Where does the Standard Model of physics come from?S

The Standard Model of particle physics is a triumph of science. It's a collection of 17 particles, and four forces. Physicists like to call it "elegant" but to the untrained eye, it looks anything but. Where does this all come from? In this week's Ask a Physicist, we'll find out.

A few weeks ago, we had a contest to come up with the some of the most interesting questions about the universe. This week's winner is Koen, who wins a copy of my new book by posing the rather deep question:

We have this amazing Standard Model to explain what the fundamental particles are. What is the mechanism 'behind the curtain' that generates these laws?

This is a little more esoteric than my normal fare, but, it is such an astoundingly good question that I wanted to give you a sense of what makes the Standard Model so beautiful (and what is hiding behind the scenes). As always, I expect plenty of debate in the comments section.

The Standard Model

The universe is filled with stuff. That stuff is made of molecules, and those molecules are made of still smaller protons, neutrons, and electrons. The rabbit hole goes even deeper; the protons and neutrons are made of still more fundamental particles: quarks, which are, in turn, held together by odd little buggers called gluons. There are particles called neutrinos which don't get bound up in matter at all, and others, like the Higgs, which exist for only the merest instants before decaying into other stuff.

The list of particles, and how they interact, are collectively known as the Standard Model, and so you don't have to completely reread Alasdair's excellent review on the subject, let me summarize with a table:

Where does the Standard Model of physics come from?S

Credit: Wiki Commons

So let me anticipate your first question: do you need to memorize all of this? No.

But looking at it, you might be tempted to ask: How in god's name does this look elegant to you physicists? And more to the point, what's to prevent me from just drawing another square and inventing my own particle?

Symmetry lies at the heart of physics. Almost all particles are essentially cast out of the same mold. What appear to be two different particles are actually two different ways of looking at the same thing. Almost.

There are two fundamental types of particles. One are called fermions, which include the quarks and electrons – the particles that ultimately make up you, along with the neutrinos which don't seem to matter much in your everyday life.

The others are bosons – and they're the particles that communicate the various forces: photons, W & Z Bosons, Gluons, and the infamous Higgs Boson.

But let's start with the fermions. The basic idea of the Standard Model is that there is really only 1 type of fermion, a sort of meta-particle from which all other particles can be created.

Sound weird? Of course it does.

Spin and SU(2)

I'm not going to derive all of the Standard Model. There's obviously a lot of math involved. But to give you a sense of how it fits together, I'm going to start with spin. What the hell is spin? Funny you should ask.

In simple terms, you can imagine that electrons – and all fermions – are spinning like a top. Yes, yes, it's an oversimplification, but it'll do for now. An electron can spinning either counterclockwise, as seen from above, known as "spin-up", or clockwise, "spin-down," and since a spinning charged particle creates a magnetic field, it's relatively easy to tell which kind of electron you have.

Spin-up and spin-down electrons are awfully similar to one another. They have the same charge, the same mass, and will repel each other electrically the same. What's more, it's super easy to turn a spin-up electron into a spin-down or vice-versa. Just run it through a varying magnetic field.

Depending on your point of view, you can think of spin-up and spin-down electrons as being either two different kinds of particles or one particle with two different states. This is a symmetry, and the mathematicians have a fancy name for it: SU(2) (please don't click if advanced math will aggravate a heart condition).

Symmetries of this sort show up all the time in everyday life. Describing something as being "to your left" or "to your right" depends very sensitively on what direction you're facing in the first place. Turn yourself around, and the two get switched. SU(2) is basically a formalism for describing the mechanics of rotating quantum mechanical spins.

You may not think it matters much whether an electron is spin-up or spin-down, but from the point of view of particle physics, they really are two different particles. They're deflected differently by a magnetic field, for instance.

Seems like a small difference, but it's an important one. As you may remember from your chemistry classes, an atom can hold 2 electrons in the lowest energy "shell" (instead of 1), which means that elements like helium (with 2 electrons) are so full that they don't bond with other atoms.

The Weak Force

The symmetry of spin is just a starting point. It turns out that the relation between electrons and a neutrinos are almost exactly as tight as that between spin-up and spin-down electrons.

Electrons and neutrinos do have a lot in common. They're both very light – although admittedly a neutrino is much lighter than an electron; they both have the same spin; and they both fall into the pile of particles labeled as "leptons."

Just like with spin-up and spin-down electrons, electrons and neutrinos are almost interchangeable for one another – in certain circumstances. The "weak nuclear force" – which, despite the name, is important enough to power our sun – couldn't tell the difference if you swapped all electrons for neutrinos and vice-versa.

Let me be clear here. The mechanics of the weak force were discovered long before we had a mathematical model to describe it, but once we did, and once we discovered the neutrino, the whole thing fits together with a fairly simple conceptual framework.

To add another detail, while neutrinos and electrons are symmetric with regards to the weak force, they are not symmetric for the good old-fashioned electromagnetic force. After all, one (the neutrino) is electrically neutral, while the other (the electron) is charged.

Each symmetry is particular to a certain fundamental force. The mathematics describing the relation between electron and neutrino are identical to those relating spin-up and -down electrons: they have an SU(2) symmetry.

And the connection doesn't end there. It takes a magnetic field – interactions with a particle called a photon – to change the spin of an electron. Likewise, to make the model work, we had to suppose that change from an electron to a neutrino or vice-versa required one or more new particles – what turns out to be the W and Z Bosons.

Inventing particles might sound like the fevered scribblings of an overzealous theorist, except that the W and Z Bosons (and now, every other predicted particle in the Standard Model) have actually been discovered.

There's a complication to this. The W and Z Bosons should naturally be massless, but in reality they are very massive, about a hundred times as massive as the proton. The Higgs – the 17th particle on the chart – was introduced to address this and give mass to the W and Z Bosons (and probably other particles). Yes, it's a kludge, but apparently a correct one. A year ago today various groups at the Large Hadron Collider announced that they'd discovered the Higgs.


The Standard Model doesn't end there. Just as the electron and neutrino are in some sense "the same particle" by virtue of the weak force, an up-quark can be turned into a down and vice-versa by the same mechanism.

But there's more. Quarks have another property called color – roughly the equivalent to electrical charges. There's a crucial difference, however. While charge only comes in two types, positive or negative, there are three colors, called (by convention, not because quarks actually have what we'd really call a visible color): red, green, and blue.

Just as electron and neutrino can be swapped without affecting the weak interactions of particles, all reds can be swapped for greens or any other color combination, without affecting the strong force. If you want to impress people at parties, this is known as SU(3).

And again, mediator particles need to be invented to allow one color to turn into another. In this case, it's the gluons, the particles that ultimately hold protons, neutrons, and the nuclei of atoms together.

You can almost immediately see the symmetry of the Standard Model by just showing the particles in a different way:

Where does the Standard Model of physics come from?S

Credit: Herb Thornby

If you want to lose a good hour of your life, you can play around with these sort of relations dynamically on Garrett Lisi's particle explorer.

Some unanswered questions

Pretty neat, eh? Just make an educated guess about the symmetries of nature, start with one particle, and soon you have a zoo. But I've always tried to be honest with you guys, and I'd like to finish out by pointing out that the Standard Model leaves open a lot of unanswered questions.

  • Why these symmetries, and not others?

    We observed the fundamental interactions of nature before we came up with a model for them. The SU(2) and SU(3) symmetries of the weak and strong forces, along with the U(1) symmetry of electromagnetism are things we observed and then modeled. If we were simply brains in a jar, we wouldn't necessarily have guessed at these from first principles.
  • Why 3 generations?

    The elegance of the Standard Model is based on a lie. All of it isn't explained. You may notice that there aren't just electrons, but also muons and tau-particles – essentially heavier versions of the same particles. All of the fermions have three nearly identical generations, each heavier than the last.

    There's no good reason to have 3 versions of basically the same particles. But here's the thing, even those 3 generations are essentially just different ways of looking at the same particles. The different versions of neutrinos, for instance, will just spontaneously morph into one another. How messed up is that?

  • Why are the Symmetries Broken?

    Even the symmetries we have aren't perfect. Consider this truth bomb: when they're produced in nuclear reactions all neutrinos are created so that they spin clockwise as they head toward you – they're what are called "left-handed." Why does the weak force know left from right?

    What's more, if the symmetries were perfect, we wouldn't need a Higgs particle. It's meant to patch a hole.

  • Why are there so many Free Parameters?

    Finally, even though symmetries describe the relations of the particles in a general sense, they don't tell us why the electrical charge is the value it is, or why the weak force has the strength that it does, or the mass of the electron, or any of the 25 free parameters of the model. That's an awful lot of knobs to turn.

The point is, there's a lot behind the curtain of the Standard Model, but that may be because we still have a few skeletons we're not entirely proud of.

Dave Goldberg is a Physics Professor at Drexel University. His newest book, The Universe in the Rearview Mirror is coming out July 11 – only one week from now – but, if you can't wait that long, you can totally pre-order it. You should definitely become a fan on facebook, or better yet, send a (non-contest) question about the universe.