Implications of the Higgs boson, part II

Massive blue marble, African version, NASA.

Part I

If you have been following the news about the Higgs boson, you may have heard the standard explanation to why discovering it is such a big deal: it is the provider of mass in the Universe. Too often, that explanation is left hanging there, and people are still wondering why this is such a big deal. It is also slightly misleading. So let’s try to get to the bottom of things.

The Higgs boson as the provider of mass in the Universe

It all begins with E=mc². The true meaning of that equation is that mass is just another form of energy. In fact, mass is the result of energy being bottled up. Bottled up energy is often called potential energy in the physics jargon, and potential energy can arise in a number of ways. Take a pendulum. You find a pendulum that is not moving at the moment. If you give it a small push, it starts oscillating. You bottled up the energy of that little push inside the motion of the pendulum. You could place a marble in the path of the pendulum, and as soon as the pendulum hits the marble, the pendulum would stop and the marble would roll away. You just un-bottled the energy in the pendulum. Potential energy is stored energy that can put things in motion once released.

This is also what happens in atoms. Atoms have a bunch of electrons trapped around a nucleus. If the nucleus were to suddenly vanish, the electrons would fly apart. You can see the electrons as little pendula oscillating around the nuclei: the electromagnetic force replaces the string, and the nuclei replaces the pivot. So there is some energy bottled up there. This is the realm of chemical energy. Chemical reactions capitalize on the energy bottled up in electrons trapped around nuclei. It’s that kind of energy that powers your cell-phone and it’s that kind of energy that can do this.

But that’s not the only place where energy is bottled up in an atom. In fact, there is only a tiny fraction of an atom’s energy in the electrons. Turns out the nuclei is also full of energy. The protons and the neutrons making the nucleus are tied together via the strong nuclear force. If we keep with our metaphor of the pendulum, the string is now that new exotic force. However, it becomes more difficult to define a pivot. I can you could say that the pivot for one proton in the nucleus is all other particles in the nucleus, if that makes any sense.

The energy bottled up in nuclei is responsible for that kind of explosion. It is also the instigator of everything that happens in and on the sun. Grasping how much energy the sun produces is as difficult as understanding how big a galaxy really is. The take-home message is, chemical energy is nothing compared to nuclear energy.

But we are not done yet. Turns out there is another level. The protons and the neutrons also have unimaginable amounts of energy bottled up, and that’s because they are made of quarks. The quarks are also like pendulums oscillating around each other, also held together by the same strong nuclear force. You may have guessed by now that anything that is made of parts and that is held together by something has bottled up energy. That is true of anything. By pulling the parts apart, you can release that bottled up energy. However, sometimes, the energy it takes to take these things apart is greater than the energy it would release.

Another observation you might have made to this point is that the smaller the objects, the more potential energy they contain. That is as long as they have parts. So what does E=mc² have to do with anything? That’s because that bottled up energy in small composite objects turns out to make for most of the mass of the things around you. Take a proton for example. It is made of three quarks. Sum the masses of these three quarks together (~10 MeV) and you get nowhere near the real mass of the proton (~1000 MeV). So what’s going on here?

It turns out the rest of the mass of the proton is the energy bottled up between the quarks. There is so much energy in there that this account for almost the entire mass of the atom. At this point, you may ask, what about the quarks? Are they made of smaller components too? Surprisingly, until last summer, we had no clue. And by no clue, I mean we had no data that pointed directly to an answer. Now we do have a clue.

There is a number of particles that we think are not made of parts at all. These are the ones we call fundamental and the quarks are among them. Other famous fundamental particles include the electrons and the neutrinos. So if these particles are not made of parts, how can they even have mass? Now we know that it’s all thanks to something very similar to the Higgs boson (if not exactly the Higgs boson).

Unfortunately, this is where it gets complicated. Our pendulum metaphor completely breaks down: it is utterly inadequate to explain how the Higgs boson gives mass to fundamental particles. So how do you get energy bottled up without a pendulum? It all boils down to the fact that the Higgs boson is a scalar field.

Mathematically speaking (and I swear this is the closest we are going to get to actual maths), a scalar field is something that is present throughout space. At each point in space, it takes on a particular value. Think of a room full of air. The air is everywhere in that room. If nothing happens inside that room, the air pressure is the same everywhere. The air pressure here is our example of a scalar field.

If you drop a penny inside the room, the penny will disturb the air pressure. When it falls, the air ahead of it will compress, and the air behind it will thin. When it touches the ground, it will send ripples of air pressure throughout the room, commonly known as sound. But notice how, at any single moment, you can describe the entire air pressure situation in that room with a single number at each point in space. If nothing happens, that number is the same everywhere. When the penny falls, that number rises ahead of the penny, and drops behind it, but stays more or less the same everywhere else. When the penny touches the ground, the numbers at each point in the room goes up and down as the sound waves go through them. We use a scalar field to describe air pressure.

The Higgs field is just like that. It has a single value at every point in space. That single value is in fact energy. Since the Higgs field interacts with fundamental particles, that value will change in the vicinity of fundamental particles. In fact, it will rise. There will be energy bottled up in the Higgs field around a fundamental particle caused by the mere presence of the particle. Also, how much energy is bottled up in the Higgs field will depend on the type of fundamental particle.

At this point, you may have many questions. I know I do. I can guarantee you that it will be very hard to find a question about the Higgs boson to which we have an answer. You may ask:

  • Why do the Higgs scalar field have different amounts of energy for different types of particles?
  • Fundamental particles are organized in generations, within which the only thing that changes is the mass. Does the Higgs explain that?
  • What about dark matter and dark energy? Does the Higgs explain the mass they contain as well? They are after all, most of the Universe’s content…
  • You talk about the Higgs boson, the Higgs field, the scalar field, it’s getting confusing!
  • Where does the energy found in the Higgs field come from?

At least, the last two questions have answers. But that is a topic for another post!

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