Yesterday was our faculty's postgrad symposium, where science students of all descriptions attempted (usually with some measure of success) to explain to science students of all other descriptions what their research is all about. This necessitates some creativity and has left me thinking (not for the first time) about whether or not QFT is indeed inexplicable. It seems worth writing up a few thoughts here.
QFT is hard.
There's a reason that nobody less than four years out of high school gets QFT (for an approximate value of nobody and allowing 'gets' to be ill-defined) and nobody with less than six years of tertiary education has actually used it in any practical way. (Again, generalisation, but I don't think it's far off the mark.) QFT is a very abstract, mathematical theory and divorcing it from the mathematics is like trying to explain swimming without water. If you want to understand QFT, come back when you have a degree's worth of mathematics. This is perhaps a little too depressing, so let's try another tack.
QFT is not hard
Sure, the scientists who do QFT research need lots of training and deal with scary equations all day, every day, but that's not the heart of what they're doing. They're actually doing calculations on "god particles" and quarks, which are basically very small marbles glued to elastic bands which are other particles called gluons and the gluon is massless which means it's like a fish that can swim through the god particle molasses slickly, unlike the other particles, which are like whales because they have masses.
Now, I will admit that our building houses not just the physics department, but also the oceanography department and the Marine Research Institute, but we are separate departments. A quark or a Z boson is nothing at all like a whale. In fact, the work I do on a day-to-day basis involves talking about mathematical abstractions that can be experimentally tested using the ideas of such particles, but doesn't really talk about particles at all. So while I do think that non-specialists should be able to get an idea of what's going on in QFT, I'm not convinced that these analogies do much more than make people think they know what's going on. Which is perhaps worth something, but seems suboptimal.
QFT is (not) hard
QFT is an abstract theory based on abstract mathematics. If you want a genuine feeling for how it behaves, you need a genuine feeling for how maths behaves. To reuse an analogy (since I've decided they're not all bad), you can't understand swimming if you don't know what water is. QFT is related to abstract maths just as intimately and shying away from it doesn't help. But what I think we miss is that all you need is a "genuine feeling for how maths behaves". I say 'all', but of course such a feeling can be hard to come by. However, it's an awful lot easier to come by than a degree in mathematics. It almost has to be.
I don't think you need to be able to calculate a commutator to get a feel for what's going on in QFT. I do think you need to know that sometimes in maths, as in life, order matters. 2 + 3 = 3 + 2. I don't care whether you put on your hat and then scarf or you scarf and then hat. But pq is not the same as qp and you should put on your socks before you put on your shoes, unless perhaps you're going to a fancy dress party.*
For some reason we don't seem to want to explain QFT this way. Perhaps it's because we've all learned in school that maths is terrifying. Perhaps it feels like it takes us too far off topic. (I feel this every time I try to give a talk about QFT, but I find there's nothing to say if I take out the maths.) Perhaps we just haven't thought about it enough. (We almost certainly don't think about science communication enough.) Perhaps it is happening, but I'm not aware of it (and neither are my scientist friends, which would mean it needs way more publicity).
I'm still working out where this leaves me. It means that when I talk about QFT for a general audience, I don't shy away from the maths. Maybe it means I need to write and/or talk about these ideas more often (she said, guiltily writing her first blog post in months). Maybe it's enough to be aware of it and to talk about. Maybe I need to pick fights about it. Maybe (definitely) it's not all a problem for me to solve, all on my own, today. But it's a topic that deserves some thought, in the midst of marking and debugging and trying to put in those six years you need to learn to use QFT. We'll see.
* I feel like a cheat putting in mathematics without explaining the physical significance. The p and q here are representing the tools we use to measure the position and momentum (which gives us the speed) of a particle respectively. The maths tells us that the order in which me measure them matters, because pq ≠ qp. This means that making one measurement must somehow corrupt the other (it doesn't tell us how that happens, sadly). This in turn means that if we measure the position correctly, we can't measure the momentum and vice versa. This is Heisenberg's Uncertainty Principle (which is one of the most obvious and well known consequences of order mattering, although not the only one). You can talk about thought experiments, like the Heisenberg microscope, to make it seem more intuitive, but it comes from the fact that if we choose maths that gives us the right answers, order matters when you write down p and q.