Implications of the Higgs boson, part I

Cosmic microwave background from WMAP, NASA.

It feels like it’s been a while since I talked about some physics. I planned to do a quick list of the different implications of the Higgs boson, but then I got carried away by how fun the details actually are. I hope you reciprocate that feeling.

Here is a collection of thoughts on the Higgs boson. It has been on my mind a lot since July. After all, it is the object of my graduate student efforts. You may ask: Isn’t it already discovered? Why are you still spending time on it? I will answer: What if we never went back to space after Gagarin? There is no such thing as an endgame in the quest of science. If we don’t keep on digging, we may miss out on the deepest implications of the discovery. Possible implications like…

The Higgs as the driver of early Universe expansion

The particle we just discovered at CERN, even if it turns out to be something else than the Higgs, is still something rather special. It is the manifestation of a scalar field, something we never saw before in nature. Wait, what? What is a scalar field and how come nobody makes a big deal out of it? To that second question, I honestly don’t know. I guess only an experimentalist can truly be startled by the fact that we finally observed a fundamental scalar field in nature since theorists have been playing with scalar fields for decades in their models. But the thing is, we know something is amiss in our current understanding of particle physics, and it could have turned out that Nature does not allow scalar fields to exist. For most physicists, scalar fields have been among the first things they played with when learning quantum field theory, so it is pretty easy to forget that we did not even know if they existed.

So what is a scalar field? This is a bit difficult to explain because it requires an understanding of the most (or second most) counter-intuitive concept to come out of quantum mechanics. I name thee, spin! So let’s start from the beginning to make it easy.

We have conservation laws in physics. In fact, if there is one thing you really need to learn from physics, it is the absolute ruling of conservation laws in the Universe. We have conservation of energy, which is the most familiar. But we also have conservation of momentum, which is a little more subtle. Momentum can be seen as “movement energy”. Movement has a direction in space. So to specify the momentum of an object, you need to specify three things: how fast it’s moving, where it’s going, and how massive it is. If the object is twice as massive and going at the same speed, it will carry twice the momentum.

You may already know that everything wants to go in a straight line. In the Universe, going straight is the easy way. If you want to follow a curve, you need a force to help you. The most classic example is being in a car going down a curve. You feel like you are being pulled outwards, but that is just your body resisting going in a curve. Your body wants to go straight ahead, but the car which is turning is not letting you do that. Another classic example is the slingshot. You spin a projectile, but as soon as you release it, it flies away in a straight line. Well, you wish it went in a straight line, that would make it very easy to aim, but it curves back down to Earth because of gravity. Gravity also keep things from going in straight lines, that’s why every body travelling in the solar system is following various curves.

So everything following a curve is subject to a force. Notice that this is true of every object, even it you can’t readily identify the force that keeps it on a curve. If you look at an airplane propeller, what keeps its atoms from flying apart in straight lines away from the rotor is the force that makes it solid: electromagnetism. Electromagnetism is what glue atoms together in the form of various types of chemical bounds.

When things are spinning, we are talking about a special kind of momentum. We call it angular momentum, and it is also a conserved quantity. It is conserved just as tightly as linear momentum and energy. Although to be precise, you can exchange them: you can trade some angular momentum for some linear momentum by suddenly eliminating the force that makes things go round, as in the slingshot example. But if the force that makes the object spin isn’t going away, angular momentum will be conserved.

The big question is: what happens when it comes down to objects so simple they are not held together by any force? If the object has not components, there can be no force holding these components together. Can this object still spin? Can it still have angular momentum? It turns out it can, but in a really, really weird way.

That object without components I am talking about is a fundamental particle such as an electron, a photon, a Z boson, a Higgs boson… What is extremely weird about the angular momentum of these single particles is that it comes in discrete bunches. Wait, what? What do you mean? Speed of rotation is discrete? My brain hurts… Mine too. That special kind of discrete angular momentum, we call it spin. Electrons for example, can only have two possible spin values. Whaaat? You mean, spinning and not spinning? No, even weirder. It can only spin clockwise and counter-clockwise. It cannot not be spinning.

The fact that an electron always have spin makes it a special kind of particle. In the trade, we call these particles fermions. The fact that they always spin makes them behave in funny ways. You can’t pile up fermions in the same state (same position, same momentum, same spin), no matter how hard you try. They will always find a way to distinguish themselves. This is the reason why electrons make up special structures around atoms. You can put two electrons on the same orbit around an atom, but only if they have different spins. If there already is two electrons in that orbit, you can’t put a third, since that third electron wouldn’t have any choice but to spin the same way as one that is already there. If you try to add a third electron to this atom, it will fall on a different orbit, and so on.

Why do electrons behave this way? What does that behavior have to do with their weird “impossible to not spin” property? I have to admit this is very tough for me to answer without pulling out some maths. I have no intuitive understanding of it, only a mathematical one. If you have the patience to go down that road, I recommend reading about Fermi-Dirac statistics. There may be good non-mathematical explanations out there. Let me know if you find one!

There are other types of particles. Some particles are allowed to have no spin. These particles are called bosons. They do not behave like fermions at all: you can pile up as many as you want in the same state. But there are two kinds of bosons: those that can spin, even if they don’t have to, and those that simply can’t spin. The bosons that simply cannot spin are the scalar bosons. This is what the Higgs boson is. This is what the particle that we found recently at CERN is. And this makes it a special particle indeed. You may already have guessed that spin properties give weird super-powers to fundamental particles, and scalar bosons are no exception.

We have this big problem right now in our understanding of the Universe. We are having trouble explaining why the Universe looks the same in all directions. If you have seen images of the cosmological background radiation, which represents the state of the Universe at a very early stage, don’t let it fool you. The fluctuations you see are exaggerated so that you can see them at all, because they are variations of less than 0.01%… So the universe is pretty uniform, but that is not what we would expect from the mind-bending scenario that is the big-bang model.

The big-bang alone predicts much larger fluctuations in the distribution of matter in the Universe than what we currently observe. So we need either a new theory entirely, or an additional mechanism that would smooth things out. What if you just stretch things out until the fluctuations are just too large to be seen? This is what inflation is all about. It is a fairly well-tested idea in the sense that it survived some very precise cosmological data so far. A big-bang model with inflation has something to say about the remaining fluctuations seen in the cosmic background radiation, and it’s all in accordance. Although, in order for inflation to happen, you need a new fundamental field in nature, a scalar field…

So maybe the Higgs boson is the thing that drove inflation, but even if it isn’t, we now know that scalar fields are not just figments of our imagination. In any case, the discovery at CERN changed how I perceive the idea of inflation. It made it more plausible than it was before.

**EDIT: I was told by an esteemed colleague that there are indeed other scalar fields in nature than the Higgs boson. You can indeed take existing fundamental particles and bind them together in a way that will cancel the overall spin of the system. You can have composite scalar fields. A good example are the pairs of electrons formed in superconductors, usually called Cooper pairs. However, a fundamental particle that is a scalar field has remained unseen until this year. A composite scalar field would not have been able to drive inflation because at the time of inflation (10−33 and 10−32 seconds after the Big Bang), the Universe was screeching hot. Bound systems simply could not form: they would be immediately destroyed by colliding with other particles existing at that stage. This is why a fundamental scalar field is necessary for inflation in the early Universe.

Part II

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