'lass a lalaith.