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….
4 gravitons 
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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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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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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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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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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Wait, the temperature on earth surface is also scalar. Scalar fields can have a gradient. Gradient can have a direction.
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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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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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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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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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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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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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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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The ripples of particles in the fundamental fields, and the scalar nature of the Higgs field resembles the Aether medium. To be specific, aether is not the medium that fills the space, instead it is space where the manifestation of atomic constructions takes place like electrons and quarks are ripples in the aether itself.
Also as Sir Oliver Lodge says that,” We can’t get hold of aether mechanically(like Michelson-Morley experiment), we can only get through electrically”. CERN detected Higgs field using electricity.
So do Higgs field also a manifestation of aether?
How should we need to consider the ideas of Sir Oliver Lodge in aether? Is it worthy to do the research in Aether ?
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I don’t think it’s a good idea to think of the Higgs as like Aether. The Aether was supposed to be one medium that other things moved in, but the Higgs is just one field among many. It interacts with many fields, but not all of them, it’s not really something that should be singled out beyond having slightly different mathematical properties.
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But what if the Higgs field does have direction, it’s just perpendicular to our 3-space? What if our 3-space is just a membrane defined by the intersection of two 4-spaces with differing physical properties, and what we identify as the Higgs field is just a consequence of the physical properties of the two 4-spaces that intersect to form our 3-space? A 2-space is defined by the intersection of two 3-spaces of different physical properties (if they have identical physical properties no intersection is created), and if you can imagine a consciousness exploring its 2-space and trying to figure out how 2-dimensional matter interacts with its 2-space, that consciousness would have no easier time making sense of the two 3-spaces that create its 2-space than we have making sense of two 4-spaces intersecting to create our 3-space. To my engineering brain this is a more satisfying solution than imagining an in finite and unexplainable scalar field that has arbitrary value “everywhere”.
To me, this also helps to visualize how/why matter “distorts” our 3-space, and gives it a place/direction into which it can actually distort.
It also implies the existence of at least one physical-type property we can attribute to our 3-space: something like a constant of elasticity.
I’m interested in thoughts from people who know more about this stuff than me.
–Mark
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So, while it largely isn’t relevant to what you’re asking, I feel the need to point out that this statement: “if they have identical physical properties no intersection is created” is false. Think about the join line between two pieces of wood, it still exists even if the two are made of the same type of wood.
While there are certainly ways of thinking about the Higgs as linked to some higher-dimensional structure (this is how it often works in string theory for example), it’s not for the reason you seem to have in mind. You seem to think that it would be more plausible if the Higgs, instead of an unexplained scalar field that covers everywhere, was a result of intersecting two four-spaces with different properties. But how are you defining the properties of those four-spaces? If the properties don’t point in a special direction in those four-spaces, then they’re scalars, if they can have quantum oscillations then they’re fields. You’ve just reduced a scalar field to an interaction of two scalar fields, which doesn’t make things any simpler!
Unless you’re imagining these spaces having properties for the same reason everyday materials do, because of what they’re made of? It’s hard to make that kind of thing work without violating special relativity in a detectable way. Probably not impossible if you shrink the scale enough…but ultimately, any explanation of nature would need to be in terms of some sort of simple basic properties of the world like fields, not in terms of objects like atoms, otherwise you’d end up with an infinite regress where everything is made of another smaller thing.
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Thanks for your reply! I really appreciate it!
I want to add some detail to a few of my points. I’m far outside of my day job here, but have been thinking about this for quite a while, and this is my first time to try to measure my wild imaginings against real theory.
First, regarding materials and interfaces…wood is really not homogenous enough to use as an example here. I’m really thinking (in 3-space) of the way energy interacts with (2D) boundaries between different (homogenous) materials that have different material properties. Easy examples include a water/air boundary, water/oil, or two transparent materials of different refractive index (related to density and some other properties). In the macro (non-quantum) world, transverse waves propagate along boundaries between two different sets of material properties. Ripples on the surface of water when a stone is thrown, etc. Key characteristics of that wave propigation are related, not only to the material properties of the water, but in fact to the difference in material properties between the two intersecting materials. Low difference in key material properties (density, viscosity) at the boundary results in relatively low natural frequencies for these waves while large difference in these properties results in a comparatively high natural frequency for the waves. Examine the speed of waves on the surface of water in air compared to the speed of waves on the surface of water in oil, or the speed of waves across a solid homogenous surface (like an iron block) in air. Think further of the way light refracts when it crosses a boundary between two transparent materials of differing properties. In both examples, if somehow two sets of homogenous materials made a clean (idealized) interface but had zero difference in any material property, then no transverse waves would propagate along the interface, and light would not refract when it crossed the interface.
I’ve extended this thought process to the concept of an interface of two different sets of 4D “properties”, just for lack of a better word. And in fact the model in my head DOES have direction. One set of 4D properties is somehow “more” and the other is somehow “less”. It is difficult, and maybe not necessary, to clearly define what the specific properties are as long as we imagine that they are different, and their difference defines the 3D membrane we call home. Enter this new force (or field?) that may or may not be actually working to hold the two 4-spaces together, and in doing so somehow interacts to some extent with things (Higgs bosons? I don’t know…I’m just an Engineer) in the 3D membrane it crosses in a way that pulls (the stuff we call matter) “into” the 3D membrane in the direction of “down”, meaning away from the “less” structure and into the “more” structure.
It bothers me to think that matter, on its own, just because it exists, can act on our 3-space with detectable distortions (gravitational lensing being the easy example). Thinking in simple geometric terms, if all of the interactions that lead to distortion of our 3-space are confined to our 3-space, then the only way a region of space can distort in the presence of matter is through a change in density (matter displaces “something” in space, causing the gradients we can see and measure). I guess to cause the distortion we experience as gravity in that case, there would have to be some kind of reduction in something like density of space elsewhere to make things balance out. So…if space is distorting because of the presence of (massive) matter, and it’s not through displacement or any kind of change in density, then it must be distorting in a direction. And the only logical thing to me, is that it must be distorting in a direction that is mutually perpendicular to our 3-space. To me, this does imply direction, and it does suggest that something outside our 3-space is acting on matter and pulling it in that direction against the resistance of our 3-space membrane. Which leads to my next point:
It strikes me that our 3-space itself needs to possess at least one property very similar in nature to a material property: some kind of elasticity. Simple test: when a massive object (star, planet, black hole, etc.) occupies a particular space, I think we’re all agreed that there’s a distortion in that space (gravitational lensing). But when that object is no longer in that specific space…presumably, that space returns to its normal shape. Regardless of whether or not anyone is comfortable attempting to assign material properties to space itself, it seems to me from this perspective at least that “space” exhibits some behavior that is eerily similar to elasticity.
To bring it all home…in my model, the thing we all experience as gravity is actually the result of some kind of force acting on matter in our 3-space in a direction perpendicular to our 3-space, with the specific numerical values for the relationship between the distortions and the mass being directly related to the difference in “material properties” of the two 4-space structures forming the 3-space membrane we call home. This 3-space membrane is elastic, but not perfectly so—gravitational waves being evidence of losses as massive objects interact with our 3-space. (Is Hawking Radiation actually loss of some energy/material across our 3D membrane, doomed to fall endlessly into the 4D structure I labeled “more” earlier? I don’t know.) Some key characteristics of “physics” in our 3-space are directly tied to “stiffness” of our 3-space, which is in turn a consequence of the difference in the two sets of 4D properties. Maybe even the speed of light itself. Past this point I don’t know enough to tie that together. You mentioned problems with special relativity, and it had already occurred to me that I don’t know if my model can accommodate what we think we know about that (and if it can’t it’s probably super wrong).
I’d love further conversation on why I’m wrong, or what we should do next if I’m right.
Thanks!
—Mark
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Ah ok, you’re thinking about boundaries, not intersections. So not two orthogonal 4-spaces intersecting in a 3-space, but a 3-space as a boundary between two adjacent 4-spaces. That’s also the kind of thing that people investigate in the context of string theory, but it’s also not the kind of thing you need two spaces to get. Think about a video game on a map of fixed size, where the map doesn’t wrap around. When you go to the edge, you run into a boundary, but there doesn’t have to be anything beyond the boundary, it could be that giving the game any coordinate beyond the boundary just makes it crash. You still have a boundary. And if instead of a video game it’s a physical system, you can still have transverse waves on the boundary.
I think you misunderstood what I was saying about directions. I was talking about directions in space-time, not in “property-space”. So yes, your setup has the two 4-spaces with different properties, which can include one of them having more or less of something than the other, analogous to one having a higher refractive index. But within each 4-space, the refractive index is just a number. Compare that to an electric field. An electric field isn’t just a number, it has a direction in space in which it points. That was the distinction I was trying to draw. If you’ve got a number defined at any point in a given space, you generally have a scalar field in that space. If you have something with a direction, then you’ve got a vector field instead. A field is pretty much just a property made physical. That’s why I’m trying to warn you that your instincts here seem to be setting you up for an infinite regress: you can explain fields in our 3-space with properties of hypothetical 4-spaces, but then how do you explain those properties without using fields? Either you keep stringing together higher- and higher-dimensional spaces, or you accept fields as a final explanation at some point.
But thanks for the longer description. I think I understand now what’s making you uncomfortable about gravity and space-time. It seems like a key question for you is whether space-time is a “thing”, with its interactions with matter suggesting that it ought to be. And I can tell you that in a sense space-time is absolutely a thing, it’s the “metric field”, a field that controls distances. One of my old Pages talks a bit about this: Einstein’s theory of general relativity is a field theory, and it has a field that represents the shape of space-time. That field can indeed as you imagine deform and then relax, though for the most part it relaxes much faster than any ordinary material, so it’s not really that helpful to think about it as an elasticity. Matt Strassler has a post coming up on his blog where he’ll describe a property of fields which he’s taken to calling “stiffness”, in those terms the metric field has zero stiffness.
Does that help? I think the reason you’re proposing the kind of picture you are is because pop physics descriptions are usually incomplete, mine included, so it can seem like there’s a big mystery about things that aren’t actually mysterious.
(As an aside: one thing people have looked for at the LHC and elsewhere is “missing energy” of some kind, in part because there are hypotheses in physics that do introduce extra dimensions where we can lose energy. The motivation there isn’t to explain gravity itself, since you’d still need gravity in the higher-dimensional space. Instead, it’s to explain why the Planck scale is so much smaller than other scales of nature, which is a genuine mystery. No “missing energy” has been found though.)
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