Reading an MSc dissertation is not a task for the faint-hearted. Even for an expert in the field, wading through all the detail that’s necessarily part of a two-year project is a substantial undertaking. However! It seems a pity that two years of (often) publicly-funded work should be buried in the obscurity of that part of the library. Publishing papers on the work helps some, but does nothing to clear the traditional (and admittedly useful-in-context) fog of jargon.
As a result of these regrettable complications, it seems like there could be value in a step-by-step, fifteen-minutes-a-week, minimally-technical walkthrough of such a dissertation. It occurred to me (no doubt purely by happenstance) that I am particularly well situated to produce such a walkthrough, having just submitted a dissertation that contains such phrases as
The simplest, although not necessarily the most elegant, solution is to simply factorise the average (the so-called large-Nc approximation) so that the dependence is instead over a set of 2-point functions.
The attempts at introducing humour or otherwise amusing elements into the narrative will no doubt render the entire project repugnant to beings of higher taste than the author, but I hold out hope that a few people may nonetheless find it instructive, or at least entertaining. Thusly, I present step the first: A standard model of what stuff is made from (AKA “The Standard Model of Particle Physics”).
A “model” is simply a “tool for describing something,” so our task is to elucidate this standard tool for describing what stuff is made of. Let’s use the example of table salt, since it’s a relatively simple material (if you’re reading this, you’re definitely a lot more complicated than table salt), but it shares the features we want with all those more complicated systems.
We can zoom in to look at the underlying structure of the salt crystals. Since we’ll rapidly get to the stage where photographing the things I”m talking about is downright impossible, I’ll make use of a cartoon microscope right from the start. We can immediately see that the salt crystal is made of two kinds of stuff: in the picture, the small purple balls and the big green balls. The big green balls are chlorine (like the stuff that goes into swimming pools) and the purple balls are sodium (which is why salty food is sometimes described as having “high sodium content”). It turns out that you can’t get chlorine or sodium in smaller chunks than these balls, so the balls are called atoms. ‘Atom’ is really just a name for the smallest chunk you can have of any particular chemical. For a long time this was considered a good model for what stuff is made of: stuff is made of atoms.
Because scientists can never leave well alone (that’s why they’re scientists, after all), people began trying to shoot things through atoms to see what happened. In general atoms seemed to be pretty fuzzy — it wasn’t too difficult to get things through them. However, sometimes this didn’t happen at all and the things that were shot at the atom bounced right back. I like the way Ernest Rutherford described this:
It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.
One might begin to suspect that the tissue paper was not entirely tissue paper after all. A more detailed model of what things are made of was in order. It was pretty well established that there was some part of the atom that makes electricity work. This electricity part of the atom is made up of electrons (as far as I can tell, ‘electron’ just means ‘thing that makes electricity work’). The electrons turn out to be (more or less) the fuzzy part of the atom. The less fuzzy part of the atom was called the nucleus (which means ‘the thing in the middle’). The rule of thumb is that each electron contributes a particular fuzzy area. Where exactly is the electron itself? That’s rather contentious, actually — it turns out that the fuzzy cloud is all we can really see of the electron anyway. (We’re seeing it through a cartoon microscope, so perhaps I mean all we can know about it — although recent experiments have captured more ‘real’ images of these clouds.) The various electron clouds combined produce the green and purple balls that we saw earlier. Now that we’ve zoomed in, we see that they aren’t perfectly round, but it wasn’t a bad approximation.
So much for the fuzzy electrons. What about the thing at the centre, that seemed to be responsible for bouncing things back at the bemused Ernest Rutherford? The nucleus turns out to be pretty fuzzy too, although it’s in some sense ‘more concentrated’ than the electron cloud. (One of the fundamental insights of quantum physics is that everything is a bit fuzzy if you look closely enough — this comes from Werner Heisenberg’s famous uncertainty principle.) One of the first things we can discover about the nucleus is that it has clumps. Some clumps change the way the electron cloud behaves (and determine the number of electrons in the typical atom) — these are called the protons (which means something like ‘first thing’, although they aren’t). Other clumps seem to ignore the electron cloud: the neutrons (‘neutral things’, since they don’t interact with the electrons). This is a good start to an explanation, but it doesn’t answer all the questions one might ask. For one thing, if the neutrons are so neutral, why do they insist on hanging around with the protons? This leads to the idea that being electrically neutral (and ignoring electrons) doesn’t necessarily mean being completely neutral — there must more than electricity involved. Another question that physicists doing experiments began to ask is, “Why are there so many threes?” This turns out to be an important question.
Whenever a proton or a neutron — one of the chunks inside the nucleus (middle bit) of the atom — can do something, it seems to be able to do it three times. The more one does different experiments, the more threes one finds. Eventually Murray Gell-Mann produced an explanation based on the idea that protons and neutron were made up of three smaller things. He thought it would be amusing to call the smaller things ‘quarks’ and so he did. (You can make different people think you’re wrong depending on whether you make ‘quark’ rhyme with ‘squawk’ or with ‘mark’, but that’s a story for another day.)
This explanation of having three quarks inside each proton and neutron explains the threes so perfectly that it’s generally accepted to be correct. However, it’s impossible to break a proton or a neutron up into quarks, which makes them very strange objects indeed. In fact, putting enough energy into a proton (or neutron) to separate out a quark tends to produce antimatter instead. However, since antimatter isn’t a defining feature of most everyday stuff (like our original example of table salt), I’ll gloss over that for now.
To describe the way that quarks are always found in groups of three, they were named after the three primary colours: red, green and blue. A package of quarks always contains one of each ‘colour’ (we can make this slightly more complicated by including antimatter). This deals with most of the threes in the experiments, but not quite all of them. To deal with the remaining threes, the quarks are also named after various flavours. The flavour pairs (yes, flavour now comes in pairs) are up and down, strange and charm, and top and bottom. Very strange flavours indeed, but then quarks are very strange objects. The quarks in the picture above are up and down quarks: two ups and a down form a proton. Two downs and an up would form a neutron. The other flavours form more exotic things, which I’ll skip over on account of their not being required for table salt.
In fact, at this point, we can begin to think of making table salt from scratch. Salt is made of chlorine and sodium atoms. Those atoms are made of fuzzy electron clouds and a things at the centre. The thing at the centre has neutron chunks and proton chunks. Those chunks (like bureaucrats, perhaps) do everything in triplicate, which leads us to believe that there are even smaller things, called quarks, inside. Since quantum physics tells us everything is fuzzy, the quarks must be fuzzy too, but we expect them to be fuzzy in groups of three. And that’s it. Stick it all together and you have table salt.
How do we stick it together? Well, that’s a good question. As we noticed earlier, there seem to be several ways for things to interact (or not interact). Come back next week for photons (‘light things’), gluons (‘glue things’), W’s and Z’s (‘we ran out of names things’). If you have questions, feel free to ask in the comments and I’ll do my best to answer!