Solving Higgs Field Questions: A Guide

[Coin]

So there are a couple of things I've read lately which at some point attempt to explain the Higgs Boson, one of which is "The Road to Reality" by Roger Penrose and the other one is this page of "one page explanations" of the Higgs Boson. I'm kind of confused by the depictions of the Higgs in both; I get the general idea of the Higgs that's being described, but some of the details have me very confused, and I'm realizing that the confusion I'm feeling over the Higgs indicates I'm confused about what it means for something to be a "particle" in quantum physics altogether. So, I've got a handful of questions if that's okay. I don't know if any of these questions make sense, are stupid, or what. So If there's anything I ought to be reading instead of asking these questions, feel free to just tell me that...

1. The first and main thing confusing me is the way that descriptions of quantum physics, popular ones at least, seem to alternate back and forth between viewing fields as something that particles inhabit, and viewing a particle as being an "excitation of a field". Except I don't think, before I started looking at this Higgs stuff, i'd ever seen a clear explanation of what "excitation" meant. One of the "one page Higgs explanations" says:

Imagine a cocktail party of political party workers who are uniformly distributed across the floor, all talking to their nearest neighbours. The ex-Prime Minister enters and crosses the room. All of the workers in her neighbourhood are strongly attracted to her and cluster round her. As she moves she attracts the people she comes close to, while the ones she has left return to their even spacing. Because of the knot of people always clustered around her she acquires a greater mass than normal, that is she has more momentum for the same speed of movement across the room. Once moving she is hard to stop, and once stopped she is harder to get moving again because the clustering process has to be restarted.
...
Now consider a rumour passing through our room full of uniformly spread political workers. Those near the door hear of it first and cluster together to get the details, then they turn and move closer to their next neighbours who want to know about it too. A wave of clustering passes through the room. It may spread to all the corners or it may form a compact bunch which carries the news along a line of workers from the door to some dignitary at the other side of the room. Since the information is carried by clusters of people, and since it was clustering that gave extra mass to the ex-Prime Minister, then the rumour-carrying clusters also have mass.

As I understand this analogy, in the first case, the field is deforming because something's passing by it-- specifically some other particle which can interact with the Higgs field. But if the field just deforms, and a ripple of some kind is passing through it, then that ripple, or "excitation", itself, is a "Higgs boson". Okay, I think I get that. Here's what I want to know, though:

Do other fields work the same way? Like, the EM field. Is the idea that when a charged particle passes through an EM field, the EM field warps to accommodate the passing particle; but if the EM field just warps on its own, then that's a "photon"?

Is the implication then that ALL the kinds of particles can be viewed this way? Is there an electron "field", such that electrons can be viewed as an excitation or ripple of that field in the same manner higgs bosons are an excitation of the higgs field? Or are there only some particles that can be looked at like this? Just the bosons?

2. The next thing confusing me is the explanation of the Higgs field as being a "scalar field". This is actually something that's been confusing me for awhile-- following physics stuff I occasionally see references to "scalar" fields (such mentions are usually accompanied by a vague air of disgust, like "well, it's a nice theory, but it requires a new scalar"). The Wikipedia page on scalar fields says:

In quantum field theory, a scalar field is associated with spin 0 particles, such as mesons or bosons. The scalar field may be real or complex valued (depending on whether it will associate a real or complex number to every point of space-time). Complex scalar fields represent charged particles. These include the Higgs field of the Standard Model, as well as the pion field mediating the strong nuclear interaction.

Okay, so just to make sure I've got this right: a "scalar field" just means a field where every value is a single number rather than a vector, and the only "known" scalar fields are the Higgs and the Pion. That does make sense. What's a little bit confusing me though is the implication that the fields are scalar because they are spin 0. Is there some kind of simple translation table somewhere where knowing something's spin tells you what kind of vector is described by each point in its field?

(I'm overall kind of curious, for the fields which are vectors rather than scalars, if there's some particular way to interpret the "vector". Is the idea that the EM field is a vector because each point is composed of a value for the electric field and also a value for the magnetic field?)

3. The last thing that's confusing me a bit comes from this one sentence in The Road To Reality:

One of the effects of the act of spontaneous symmetry breaking in the very early universe is taken to be that the Higgs field settles down to have a constant value everywhere. This value would fix an overall scale for the determination of the masses of all particles, the differing values of these masses being scaled by some numerical factor that depends upon the details of each particular particle.

3a. When he says "a constant value everywhere", surely this means "a constant value, except where deformed by the presence of a Higgs-interacting particle or a Higgs Boson"-- right?

I mean, most of the descriptions I'm seeing of how the Higgs field works mention or imply the idea of the Higgs field "bunching up" around massive particles or Higgs bosons. I'm trying to work out how to interpret this in light of the idea the Higgs field is just a mapping from points in space to complex numbers. I'd tend to take this as meaning that in the immediate area of some perturbation in the Higgs field (a Higgs Boson or a massive particle), the values of the Higgs field have a larger-than-normal magnitude, and then immediately around this would be a layer of smaller-than-normal magnitude, and it would gradually smooth out to the normal value it holds everywhere else. Is this basically right?

3b. If we assume the inflationary multiverse, could there be other areas of "the universe" where the Higgs field takes some different constant value? Would this make physics different, since the masses of everything are different?

3c. This question is probably just silly, but: If you could somehow, say you're a mad scientist from a comic book or something, cause the Higgs field to take a different value from the standard in some localized area, would the masses of all the particles in that area change? If you caused the Higgs field to locally take a zero value, would everything suddenly drop to zero rest mass and start flying off in all directions at the speed of light?

 

[di1026]

Is it more reasonable to put your question into the High energy and particle physics area?

 

[mjsd]

I'm confused about what it means for something to be a "particle" in quantum physics altogether.

for your amusement: here is something called "unparticle"

"It is hard to describe this because it is so different from what we are used to. For us it makes a big difference whether we measure masses in grams or kilograms. But in a scale-invariant world, it makes no difference at all."

see http://www.physorg.com/news100753984.html

 

[javierR]

Well, you're intuition is doing well enough...just need to see some more details.

...alternate back and forth between viewing fields as something that particles inhabit, and viewing a particle as being an "excitation of a field"...I don't think...i'd ever seen a clear explanation of what "excitation" meant...

In a classical field theory, an excitation usually refers to solutions to the field equations that propagate, like an electromagnetic wave solution of Maxwell's equations. In *quantum* field theory, the "excitations" are quantized, meaning the propagating entities carrying energy are now discrete bits (the quanta). A "coherent" state of bosonic quanta in the quantum theory can lead to cassical waves, solutions of the corresponding classical theory. This is how EM waves arise from photons. (Maybe you can find some stuff on coherent states and related issues on John Baez's site (at UC Riverside).)

As I understand this analogy, in the first case, the field is deforming because something's passing by it-- specifically some other particle which can interact with the Higgs field. But if the field just deforms, and a ripple of some kind is passing through it, then that ripple, or "excitation", itself, is a "Higgs boson".

Well, the analogy only works so far. To get the understanding you desire, you need to go more technical. Maybe it suffices to say: The Higgs field is fundamentally desacribed by 4 degrees of freedom (4 scalar fields); 3 of these degrees of freedom interact with the weak boson fields in such a way that their quanta hang out with the weak boson quanta, making the overall entity look like a massive boson, while the matter quanta slosh through a coherent state of these Higgs degrees of freedom (this is the classical constant background), which looks like a mass for the fermions; the remaining scalar degree of freedom interacts with the others such that it also feels the constant background, so they look massive as well. This last massive scalar is "the" Higgs boson that you would see in an experiment. The coherent state of Higgs quanta forms a constant background that does not have the behavior of an EM field, e.g., which as you say below is warped by the presence of charged particles...it is not energetically favorable to bunch up anyplace.

Do other fields work the same way? Like, the EM field. Is the idea that when a charged particle passes through an EM field, the EM field warps to accommodate the passing particle; but if the EM field just warps on its own, then that's a "photon"?

In a sense, yes, keeping in mind all of the stuff I said so far.

Is the implication then that ALL the kinds of particles can be viewed this way? Is there an electron "field", such that electrons can be viewed as an excitation or ripple of that field...

Exactly, there are quantum fields for every elementary particle you observe...the particles are the quanta of the field. You can even consider "effective" field theories, in which composite particles "effectively" look like quanta of some field...the theory doesn't work once you get to some high enough energy because you need to consider the interactions of the elementary particles that form the composite.

2. ... a "scalar field" just means a field where every value is a single number rather than a vector, and the only "known" scalar fields are the Higgs and the Pion...What's a little bit confusing me though is the implication that the fields are scalar because they are spin 0. Is there some kind of simple translation table somewhere...

First part, right, but the Higgs is the only example of an *elementary* field, if it exists; while a pion is a composite scalar, described by an effective field theory (see above)...you can consider other composite particles that happen to be scalars (e.g. an alternative to the Higgs mechanism is something called Technicolor wherein the scalars are composed of fermions).
The value of spin for a particle (or field) represents what kind of geometric object it intrinsically is in space...the value of the spin is 0, 1, or 2 is the *same* as saying the particle is a scalar, vector, or rank-2 tensor. You can think of it as telling you how the wavefunction for the particle changes as you rotate to a new reference frame.

...Is the idea that the EM field is a vector because each point is composed of a value for the electric field and also a value for the magnetic field?

Well, there's some technical details in here, which I don't have time for. The short answer is no, you just have to accept that some fields have single values, and some have multiple bits of information for each point they occupy. More technically: If you want to consider the quanta of the EM field, the fundamental fields are the scalar electric potential and the magnetic vector potential, which in special relativity form a 4-component vector of 4-dimensional spacetime. So the EM field in quantum field theory is a *spacetime* vector field.

I leave you here...enjoy

 

[meopemuk]

Imagine a cocktail party of political party workers who are uniformly distributed across the floor, all talking to their nearest neighbours. The ex-Prime Minister enters and crosses the room. All of the workers in her neighbourhood are strongly attracted to her and cluster round her. As she moves she attracts the people she comes close to, while the ones she has left return to their even spacing. Because of the knot of people always clustered around her she acquires a greater mass than normal, that is she has more momentum for the same speed of movement across the room. Once moving she is hard to stop, and once stopped she is harder to get moving again because the clustering process has to be restarted.
...
Now consider a rumour passing through our room full of uniformly spread political workers. Those near the door hear of it first and cluster together to get the details, then they turn and move closer to their next neighbours who want to know about it too. A wave of clustering passes through the room. It may spread to all the corners or it may form a compact bunch which carries the news along a line of workers from the door to some dignitary at the other side of the room. Since the information is carried by clusters of people, and since it was clustering that gave extra mass to the ex-Prime Minister, then the rumour-carrying clusters also have mass.

These analogies can be useful for understanding the connection between particles and fields in solid state physics. For example, the bunch of political workers can be identified with the crystal lattice. The ex-Prime Minister could be the electron which polarizes the surrounding lattice and acquires extra mass as a polaron. The rumor could be a good analogy for phonons - quanta of vibrations of the crystal lattice.

However, I believe that these analogies are not applicable to fundamental particles in vacuum. There is no any "background structure" (analogous to the crystal lattice) in the empty space of vacuum.

Eugene.