Everyday Matter, Hypercharge, Isospin, and the Three Forces
Just like the ingredients in a bakery have numbers on their nutrition labels to tell us how they will affect our health, in The Standard Model, elementary particles have quantum numbers that tell us how different forces affect them. For each particle, we will talk about two quantum numbers, hypercharge and isospin.[^1] Think of hypercharge and isospin as two different nutrients that can be found in the ingredients.
Also, just like different kinds of food are in different food groups, we can also classify elementary particles into groups using colors. These aren’t really how the particles’ look—when we say that a particle is “red”, what we mean is that it’s in the “red” group. There are three color groups, “red”, “green”, and “blue”. If we say that a particle is “black”, that means that it isn’t in any groups, and if we say that it is “white”, that means that it is in all of the groups. If we say that a particle is something like “antired”, that means it’s in all of the groups except red—in other words, the green and blue groups.
Now, according to The Standard Model, most of the stuff on earth is made from particles called electrons, up quarks, and down quarks. Before we get into patterns, let’s talk about these particles’ quantum numbers and colors (their “nutrition facts” and their “food groups”), starting with electrons. That will also give us a chance to talk about the three forces in The Standard Model.
Electrons
In The Standard Model, there are two kinds of electrons: right-handed electrons and left-handed electrons. You can tell them apart because, when a right-handed electron moves, it gives the illusion that it is spinning to the right like a corkscrew or drill bit, even though it is not actually spinning, whereas when a left-handed electron moves, it seems to be spinning to the left. A right-handed electron has a hypercharge of -2 but zero isospin. A left-handed electron has hypercharge of -1, and its isospin is -1/2. Both electrons are white, which is to say that they have all of the colors, that they’re in all of the food groups and make a balanced meal all by themselves.
What do those numbers mean? Well, the most important thing to know for an electron is the Gell-Mann–Nishijima formula, that you can add half a particle’s hypercharge to its isospin to get another quantum number called electric charge. Electric charge that tells us how the particle is affected by the electromagnetic force. For a left-handed electron, half of -2 plus 0 is -1, and for a right-handed electron, half of -1 plus -1/2 is also -1. So both kinds of electrons have the same negative electric charge. The electromagnetic force pushes negative charges away from negative charges and positive charges away from positive charges, but pulls negative and positive charges together. That means that electrons run away from each other and try to go towards positively charged particles. Because of something called “relativity”, the electromagnetic force also means that moving electric charges create magnetic fields and moving magnetic fields create electric forces. We use those effects to move electrons around—we call that electricity—and to change electricity back to motion with devices like motors.
The electrons’ isospin tells us another thing, this time about the weak force, a force that can change particles from one type to another. Since the right-handed electron has zero isospin, it isn’t affected by the weak force, so we can’t use it to make new elementary particles. But the left-handed electron does have some isospin, so if we smash it with a careful choice of other ingredients, we can make new elementary particles.
There’s also a third force in The Standard Model, the strong force, but it doesn’t affect black or white particles, so we have to wait to talk about it.
Up Quarks
How about up quarks? They too come in right- and left-handed forms. The hypercharge of a right-handed up quark is +4/3, but just like a right-handed electron, it has no isospin. A left-handed up quark has a hypercharge of +1/3 and an isospin of +1/2. Like we did before, we can compute the electric charge by adding half the hypercharge to the isospin. Half of +4/3 plus 0 is +2/3 for the right-handed up quark, and half of +1/3 plus +1/2 is also +2/3. So up quarks are positively charged and will be attracted to and attract electrons. And since only the left-handed up quark has isospin, only the left-handed up quark can be used to make new elementary particles with the weak force.
Up quarks are not color-balanced, so now we get to talk about the strong force. There are actually six kinds of up quarks: red, green, and blue right-handed up quarks and red, green, and blue left-handed up quarks. The Standard Model says that the strong force causes color confinement, which means that it pulls particles of different colors together to make a balanced meal so strongly that it’s impossible to have a combination that isn’t balanced. That means you can’t have an up quark all by itself—it would be like trying to make a healthy meal out of only desserts. But you could put a red up quark with a green quark and a blue quark since then you’d have all three colors. It doesn’t matter that the electromagnetic force is trying to push them apart when the strong force pulling them together is so much stronger. A balanced diet is important!
Down Quarks
What about down quark? Just like up quarks, they can be right- or left-handed, and they come in three colors: red, green, and blue, so there are six kinds of down quark in total. The right-handed down quarks’ hypercharge is -2/3, but they have no isospin. The left-handed down quarks have a hypercharge of +1/3, the same as the left-handed up quarks, but their isospin is -1/2, the opposite. If we do the math, down quarks’ electric charge is always -1/3, so they are negatively charged, like electrons. Only the left-handed down quarks are affected by the weak force because the right-handed down quarks have no isospin. (Notice a pattern?) The color confinement rules apply to down quarks the same as they do to up quarks.
Nucleons and Atoms
Now that we know those particles, we can make some recipes to put them together. The basic recipes for earthly matter are the recipes for protons, neutrons, and atoms.
Our first recipe will make a proton. Protons are very important for chemistry because you can control the kind of chemical you have by changing the number of protons in each bundle of quarks. The recipe for a proton is two up quarks and one down quark, all of different colors. (Actually, something interesting happens when you put these ingredients together. The “up” and “down” gets mixed all around so that it’s like each individual quark is actually two parts “up” and one part “down”.) A proton’s electric charge is 2/3 + 2/3 - 1/3 = +1, which means that it is the electromagnetic opposite of an electron.
Our second recipe will make a neutron. Having the right number of neutrons in the right places helps keep big balanced meals of quarks from splitting into smaller balanced meals, and without them, most chemicals would just fall apart. On the other hand, by purposely using the wrong number of neutrons, we can make a pile of quarks break into pieces and maybe get some energy out of the split. That’s how nuclear reactors work. The recipe for a neutron is one up quark and two down quarks, all different colors. A neutron’s electric charge is 2/3 - 1/3 - 1/3 = 0, which means that they aren’t easily affected by the electromagnetic force. (But the quarks themselves are! That’s how scientists first figured out that neutrons are made up of smaller ingredients.)
Since quarks have different colors, and different colors like to be near each other, if we can get them close enough for the strong force to start pulling, we can stick a bunch of protons and neutrons together to make a jumble of quarks called an atomic nucleus. Then, if we surround an atomic nucleus with electrons, we get an atom. Almost everything you see around is you is made from atoms.
[^1]: A note for once you’ve read about forces and fermions: When scientists first discovered hypercharge and isospin, they were working with the strong force, so they only thought about using these numbers for quarks. But when they were studying the weak force, they found out that other fermions have similar numbers. Everyone had been saying things like “leptons have zero isospin”, and they didn’t want to confuse people, so they decided to pick new names for these similar numbers. They still said “isospin” and “hypercharge” for the old numbers, but they said “weak isospin” and “weak hypercharge” for their new numbers. The word “weak” doesn’t mean that the isospin or hypercharge are actually weak; it just means that we learned about them because of the weak force. But nowadays, a lot of people don’t think its important to keep saying “weak” all the time. I’m one of them; I will just say “isospin” and “hypercharge”, but you should know that I’m talking about “weak isospin” and “weak hypercharge”. Still, be careful—if you are talking to someone else, they might get confused if you don’t say “weak”.