So the Higgs is like, everywhere, right?

When I tell people I do particle physics, they generally jump to the first thing they’ve heard of, the Higgs boson. Unfortunately, what most people have heard about the Higgs boson is misleading.

The problem is the “crowded room” metaphor, a frequent favorite of people trying to describe the Higgs. The story goes that the Higgs works like trying to walk through a crowded room: an interesting person (massive particle) will find that the crowd clusters around them, so it becomes harder to make progress, while a less interesting person (less massive or massless particle) will have an easier time traveling through the crowd.

This metaphor gives people the impression that each of us is surrounded by an invisible sea of particles, like an invisible crowd constantly jostling us.

I see Higgs people!

People get very impressed by the idea of some invisible, newly discovered stuff that extends everywhere and surrounds everything. The thing is, this really isn’t the unique part of the Higgs. In fact, every fundamental particle works like this!

In physics, we describe the behavior of fundamental particles (like the Higgs, but also everything from electrons to photons) with a framework called Quantum Field Theory. In Quantum Field Theory, each particle has a corresponding field, and each field extends everywhere, over all space and time. There’s an electron field, and the electron field is absolutely everywhere. The catch is, most of the time, most of these fields are at zero. The electron field tells you that there are zero electrons in a generic region of space.

Particles are ripples in these fields. If the electron field wobbles a bit higher than normal somewhere, that means there’s an electron there. If it wobbles a bit lower than normal instead, then it’s an anti-electron. (Note: this is a very fast-and-loose way to describe how antimatter works, don’t take it for more than it’s worth.)

When the Higgs field ripples, you get a Higgs particle, the one discovered at the LHC. The “crowd” surrounding us isn’t these ripples (which are rare and hard to create), but the field itself, which surrounds us in the same way every other field does.

With all that said, there is a difference between the Higgs field and other fields. The Higgs field is the only field we’ve discovered (so far) that isn’t usually zero. This is because the Higgs is the only field we’ve discovered that is allowed to be something other than zero.

Symmetry is a fundamental principle in physics. At its simplest, symmetry is the idea that nothing should be special for no good reason. One consequence is that there are no special directions. Up, down, right, left, the laws of physics don’t care which one you choose. Only the presence of some object (like the Earth) can make differences like up versus down relevant.

What does that have to do with fields?

Think about a magnetic field. A magnetic field pulls in a specific direction.

So far, so good…

Now imagine a magnetic field everywhere. Which way would it point? If it was curved like the one in the picture, what would it be curved around?

There isn’t a good choice. Any choice would single out one direction, making it special. But nothing should be special for no good reason, and unless there was an object out there releasing this huge magnetic field there would be no good reason for it to be pointed that way. Because of that, the default value of the magnetic field over all space has to be zero.

You can make a similar argument for fields like the electron field. It’s even harder to imagine a way for electrons to be everywhere and not pick some “special” direction.

The Higgs, though, is special. The Higgs is what’s known as a scalar field. That means that it doesn’t have a direction. At any specific point it’s just a number, a scalar quantity. The Higgs doesn’t have to be zero everywhere because even if it isn’t, no special direction is singled out. One metaphor I’ve used before is colored construction paper: the paper can be blue or red, and either way it will still be empty until someone draws on it.

A bit less exciting than ghosts, huh?

The Higgs is special because it’s the first fundamental scalar field we’ve been able to detect, but there are probably others. Most explanations of cosmic inflation, for example, rely on one or more new scalar fields. (Just like “mass of the fundamental particles” is just a number, “rate the universe is inflating” is also just a number, and can also be covered by a scalar field.) It’s not special just because it’s “everywhere”, and imagining it as a bunch of invisible particles careening about around you isn’t going to get you anywhere useful.

Now, if you find the idea of being surrounded by invisible particles interesting, you really ought to read up on neutrinos….

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13 thoughts on “So the Higgs is like, everywhere, right?

  1. Wyrd Smythe

    It’s fun to try to imagine the many, many billions of neutrinos sleeting through my body! Or to try to imagine what it must be like near a supernova where neutrino densities are so high as to make them dangerous.

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  2. Al Sears

    So, what is the meaning of a non-zero Higgs field value? Is there a continuity to the field? I get from the paper analogy that there needn’t be a particle present, but something must (?) be different to account for the different values. Or maybe these aren’t the right questions to ask…

    This is fascinating stuff. Thanks for taking the time to inform us.

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    1. 4gravitonsandagradstudent Post author

      Yes, the field is continuous.

      As for “what it means”, there are two answers I can give you. There’s the procedural, “this is how we do the calculation so this is how it is” answer, and the physical, “yes but what is it” answer.

      The procedural answer is that the Higgs is a scalar field, and a scalar field is a number. 😛

      More specifically, the Higgs field is a number that (almost) all of the masses of the elementary particles are proportional to. If the Higgs field is zero, those particles have zero mass. The higher it is, the more mass they have.

      People can also say that those elementary particles have zero mass, and gain a mass by interacting with the Higgs field. This is equally true! Interacting with some ambient field and having a mass proportional to that field aren’t really different, at least from a procedural, “let’s just do the calculations” point of view.

      All this doesn’t tell you what the Higgs “is”, or where it comes from, though. On that front, it depends on how deep you want to go. In String Theory, scalar fields usually come from the shapes of curled-up extra dimensions. One of them might be the radius of a circle, or the distance between two membranes. Broadly speaking, the Higgs could be something like that. (Unfortunately I don’t know much about the state of the art in using String Theory to produce the Higgs, otherwise I could be more specific!)

      In between those two explanations…well, it’s a field. You’re used to electric fields and magnetic fields, and depending on your familiarity with physics you might have heard that light is just a vibration in electric and magnetic fields. The Higgs is another field, one that doesn’t have a direction, just a value. And just like light is a vibration of the electro-magnetic field, Higgs particles like those seen at the LHC are a vibration of the Higgs field.

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      1. Al Sears

        Aha, thanks for the answers. Fortunately, you didn’t decide to stop after your procedural explanation of the Higgs field! And, to ask a procedural question (I think), is the Higgs field restricted to non-negative values? Also, what, if anything, does the lack of direction imply for the behavior of particles in the Higgs field? I think that I could ask many more questions (some even intelligent), but I’ll stop there for now.

        I love this material. Why didn’t I study more physics?

        Thanks again.

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        1. 4gravitonsandagradstudent Post author

          It’s allowed to be negative, but it wouldn’t do what you’re probably thinking. 😉

          A negative Higgs field means “negative mass”, but in terms of the equations that just ends up switching particles and antiparticles, and the world ends up looking essentially the same.

          The lack of direction essentially means that mass doesn’t have a preferred direction. Whichever way something is traveling, its mass remains the same.

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            1. 4gravitonsandagradstudent Post author

              Sure, scalar fields can certainly have a gradient. But if they have a uniform gradient over all space, then something has gone wrong, much like if there was a uniform electric field pointing one way through all space. The key here is that scalars can have a constant value over all space, with gradient zero and hence no preferred direction. Other fields can’t do that.

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  3. Ben R

    Well, this is a very late reply, but…

    I don’t see how you can argue that only a scalar field can have a VEV because fields aren’t “allowed” to break symmetries. The vacuum Higgs field does break a symmetry. That’s sort of the point of the Higgs mechanism. I don’t know why there’s no vacuum field that breaks Lorentz symmetry (at least none that we’ve detected), but it isn’t because fields aren’t allowed to break symmetries.

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    1. 4gravitonsandagradstudent Post author

      I think the key here isn’t so much that fields aren’t allowed to break symmetries, as that fields aren’t allowed to break epistemically important symmetries. Lorentz invariance isn’t just a symmetry, it’s tied to a pretty basic principle of how we do science, the idea that the laws of physics should be the same everywhere. Electroweak symmetry doesn’t really have that baggage.

      On a more practical level, one can say that the Higgs has to be a scalar because even if Lorentz symmetry is broken, it clearly isn’t broken enough for there to be a constant fermion VEV.

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      1. Ben R

        You seem to be making a sort of anthropic argument that without unbroken Lorentz/Poincare symmetry we would never have developed enough physics to have this conversation. I don’t see why that would be true. Poincare symmetry is in fact grossly broken at everyday scales, and we found it anyway (though it took a while). I imagine we could have done it even with a fairly large Lorentz-violating vacuum field, since it’s just one more layer of obfuscation among many.

        There probably is a gravitational wave background that singles out a preferred state of motion (the Hubble flow) and that can be detected even in a sealed laboratory (since nothing is opaque to gravity). If we manage to detect it, I don’t think it will be a threat to the scientific method.

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        1. 4gravitonsandagradstudent Post author

          Not an anthropic argument so much as an ontological argument. We generally attribute breaking of things like Lorentz symmetry to local conditions (our position on the Earth, in the galaxy, in the Hubble flow), not to global ones. That is, we think of it as being connected to the presence of a thing, rather than simply being a fact of how things are.

          And yeah, now that I think about it that doesn’t really get in the way of a fermion or vector Higgs, since even the scalar Higgs vacuum is potentially also a local condition if you buy in to the relevant multiverse scenario.

          But again, the more relevant point is simply that we don’t see enough Lorentz symmetry-breaking for the Higgs to have plausibly been something other than a scalar.

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  4. Simon Pringle

    Particles are like ripples in these fields….does it follow that the earth or the planets are ripples in the gravitational field?

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    1. 4gravitonsandagradstudent Post author

      No. They cause ripples in the gravitational field, but the earth and the other planets are made of electrons and quarks, so what they are are (complicated combinations of) vibrations in the electron and quark fields.

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