Saturday, October 16, 2004

Problems with Time and Space

I've been so busy lately. See, I'm a teaching assistant, and I'm taking quantum field theory, and I'm working in the lab. And then, yeah, there's Ken.

Lab work takes away from my quantum field theory time. To really understand what I'm learning in QFT, I'd need to teach myself complex analysis (I never took it) and relativity and review a number of other subjects that I have been taught, but never properly learned.

The professor started by talking about physical descriptions of rubber bands (a continuous medium in which for instance, waves can move... You can describe it mathematically with a "field") and then suddenly was talking about particles that go back in time. The idea of quantum field theory is, in a sense, that it makes no real sense to describe a single particle. You have to describe the whole system. All your particles, and the empty space between them, because the energy is constantly being exchanged. Oh, when I say "space" -- time is a dimension, almost but not quite like the others... If that sounds confusing, well, it is.

One class seems like more work than the seven I took in high school. But I don't have the time I need to spend. And it's worse because I really do want to understand this stuff. I'm wondering how the other half dozen in the class are doing, and convinced, of course, that they're all finding it easy. At least one of them is taking two other classes as well as being a TA and research assistant. But I'm used to feeling dumb.

Being a TA takes away from the time I spend in the lab. I'm just starting to understand what's going on there, to understand the point of the things I'm being asked to do. (It turns out that the project I was working on up until now may not really happen, but the new one is more interesting, and I don't really mind.) Right now, I'm working on building a control system for a laser. Now I've never studied control engineering, never heard of an "error signal before," have only a hazy idea of how feedback works. My entire knowledge of electronics comes from ten lectures and a half dozen labs I had in Durham, and here I am building adder and subtractor and integrator circuits with op amps... I can't even remember what an op amp does. I'd really like to understand how the thing I'm building works, but I'd need to relearn my electronics, and teach myself control systems out of a book, or something. I can't seem to keep hold of the various explanations I've been given... I do know that the purpose of it is to stabilize the laser, so that the frequency doesn't change when the temperature goes up or down, or when the pressure changes in the room, or whatever. I also know that if they really needed this right now, Pati and Venketesh and George and Joe could design a circuit in a few minutes. But they want me to learn.

This is the first step in the process of building a slow-light system in a vapor cell, which is the first step toward building a new kind of optical gyroscope. (I've been trying to study optical gyroscopes. It requires a little general relativity, and a lot of interferometry that I've never had. Also, I really struggle the problem of how pulses travel in cavities.) To make slow light you need a stable laser. I am also trying to understand slow light. In our experiment, it will be a side effect of something called "electromagnetically induced transparency." I am trying to understand electromagnetically induced transparency. What I understand so far is that if you use one laser to put all of the atoms in your sample into a superposition state such that the other laser tries to distort them in two directions at once, the atoms won't be distorted by the other laser, and so won't absorb its energy. That specific frequency will be able to pass through the material unabsorbed -- the material will be transparent to that color. But apparently if I send in a pulse made of that color and a lot of nearby colors, the pulse will be transmitted only very slowly. I am not sure why this is so. I do not really understand the way that the index of refraction -- the speed of light in a medium -- depends on the states of the atoms.

Ken has been helping me with this, and with QFT. He's in the same position as I am -- teaching, taking QFT, and working in a lab -- except his teaching assignment is twice as many hours, and he has a two hour a day commute. He's not taking QFT for credit, but he's doing the homework anyway, mostly so he can help me. He wants to learn this stuff too, but if not for me he would probably be trying to do it at a more convenient time.

I don't really feel like either of us is shortchanging the students, since mostly what I do is grade and supervise, and since I've seen Ken in office hours, patiently working through problems and giving advice... His students have a great TA. But we are both resenting the students, for the time they take, and I don't like that either. I don't want to resent my students. I usually like teaching. I usually get more out of it than this.

Meanwhile I haven't been posting to AFP, or to this blog (yes, that's my excuse), nor have I been watching TV (new fall season?) nor even reading much (though Ken and I are going through Catch 22 together...) We've missed concerts and movies we've wanted to see, haven't been down to Chicago since summer. And I haven't been phoning my family lately, although they're used to that...

I kind of thought that after my qualifiers, it would be easier than this. But I guess I didn't choose an easy life.

I chose a rewarding life. I chose teaching, and learning, and building things. I choose to try to balance all of that with meaningful relationships, a personal life, my family, friends, cultural stuff. I guess I shouldn't complain. I've got all of that. I've got an embarrassment of riches. Only I don't have time to enjoy them all...


Eric said...

What everyone seems to need is a way to pack more time into a day. Shame that it's the least understood dimension of space-time, we really don't seem to be able to manipukate it half as well as we can mess about with space.

I loved what little I did of QFT. I found the maths hellish, but the basic concept seems utterly natural to me. I can sort of explain it to the extent that somebody else gets something from the explanation, but it takes time (and coffee) and can't be done purely in writing. I'm not that good a comunicator. The key is getting to grips with the concept of "stuff". I'm afraid that's entirely mine and I can't point to any books that explain it, though it owes a lot to Feynmann it also owes a fair amount to conversations in the IC Physics tea room. The important thing being to get very clear in ones head that what matters is stuff, not the various names we give to different small bits of stuff, or the ways we go about pretending that stuff is actually lots of different things. REALLY looking at how a guitar or violin works helps. You can talk about playing a single note, but you never actually can, all sorts of other things are inherent in it. Because you don't have a string vibrating in isolation on a single frequency, that's only theory, in practise it actually vibrates with a huge range of harmonics all of which affect the rest of the instrument as well as the rest of the instrument affecting the string and doing its own thing simultaneously. We do that to stuff. We label it and treat it as if we deal with a single note, just as musician does when playing a guitar. However what's really happening isn't what we say it is. All the stuff is vibrating with different harmonics and making other bits of stuff resonate.

That probably didn't help.

On the other hand I'm with you on the rest of it. I never did really get to grips with any interesting aspects of optics, and in my day we were excited about the fact that we could not quite make a hologram on a good day.

Heng on in there, try and keep the Christmas break clear of stress, you are long overdue a few weeks of real relaxation.

Anonymous said...

*scratches his head* I'm not sure about some of the things you said, but the example with the lasers and the atoms/molecules SOUNDS to me like it's easily explained by wavepackets, although that wouldn't make the math easy:P Plus, my understanding of this is naive at best.

I'm skeptical but curious about the light at 2 meters per second or so (unless it's in an unusual medium, e.g. a plasma or solid with strong fields, then maybe I'll believe it :P else I won't believe it until I scrutinize the equations myself)

At any rate, it's too bad you're having such a taxing life right now. Presumably, someday, ultimately, you'll be beyond this grueling time period, and maybe you'll be able to come out sometime then:)