# Why is the Higgs Mechanism so complicated?

Credit: Nature Physics

I’ve done a fair amount of writing describing the discovery of the Higgs, why it’s important, and (a pet peeve of mine) why you should under no circumstances call it “The God Particle.”

The Higgs is now an accepted part of the Standard Model, and while I spend a full chapter in my upcoming book describing the Higgs mechanism, I’ve come to the conclusion that there is no simple, accurate way of describing what the Higgs really does in any amount of detail.

Oh sure, I can say, “The Higgs gives other particles mass.” But that’s not likely to be instructive. I could even late it a step further and say, “It’s all about interaction energy.” Since:

$E=mc^2$

it must also be the case that:

$m=\frac{E}{c^2}$

Then I can simply point out that if, for instance, the W and Z Bosons interact with the Higgs (and they do), then the Higgs must interact with the W and Z Bosons. “Interaction” to a physicist, means energy, and energy means mass — as Einstein tells us. I could even take it a step further and explain how mass shows up in various equations, and put a figure like the one at the top.

I’m not going to.

The Higgs is worth understanding, but if you want to get it beyond an incredibly superficial explanation, I haven’t seen any analogy that does the trick. Richard Feynman once commented about phenomena like this. He was referring to quantum spin, but I think it works equally well here:

We apologize for the fact that we cannot give you an elementary explanation… It appears to be one of few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation… This probably means that we do not have a complete understanding of the fundamental principle involved

And how bad are the normal explanations? Let me give you a few that show up in a lot of the popular press — and more importantly, what’s wrong with them.

1. Some scientists will liken the Higgs field to a cosmic pool of molasses. As particles move through it, they acquire a resistance to their motion — just like mass!

At first blush, this seems like a great picture, until you realize that it leaves a lot of questions unanswered. For instance, why should it be that only some particles interact with the Higgs molasses, and why don’t they interact equally? You and I would be equally impeded by swimming through a thick, syrupy pool, but yet a $Z^0$ is far, far more massive than an electron. And a photon, of course, is completely massless.

The analogy breaks down once you see how it would play out in the real world. Try swimming through molasses. You’ll continually slow down until you come to a stop, and you know that’s not how particles really move. If you remember one thing from your high school physics class, it’s probably Newton’s old (and still true) “Objects in motion stay in motion…”

2. In a related, and somewhat better analogy, Ethan Siegel describes the Higgs field like rain, and all of the particles like sponges. This is better than most, and Siegel does a nice job of pointing out that some sponges hold more water than others (and hence are more massive), but ultimately this gives the false impression that particles have mass because they have Higgses in them.
3. Others describe a celebrity walking into a party. When she walks in, she’s immediately swarmed by admirers, greatly impeding her progress, and significantly increasing her mass. You, on the other hand, can proceed unimpeded. You are meant to be a photon, while the celebrity might be a $Z^0$.

This analogy even won a prize for the best metaphor, but still, it has problems.

The Higgs (the fans) couples to the celebrity, but not to you. Once in motion, the celebrity is then pushed along slowly by her admirers, making stopping difficult. The problem is that the Higgs is one of the heaviest particles, which would mean that there was no explanation for any massive particle to be lighter than the Higgs.

4. Peter Higgs has likened his eponymous field to the index of refraction of glass. Simply by moving through glass, light goes slower than c. Since light travels at a constant (albeit slowed) speed through glass, water, or another medium, at least Newton’s 1st law seems to be satisfied. The problem is that with enough effort you can mostly overcome the limits of mass. Particles have mass, but we’re still able to accelerate them to speeds greater than 99% the speed of light.

The point is that no matter the analogy, you’re likely to encounter a problem. Your gut intuition makes it seem as though mass is fundamental. The idea that mass can imbued through interaction energy just seems anathema to our everyday experience.

-Dave

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