So, I started this with the intention of writing a sort of “guide to particles” that would take the reader on a tour of electrons, quarks, photons, and so on, all the way into hypothesized beasts like the pentaquarks, gravitons, and higgsinos. I still intend to do that – but as I thought more about it, I realized that if I’m to do this properly, there’s a some preliminary stuff that I ought to talk about first. And after all, that “preliminary stuff” is pretty interesting in itself, if you ask me, and worth spending a bit of time on.
So part 1 of this series will address what particle physics is, conceptually, all about; part 2 will get into some more particular features of particle physics; and part 3 will be that guided tour of the particle zoo that I was originally interested in giving. (Depending on how much detail I end up wanting to go into, and on people’s interest, that third part might end up getting divided into multiple parts as well; we’ll see). This will move us from the abstract to the specific. So if this first part makes your eyes glaze over, I invite you to come back and give parts 2 and, especially, 3, a try – my hope is that you’ll still get something out of them.
As with my previous physics articles, my goal here is to simplify without dumbing down. This stuff is weird, and it can be a lot to wrap one’s head around, but I honestly do believe that it’s possible for a non-math/science audience to understand the concepts here.
OK, so what is a particle? That may strike you as something of a daft question, but it turns out that in our most fundamental theories of the universe, particles are rather different objects from what you might expect. To talk about this, we need to talk a little bit about Quantum Field Theory. So bear with me for a little bit here.
The upshot is going to be that in QFT, particles are actually excitations of fields. So first let’s talk about fields, then we’ll talk about quantum fields, and then finally we’ll get around to particles.
OK, fine, so what is a field?
You know what a field is, even if you don’t think you do. A field is something that has a value at each point in a space. When you look at a weather map showing current temperatures, you’re looking at a representation of a field – at every point on the map, the temperature has some numerical value. A field like that is called a scalar field, because its value at each point is just a number, or a “scalar”. In contrast, think of something like wind velocities – at each point, the wind has both a numerical speed and a direction; this is a vector field, because its value at each point is a vector.
So, imagine a field extending through three-dimensional space. At each point in space, it has some value. Now, there are going to be some rules for how this field behaves. First of all, the value of the field at each point in space is going to behave like something called a harmonic oscillator. Imagine, if you like, that space is filled with an infinite number of tiny springs. If one of the springs is displaced away from its resting state (i.e. if the value of the field at that point in space is above or below its zero point), then it will bounce back toward its resting state, and will end up oscillating up and down. A spring that is bouncing up and down is said to be “excited”. If we imagine that each spring can only bounce up and down in one direction, then we are imagining a scalar field. If, instead, we imagine that the springs can bounce in any direction, then we are picturing a vector field. (Both kinds of fields play a role in particle physics, but for now I’m going to stick with the picture of the simpler scalar field.)
Now imagine that these springs are all attached to one another. Imagine, say, that each one has a little string connecting it to each of the other springs surrounding it. Then if a spring in one place is bouncing up and down, it will pull on its neighbors, making them start to bounce up and down as well, and in the process transferring some of its energy to its neighbors. If you push one spring down and then release it, its neighbors will start to bounce, and then their neighbors, and so on, and you end up with a ripple of bouncing springs emanating away from the initial excitation.
Let’s pause for a moment and note the major limitation of this analogy. Namely, a spring takes up some space, and you can only fit a finite number of them into a given region. We could try to improve the picture by imagining smaller and smaller springs, and more and more of them – but to get a truly accurate representation of a field, we have to imagine the “limit” of that, where we’ve shrunken the springs down to an infinitesimal size, and packed infinitely many of them within any finite region of space. But if you bear this in mind, I think that this image – of space filled with these little bouncing springs, linked by tiny strings – is not a bad way of visualizing what a field is.
Quantum Fields
So far, we’re describing classical fields. This is more or less how everything from sound waves to waves in water work, and it’s how electricity and magnetism were modelled before the discovery of quantum mechanical effects. The quantum version of field theory introduces a few wrinkles. For one thing, the excitations of the field in QFT are quantized. In classical field theory, these “springs” could be displaced by an arbitrary amount, and thus you could have oscillations of any amplitude. But in QFT, you can only pull the “spring” up or down in discrete steps, so the springs can only oscillate at discrete amplitudes. That means that if a field is excited – if an oscillation is introduced – the size of that excitation must be a multiple of that minimum allowed value.
I’m obviously brushing a lot of math under the rug here, and obviously some of this stuff is already getting a little strange and unintuitive. (I mean, obviously we’re working by analogy here; you couldn’t really have an infinite number of infinitely tiny springs). But if you’re with me so far, and willing to suspend your disbelief on those strange bits, you now have a decent way of thinking about what a quantum field is.
Now the weird part: these excitations of the field are particles.
On the face of it, that claim might sound bizarre. Particles are little point-like objects, right? What could they possibly have to do with the land of infinite springs I’ve been asking you to imagine?
Well, suppose you pull one of those little springs down from its resting state and release it. Remember, if this is a quantum field, then you can only pull it down in discrete steps. Let’s say you pull it down by one step. What will happen? Well, it will start bouncing up and down, going up to a height of one step above its resting state, then back down to one step below, then back up, and so on. If it were isolated, it would do this forever. But it’s not isolated; we’ve said that it’s attached to its neighbors, meaning that they’ll start feeling something pushing them up and down as well. Now, if this were a classical field, each of its neighbors would start oscillating, but with less amplitude than the initial spring, and then each of their neighbors would start moving, and so on. The bouncing behavior of the springs would propagate outward from the initial point, but as more and more springs became involved, the oscillations would get smaller and smaller. You can think of it as the first spring giving some of its excitation to the neighboring springs – but as that excitation gets divied up among more and more springs, the amplitude of each spring has to get smaller.
But this is a quantum field – and remember, we excited the first spring by just one step, the smallest unit of excitation any spring can have. That means that it’s impossible for the oscillations to get any smaller. If the initial spring starts another one oscillating, then that second spring has to oscillate up and down by one unit. Moreover, if that happens, the first spring has to stop oscillating, because it has to have given all of its excitation to its neighbor. And then if the second spring starts a third one oscillating, it similarly has to give up all of its excitation to the third spring. And so on. The result, then, is that this excitation does not spread out – it moves along from one spring to another, following a single trajectory and never dividing.
Now, I’ll acknowledge that this is the point in this article where I’m sweeping the most stuff under the rug, and simplifying things the most, because I’m not saying anything about the fundamentally probablistic nature of the propagation of that excitation, or where that probability comes from. This is all neatly packaged away in my statement that the springs are “attached” to their neighbors. The math of how that attachment works is what decides when a spring excites its neighbor and stops oscillating itself, and which neighbor it excites. And worst of all, I’m saying nothing here about the fact that these oscillating springs are fundamentally quantum objects that have to be described using state vectors and superpositions and all that stuff1. Nonetheless, I maintain that the picture I’m describing captures the essentials, and that it is simplified but not inaccurate.
As a side bar, let’s imagine for a moment that instead of displacing that first spring by one unit, we’d displaced it by a million units. In that case, it can divide up its excitation among at least some of its neighbors, and they can divide it up among some of theirs. After a while, we’ll end up dividing it down to the point where each spring just has one unit of oscillation, but at least at first, if we kind of stand back and squint, it will look more or less the way things would if this were a classical field, with the excitation spreading out uniformly and getting smaller. This is an example of why classical physics works pretty well as long as we’re dealing with sufficiently big things (in this case, sufficiently big oscillations).
But back to our example where we only give the first spring the minimal oscillation that we can. In this case, if we stand back and squint, what we’ll see is a point-like excitation moving along through space. And that looks kind of like a particle. And in fact, if we do the math (and, again, there is non-trivial stuff in the math in terms of how the oscillators affect each other), we find that the behavior of that oscillation really is like the behavior we’d expect for a particle moving through space.
And that’s how the universe works
So far, this has all been told more or less in the way of a fairy tale – I’m asking you to picture a certain very specific (and weird!) kind of universe and then thinking about how that universe would work. What Quantum Field Theory posits is that this is the way the universe actually is, that the entitites we are used to thinking of as particles (like electrons, for example) are actually excitations of underlying fields. For instance, take electrons. What QFT is saying is that there is a field (an infinite set of springs, in our analogy) that we might call the “electron field”, and that every electron that exists is actually an excitation of that field – an oscillation that hops from one spring to the next to the next. And there is a different infinite set of springs, also filling all space, that we might call the “photon field”2, and so forth – every type of particle is a quantum field, and every particular instance of that particle is an excitation of that field, a little unit of bounciness that hops along from one spring to the next.
Now, you might ask why we should think of particles this way. Why complicate the picture? If the math of QFT ends up giving us things that behave just like the particles we’re used to, why bother with QFT at all? One answer is that QFT, as opposed to the original Quantum Mechanics of Schrödinger, can incorporate the Special Theory of Relativity. Quantum Mechanics, like Newtonian Mechanics, gets things wrong when particles are moving close to the speed of light. QFT fixes that, incorporating both the innovations of quantum theory and the innovation (well, one of the innovations) of Einstein.
But that’s not the whole answer. One can actually make a relativistic version of Quantum Mechanics without invoking fields, and this is what was originally done, largely by Paul Dirac, in the late 1920s, in the first efforts to combine QM with SR. The main motivation for believing in QFT – for thinking that particles are excitations of fields – is that this allows one to describe particles being created and destroyed, something that Quantum Mechanics cannot do.
Here’s an experiment you can try. Find a lamp that is off. Turn it on. Is it giving off light? Congratulations! You’ve just proved Schrödinger’s Quantum Mechanics wrong! There are now photons being created by the lamp, where there were no photons before. Quantum Mechanics by itself cannot account for this. It can describe how a particle moves, but there is nothing in it that will ever allow a particle to be created.3
How does switching to Quantum Field Theory allow for particles to be created and destroyed? Well, in QFT, a particle is an excitation of a field. So all that needs to happen to create a particle is for something to start one of those “springs” bouncing. Conversely, a particle could be “annihilated” if something damps out the oscillation. And if we have a universe containing multiple, different quantum fields, we can imagine that those different fields might be coupled – in other words, that oscillations in one field might start a spring in another field bouncing, so to speak.
Now, remember that the oscillation of these springs is quantized – the springs can only move “up” or “down” in discrete steps of a given size; this is what gives us the “quantum”, the minimum unit of energy a field can have, which corresponds to a single particle. If we’re talking about creating a particle, then, there’s some minimum amount of energy required, which depends on the size of those discrete steps for that particular field. This is why discovering new particles takes a lot of energy; when a particle collider accelerates particles to high velocities and smashes them together, we are essentially trying to provide enough energy to displace one of the “springs” in another quantum field by one unit. We’ll talk more about this later.
So, let’s review. QFT posits a universe consisting of some number of fields. Each field extends throughout all space and has a value at each point. These fields follow certain mathematical rules governing how the value of each point (the “spring” in our analogy) behaves, and how it affects the points around it. Each field corresponds to a type of particle, and each excitation of that field is an instance of that particle. And the way that these quantized fields work means that that excitation acts the way we expect a particle to act – to the point where it’s perfectly fine in most cases to not really worry about the fact that the particle is an excitation of a field.
So far, we’ve talked about Quantum Field Theory in a general sense. But QFT, per se, is not a theory; it’s a framework for a theory. It gives us a generic mathematical description of quantum fields, but it doesn’t tell us what fields exist, what their properties are, or how they interact. So to get a specific theory, you have to plug these things into the framework. I tend to think of QFT as being something like the grammar of a language; it tells you how to conjugate verbs, so to speak, but you don’t have an actual language until you also have a dictionary telling you the words that exist in it and how they’re used. Likewise, you don’t have an actual physics theory until you have a list of the fields that exist in that theory and their properties.
In QFT, this is done with something called a “Lagrangian” for a given theory. The Lagrangian of a QFT is a mathematical expression – don’t worry about what it actually looks like; the important thing is that it tells us the following things:
– What fields exist in the theory and what their properties are. Each field corresponds to a type of particle, and the “properties” of the field that I’m talking about correspond to that particle’s mass, charge, spin, and so on.4
– How the different fields/particles “couple” with each other. You can think of this as telling us how strongly an oscillation in one field will “pull” on another field. The fact that these fields do interact with each other is what gives rise to all the interactions we observe between particles.
So, for instance, Quantum Electrodynamics (QED) is a Quantum Field Theory. It includes the electromagnetic field (i.e. the field of the photon) and fields for charged particles like electrons. It specifies the properties of each of these fields, and it specifies the strength of the coupling between the electromagnetic field and each charged particle field.5 QED, which was developed in the 1940s, very successfully describes and predicts electromagnetic phenomena, and the interaction of light with matter.
But QED is an incomplete theory, in the sense that it only describes some of the kinds of particles in the universe. A complete quantum field theory would include fields for all the particles that exist, and would specify the properties and interactions of those fields. This would be the “Theory of Everything” that you hear about – a theory that so far no one has been able to develop. The most complete theory we’ve been able to build so far is called the Standard Model. It combines QED with other incomplete theories to describe not just electromagnetism but also the strong and weak nuclear forces, and a zoo of particles that interact with those forces. Even though we believe it to be incomplete, the Standard Model has proven extremely successful, correctly describing the results of essentially all particle physics experiments performed so far6 even to the point of predicting the existence of previously undetected particles.
In the interest of keeping these short-ish and digestible, I’m going to cut this off there for now. As I mentioned, this has started out pretty abstract, but next week I’ll talk in more detail about how Quantum Field Theories actually work – we’ll talk about Feynman diagrams, anti-particles, fermions and bosons, and that sort of thing. And I promise that next time, there’ll be pictures.