Monday, November 15, 2004

Quantum Field Theory

Have I mentioned that Quantum Field Theory is kicking my butt? And the more I don't understand what he's talking about in class, the more discouraged and depressed I become about the whole thing, the less motivated I am to do the work I really need to do to keep up.

I have two main problems here. The first is the math. I'm completely lost by his notation, at this point. P's and P-slashes and a gagillion different gammas. I haven't got a clue what any of these symbols mean any more. Some of them are tensors (and incidentally, nobody has every formally taught me anything about tensors, beyond the ordinary matrix kind) and some of them are functions and some of them are operators, which might mean matrices or differentials or... Who knows. Sound hard? That's cause it is. But it really doesn't need to be. You can't convince me that there aren't clearer, unambiguous ways to write this stuff. You could start by actually writing all of it down, for instance, and not just assuming that there are greek indices "implied" or that we all know the expression you just wrote is supposed to be divided by 2m. You could write the steps that get you from one line to the next, instead of saying "I hope you're all filling these missing steps in." You could refrain from throwing terms out that we've never heard, in the service of some hideously complicated by irrelevant criticism you have of the someone else's work on the theory... (Although it is reassuring, somehow, that our professor knows the people who developed the theories we're learning now. We're starting to catch up. At least it's 1960s physics that's kicking my butt now, and not 1760s...)

And you could interpret things. That's my biggest wish. Just tell me what this is a model of. Tell me what these waves are supposed to represent. Tell me what the numbers I put in here measure. This is supposed to be our best description of the physical world, and we've lost contact with the physical world altogether.

I'm starting to develop my own interpretations, which I might post here, with lots of disclaimers, if I can word them a little better. I believe that anything which can't be put into layman's terms isn't real science. It has to answer questions that are independent of its formalism -- laymen's questions. So I want to make an effort, but I'm warning you now, I don't know what I'm talking about...

Quantum Field Theory is kicking my butt. Now I have to go to class.

6 comments:

Simon said...

>This is supposed to be our best description of the physical >world, and we've lost contact with the physical world
> altogether

Welcome to my world from a few years ago. I hit this at undergraduate level, and I still haven't managed to sort out in my head whether the problem was my abilities, or the teaching abilities of my lecturers.

Plenty of physicists seem to think so much in terms of mathematics that they come to view the maths as the end product rather than a means to an end, and start to confuse the model with reality.

I can't really offer any helpful advice in dealing with this, except to challenge and ask questions as *soon* as you start to get lost before you're totally out of your depth. But that's fairly obvious, if you have the courage to do it.

All I will say is good luck - some of us out here agree with you, though obviously I can't comment on quantum field theory in particular. *hugs*

-S

Anonymous said...

Didn't Richard Feynman talk about creating an alternate notation system in Surely You're Joking...? I remember that an expression like "sin x = 34.7" would annoy him because it looks too much like "s times i times n times x = 34.7." Anyway I hope you conquer the beast and I will pray to the physics gods to help you.

love,

Santiago

Eric said...

I've always seen the insistence on separating the maths from the reality as a bit of a cop out. On the other hand I quit a good few years earlier and many years ago, so it may well be that there are huge areas of physics that can only be handled that way.

We had one marvellous lecturer who use to only ever talk whilst facing away from us. This is largely why I've forgotten pretty much all the thermodynamics I ever learned, there's no human being attached to it.

Simon said...

Feynman did, indeed, try to create his own notation until he realised that the rest of the world didn't have a clue what he was going on about... the particular example I remember from "Surely you're joking" is differentiation as being an integral sign with a cross through it, because if somebody wrote (dy/dx) he kept on trying to cancel the ds.
I kinda like the sin(x) example too...

Mary said...

In fact, some of the notation we're using was invented by Feynman, who revolutionized this area by introducing Feynman diagrams... (Which our professor has yet to officially introduce, though he, and the book, rely on them heavily.)

Anyway, I think a huge part of my problem is just due to the fact that the discipline is so young. Ever looked at 19th century papers on electromagnetism? Completely unintelligible. But with modern notation you can (sort of) teach it to undergraduates...

Give it a hundred years. We won't be using this stupid notation any more, and we'll be teaching this to undergrads...

I've spent the better part of the past two days on this stuff, and I am starting to get a kind of handle on it, conceptually, at least. Explaining is a daunting challenge, though. I think I'll wait until the quarter is over...

-Mary

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