Of Particular Significance

# The Higgs FAQ 3.0

Matt Strassler [April 9, 2024]

Today the news broke that Peter Higgs has passed away. In honor of his achievements (and those of others around him, most notably Robert Brout and Francois Englert, with special mentions to Phil Anderson and to Gerald Guralnik, C. Richard Hagen, and Thomas Kibble), it seems appropriate to update the Higgs FAQ, to bring to it the perspective of the 2020’s.

If you have no math or physics in your background, you may find it useful, before or after you read this FAQ, to read my brief literary article on Why the Higgs Particle Matters. You may also find my book Waves in an Impossible Sea useful; it covers Higgs-et-al.’s ideas in some detail (as well as exploring the nature of elementary particles and of empty space, and the role that modern physics plays in our daily experience.)

If you have a little math in your background (algebra, trig, and calculus through derivatives) and a little physics (you know what energy is, what a ball on a spring does, and have thought at least once about what waves are) then, after reading this FAQ, you may want to follow up by reading my Particles and Fields articles, followed by my explanation of the Higgs field and how it works.

Ok — without further ado, here we go.

## Basics

• What is the Higgs particle?

Well, we have to start with the Higgs field, which is the key to the story.

• And what’s a field?

As I described in detail in a recent post, a field is something that

1. is present everywhere in space and time,
2. can be, on average, zero or not zero,
3. can have waves in it,
4. and, if it is a quantum field, then its waves are made from “particles” (which, as I explained in my book, are little ripples, and might better be termed “wavicles”.)

So for example: the electric field.

1. It is a part of nature that is found everywhere. At any given point in space, and at any particular time, you can measure it.
2. If it’s non-zero on average in some region, it can have physical effects, such as making your hair stand on end, or causing a spark.
3. The electric field can also have waves, in which the size of the field repeatedly becomes larger and smaller — visible light is such a wave, as are X-rays and radio waves, and all the other things we collectively call “electromagnetic waves”.
4. Those waves are made from “particles”, called photons; the opsin molecules in our eyes absorb them one at a time.

The Higgs field, too, is found everywhere. In fact, it is non-zero everywhere, and this effect causes various other elementary particles to have “mass” (see below.) Its waves are also made from “particles”, called Higgs bosons (absurdly referred to sometimes as God particles, a term that Higgs disliked and I do too, since it distracts from the true importance of Higgs-et-al.’s key ideas.) This type of particle was discovered in 2012.

• Ok, so, what is a particle, and why do you want to call it a wavicle?

A quantum field’s waves cannot be of arbitrary intensity; they can’t be arbitrarily “dim”, or “quiet”. The least-intense possible wave that a field can have is called a “quantum”, or more often a “particle”. It often behaves in rough accordance with your intuitive notion of “particle”, moving in a straight line and bouncing indivisibly off of things, etc., which is why we give it that name.

In the case of the electric field, its particles are called “photons”; they represent the dimmest possible flash. Your eye can absorb light one photon at a time (though it typically waits for several photons to arrive before sending a signal to your brain.) A laser produces very intense waves, but if you shield a laser with a screen so that only a tiny fraction of the light gets through, you will find, if you shield it enough, that the light passes through the screen in little blips — single photons — all of them equally dim. (Click here for a video [BIG! 284 MB and 23 minutes, unfortunately; and you’ll get the point after just 10 seconds] which demonstrates this effect; the screen registers the light one photon at a time. Here’s the webpage it’s from if you want to learn what the whole video is about.) [This video is no longer available, but I’ll find another one shortly.]

Each of these little blips is a little, indivisible wave — a ripple of very small height, or “amplitude”, and of very low amounts of energy. It is to a wave as a grain of sand is to a sand pile, or a sheet of paper to a stack of paper — the smallest amount of wave that you can have. That sounds to me like a wavicle, a term that goes back to the 1920s but didn’t catch on back then. Nowadays it is gaining followers.

With regard to the Higgs FAQ, the key point is this: Higgs particle is to Higgs field as photon is to electric field. Waves in the electric (and magnetic) field are made of wavicles of light, called photons; waves in the Higgs field are made of Higgs wavicles, i.e. Higgs bosons.

• So… a Higgs wave is a ripple in the Higgs field, and the Higgs particle is the smallest — well, `dimmest’ — such wave.

That’s right. Of course this is a very short version of the full story.  To tell the full version of the story without math, in language interpretable by a general reader, was one of the main goals of my book.  A version requiring a little math and physics background, such as one would get from the first few months of university-level physics, is available on this website, here.

## Significance

• Why do particle physicists care so much about the Higgs particle?

Well, actually, they don’t. What they really care about is the Higgs field, because it is so important.

• What’s so important about the Higgs field?

The Higgs field (unlike most of the elementary fields of nature) has a non-zero average value throughout the entire universe. And because it does, many particles have mass [specifically “rest mass”, which is the amount of mass they have intrinsically], including the electron, the quarks, and the W and Z particles of the weak interactions. If the Higgs field’s average value were zero, those particles would have much smaller mass or none at all. That would be a disaster; atoms and atomic nuclei would disintegrate. Nothing like human beings, or the earth we live on, could exist without the Higgs field having a non-zero average value. Our lives truly depend upon it.

• What do we know about the Higgs field?

The Large Hadron Collider [LHC] has carried on twelve years of studies of the Higgs boson since its discovery, and what we have learned about this type of particles tells us something about the Higgs field. We know for sure now that many types of particles get the vast majority or all of their rest masses from the Higgs field. That said, there is still a lot to learn; more on that below.

• Then if the Higgs field is so important, why is there so much hype about finding the Higgs particle?

On the one hand, finding the Higgs particle is the easiest (and perhaps only) way for physicists to learn about the Higgs field — which is what we really want. In that sense, finding and studying the Higgs particle are steps toward the main goal: understanding the properties of the Higgs field and why it has a non-zero average value.

On the other hand, our modern media world insists on generating hype. And since explaining the Higgs field and its role and its relation to the Higgs particle takes too long for a typical news report or interview, journalists, and people talking to them, typically cut the story short. So the Higgs boson gets all the attention, indeed far too much [“good God, particle”!], while the unfortunate Higgs field labors in obscurity, protecting the universe from catastrophe but getting none of its deserved credit…

• Are physicists sure there’s a Higgs field?

Yes. The studies of the last twelve years make this unambiguous.

However there are still things we don’t know for certain yet. For instance:

1. There might be more than one Higgs field, each with its own type of particle (all collectively referred to as “Higgs particles” or “Higgs bosons”.)  So far the evidence is that there is only one, but this is still not firmly established.
2. It is possible the Higgs field is an agglomeration — a “composite” — of several other fields. We have examples of such things in nature already — for example, just as a proton is a composite object made from quarks, antiquarks and gluons, the proton field would be a composite field made from quark, antiquark and gluon fields.  So far, all the evidence is that it is an elementary field, like the electric field. But it’s too early, as yet, to close the doors on a more subtle possibility.

The only way to know how many Higgs fields there are, whether they are elementary or not, and how they interact with the particles we know and perhaps ones we don’t yet know, is to run an experiment: the Large Hadron Collider, or LHC.  That’s what we’ve been doing, and will continue to do.

• What does elementary mean?

Sorry about this, but the answer is circular — it means not composite. It means it can’t be broken into more elementary peices.

Even that’s not quite true. It means that it can’t be broken into parts using the technology we have now. Someday that might change. Indeed people used to think protons were elementary, and before that they thought atoms were elementary (hence the Periodic Table of the “Elements”).

• Are particle physicists sure there’s a Higgs particle?

Absolutely. The evidence for the Higgs boson is overwhelming.

But again, we’re not sure the type of Higgs boson we’ve found is the only one. Study of its properties, and searches for other particles, may give us clues as to the existence of other types of Higgs bosons, or may help confirm it is unique.

• The press — and even many physicists — sometimes say explicitly that the LHC was built to find the Higgs particle! Since that’s happened, isn’t the LHC done with its task?

These statements that you read in the press are not true. The correct statement is that the LHC was built to figure out what the Higgs field is (or Higgs fields are), how it works (or they work), and whether it is (or they are) elementary or composite. Searching for and studying the Higgs particle(s) is the way to do that.

Let’s not confuse the ends for the means! Understanding the field or fields is the end goal, while finding and studying the particle or particles is just the means. The LHC has done a lot, but there’s still much more for it to do before it is shut down. After that, a new “Higgs factory” particle accelerator (perhaps the one I discussed in this post) will help us increase our understanding greatly.

## Terminology

• Why is the Higgs particle often called the “Higgs boson”? (pronounced “boh-zon”)

All the particles in nature — whether elementary or not — can be divided into two classes, fermions and bosons. [There are some weird exceptions inside certain solid materials; I tell you this only to avoid having a brick thrown at my head by some of my colleagues.] It happens that the Higgs particle, like the photon and a few other elementary particles, is a boson. This is related to the fact that the Higgs field can have a large non-zero value across the universe.

• Why is the Higgs particle called the “God particle”?

Because the media thinks it sounds cool and that it gets readers to read their stories. The origin of the nickname is about as non-religious and non-scientific as one could imagine: it was invented as advertising. Professor and Nobel Prize Winner Leon Lederman, a very important experimental physicist who deserves enormous credit for his contributions to the field, deserves some serious demerits for having allowed his book on the Higgs particle to be assigned this attention-getting title… which is somewhere between inappropriate and blasphemous, depending on where you come from. When I first heard him use this moniker in a talk that he gave while I was in grad school, my jaw hit the floor. I knew enough physics even then to know how completely absurd it was.

I have never heard or seen a physicist refer to the Higgs particle in this way in the context of a scientific paper, a talk at a conference, or even an informal scientific discussion. There’s nothing in the mathematical equations, in the interpretation of the physics, in any philosophy of which I am aware, or in any religious text or tradition with which I am familiar that connects the Higgs particle or the Higgs field with any notion of religion or divinity. The nickname is pure invention.

Moreover, each Higgs boson “decays” (i.e. are transformed into other particles) in about a billionth of a trillionth of a second. That means

1. They are no Higgs bosons anywhere around you, or in your town or city; in fact, at this very moment, there are probably none existing naturally anywhere in our galaxy.
2. Higgs bosons haven’t done anything interesting since the very beginning of the universe.
3. We have to make our own from scratch, artificially, at the LHC.

This sounds quite un-God-like to me. The Higgs field, by contrast, is everywhere around and within is, and is of enormous importance. You can call it the God Field if you want, I suppose.

But personally I think it is not healthy for either science or religion to be pushed around by the need of the publishing industry to sell books, or the media to sell stories. The sooner we drop this notion, the better.

## I’ve heard that…

• I hear the Higgs particle decays rapidly, so how can it create or support the Higgs field? What I have read seems to imply that there is this sea of Higgs particles and this somehow sets up the Higgs field. That wouldn’t work if the Higgs particle existed for just an instant.

The Higgs field doesn’t have to be created by a process; it is just there, the way the electric field of nature is just there, always and everywhere. It is integrated into the empty space that makes up the fabric of the universe.

The Higgs field has a non-zero value in nature on average. (The electric field is zero on average). This non-zero value also is just there; it doesn’t have to be generated by a process. It is simply the preferred state of our universe for the Higgs field to be non-zero. We don’t know why, but nobody has to do anything to make it that way.

The non-zero value of the Higgs field should not be thought of as a sea of Higgs particles; that is the wrong intuition. A Higgs particle is a ripple of minimal intensity in the Higgs field; a ripple varies over space and time, just as any wave does. But the non-zero value of the Higgs field is constant over space and time; it does not vary. Here’s a pretty good analogy: the density of the air is a field; it has a constant average value; waves in the air are sound waves; and there is no sense in which the constant average density of the air should be thought of as built up from a sea of sound waves, which are evanescent ripples in the air.

Higgs particles are not formed spontaneously. You have to put energy to work if you want to make them. You have to use something like an LHC proton-proton collision to whack the Higgs field and make it wiggle, just as you have to clap your hands to make sound, hit the surface of a lake to make a ripple, or pluck a violin string to get it to vibrate. Just as a ripple dies away after a while, and a violin string eventually stops vibrating, a Higgs particle will decay away too. The air, the lake, the violin string, and the Higgs field remain behind after the vibrating dissipates.

• Then Higgs particles don’t normally exist? I think this is why you also mentioned that there are no Higgs particles in the room I am in, yet my electrons have mass. What role, if any, does the Higgs particle play in the mass mechanism? I was thinking it might be a force carrier particle like the W boson for the weak force, but it doesn’t sound like Higgs particle is supposed to do this. I also heard that Higgs bosons could bubble into existence by “borrowing” energy for a moment and then dissappearing. So there would be Higgs particles in the room. Do you agree with that picture?

The Higgs particle does not have any role to play in the mechanism by which elementary particles get their rest mass. It’s the Higgs field — in particular, the fact that its average value is non-zero — which leads the various particles to have mass. [To explain this carefully and thoroughly was one of the main goals of my book. You can also look at my video clips on the matter, taken from my old Secret Science Club talk: http://profmattstrassler.com/videoclips/] It’s the field that we really want to understand, not the particle… the particle is a means to an end, not an end in itself.

There are indeed virtual Higgs particles in the room, but virtual particles are not particles at all, despite the name. Higgs particles are nicely behaved waves in the Higgs field, whereas virtual Higgs “particles” are more general types of disturbances in the Higgs field. Higgs particles have a definite mass; virtual Higgs “particles” do not. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ What you’ve heard is the standard “little lie” (or “phib”) that many theoretical physicists usually tell the public. But it is so deeply misleading that it confuses people terribly (as I see regularly, through the questions I am asked). For this reason, I urge you to disregard it.

• If mass is created by a particle interacting (moving through) the Higgs Field then is the field moving or the particle or both? If a particle is static (not moving) relative to the Higgs Field, can it lose its mass?

No matter how you are moving, you are not moving relative to the Higgs field. That sounds bizarre, but remember something else bizarre: that no matter how you are moving, light is moving about relative to you at the same speed, namely 300,000,000 meters (186,000 miles) per second. Our intuition for space and time is not correct — that’s what Einstein figured out — and it is possible for there to be fields that are at rest with respect to all observers! [In my book, I used the term “amotional” to describe the universe and its fields.]

And so a particle’s mass is the same no matter what it is doing — stationary relative to you or moving relative to you. And that’s important, because a particle is always stationary relative to itself! so it always, from its own point of view, should have the same mass.

Analogies which refer to the particle’s mass as having something to do with the field being like molasses, or a room full of people, are deeply problematic, because they make it seem as though a particle must be moving in order to feel the effect of Higgs field, whereas in fact that is not the case. Even worse, they violate the basic principles of relativity, those of Galileo and Einstein. [Again, carefully discussed in the book.]

• Since gravity pulls on things proportional to their mass, and since the Higgs field is responsible for giving everything its mass, there obviously must be a deep connection between the Higgs and gravity… right?

A very reasonable guess, but — it turns out to be completely wrong. The problem is that this statement combines a 17th century notion of gravity, long ago revised, with an overly simplified version of a late-20th century notion of where masses of various particles comes from. Let me bring out my professorial training and correct the statement above with a red pen:

• Since gravity pulls on things proportional to their mass to a combination of their energy and momentum, and since the Higgs field is responsible of giving everything not everything, just the known elementary particles (excepting the Higgs particle itself) its rest mass its mass, there obviously must be a deep connection between the Higgs and gravity, right? wrong, there is no direct connection between the Higgs and gravity

Now let me explain these corrections. [Yet again, carefully covered in the book.]

When you first learn about gravity in school, you learn Newton’s law: that the force of gravity between two objects, one of mass M1 and one of mass M2, has a strength proportional to the product M1 M2.

But that was true before Einstein. It turns out that Newton’s law needs to be revised: the Einsteinian statement of the law is (roughly) that for two objects that are slow-moving (i.e. their speed relative to one another is much less than c, the speed of light) and have energy E1 and E2, the gravitational force between them has a strength proportional to the product E1 E2.

How are these two statements, the Newtonian and the Einsteinian, consistent? They are consistent because Einstein and his followers established that for any ordinary object, the relation between its energy E, momentum p and rest mass M [often just called “mass” by particle physicists] is

• E2 = (p c)2 + (M c2)2

For a slow-moving object, p ≈ Mv (where v is the object’s velocity) and pc ≈ Mvc is much smaller than Mc2. And therefore

• E2 ≈ (M c2)2    (i.e., E ≈ M c2 for slow objects)

Since planets, moons, and artificial satellites all move with velocities well below 0.1% of c relative to each other and to the Sun, the gravitational forces between them are proportional to

• E1 E2 ≈ M1 M2 c4

And since c is a constant, for such objects Einstein’s law of gravity and Newton’s law of gravity are completely consistent; the force law is proportional to the product of the energies and to the product of the masses, because the two are proportional to one another.

But for objects that have high speeds relative to one another, or for objects subject to extremely strong gravitational pulls (which will quickly develop high speeds if they don’t have them already), the Einsteinian law of gravity involves a complicated combination of momentum and energy, in which rest mass does not explicitly appear. This is why Einstein’s version of gravity even pulls on things like light, which is made from photons that have no rest mass at all. (And it is why gravitational waves — waves in space and time, massless just like light — can be formed by objects that are orbiting one another.) Simply put, the Einsteinian view of gravity, now reasonably well confirmed by experiment, differs significantly from the Newtonian view, and in particular, it is not rest mass but energy and momentum which are primary. And all objects, not matter what they are made from or how they are moving from your point of view, have energy — so everything in the universe exerts a gravitational effect on everything else. We say “gravity is a universal force ”(here the term is not referring not to the universe but to the notion of universality — of complete generality.)

By contrast, the Higgs field gives certain particles their rest mass. It’s not universal; protons get their rest mass from something else.

What about the Higgs field being the source for all mass in the universe? This statement, though you will often find it in the press or in glib articles written for the public, is false.

What is the true statement? Well, here is a list of the elementary particles that we know about so far. The massless ones are

• photons, gluons, gravitons (the latter presumed to exist)

while the ones with mass are

• W and Z particles
• quarks: top, bottom, charm, strange, up, down
• charged leptons: electrons, muons, taus
• neutrinos: three types (at least two and probably all three with small masses)
• the Higgs particle itself

Now it is true that the W and Z particles, the quarks, the charged leptons and the neutrinos must get their mass from a Higgs field. It’s not possible for them to have masses any other way. But this is not true of the Higgs particle itself.

The mass of the Higgs particle does not entirely come from the Higgs field!

Where does its mass come from? Oh, that’s a long story, one that ends in a question rather than an answer. [It is discussed in a late chapter of my book.] For now, suffice it to say that the mass of the Higgs particle does not have a single, simple, understood source, and the curious feature is that its mass is so small — this is one aspect of the enormous puzzle called the hierarchy problem.

But in any case, the Higgs field is not the universal giver of mass to elementary particles. The Higgs particle itself gets its mass, at least in part, from elsewhere. And it probably isn’t alone. It is very possible that dark matter is made from particles, and these too probably get at least part of their mass from another source. Dark matter is believed by most physicists and astronomers to be the majority of the matter in the universe; it is believed to provide the majority of the mass of the Milky Way Galaxy that we inhabit. The Higgs field likely provides little if any of that mass.

Other things get their masses from sources other than the Higgs particle. The majority of the mass of an atom is its nucleus, not its lightweight electrons on the outside. And nuclei are made from protons and neutrons — bags of imprisoned or “confined” quarks, antiquarks and gluons. These quarks, antiquarks and gluons go roaring around inside their little prison at very high speeds, and the masses of the proton and neutron are as much due to those energies, and to the energy that is needed to trap the quarks etc. inside the bag, as it is due to the rest masses of the quarks and antiquarks contained within the bag. So the proton’s and neutron’s masses do not come predominantly from the Higgs field. [Experts: There is a subtlety here, having to do with how the Higgs field affects the confinement scale; but even when it is accounted for, the statement remains essentially true.] So the mass of the Earth, or the mass of the Sun, would change, but not enormously, if there were no Higgs field… assuming they could hold together at all, which would not be true of the Earth.

Meanwhile, black holes, some of which have the largest rest masses of any known objects in the universe, holding court at the centers of galaxies, could in principle be made entirely from massless things. One can make a black hole entirely out of photons, in principle. In practice, most black holes are made from ordinary matter, but ordinary matter’s mass is mostly from atomic nuclei, and as we just noted, that doesn’t come entirely from the Higgs field.

No matter how you view it, the Higgs field is not the universal giver of mass to things in the universe: not to ordinary atomic matter, not to dark matter, not to black holes. To most known fundamental particles, yes — and it is crucial in ensuring that atoms exist at all. But there would be just as much interesting gravitational physics going on in the universe if there were no Higgs field. There just wouldn’t be any atoms, or any people to study them.

Finally, you can ask more technically whether, in the equations that physicists study, there is any mathematical connection between gravity and the Higgs field. The answer is no. Gravitational fields have spin 2 and are described as part of space and time; they interact with all particles and fields in nature. The Higgs field, which has spin 0, only interacts directly with elementary particles and fields that also participate in the electromagnetic and weak nuclear forces.

So — the natural guess that the Higgs has something to do with gravity turns out to be false.

1. The Higgs field is not universal: it gives masses to most of the known elementary particles but not to the Higgs particle itself, and not to protons and neutrons, dark matter (most likely), or black holes,
2. Einstein’s gravity is universal and has to do with energy and momentum but not mass directly, and most certainly does pull on protons and neutrons, dark matter and black holes even though their rest masses don’t come entirely from the Higgs field.

It’s really true: despite appearances at first glance, the relation between gravity and the Higgs isn’t even skin deep.

• Since it makes sense to seek a fundamental explanation for the values of the *masses* of elementary particles, why do we not also seek explanations for the particular values of the *charge* and *spin* of these particles?

We do. But in quantum field theory (the type of equations used in particle physics) mass turns out to be very different from charge and spin. The charge and spin of a particle are fixed; once specified, they are determined. But mass can be changed dynamically from zero to non-zero, and once non-zero the precise value of a particle’s mass is determined, in a very complex quantum mechanical way, by the strength and nature of that particle’s interactions with all of the other types of particles. [A similar complexity affects the strengths of forces.] So the question of where the masses (and strengths of forces) come from turns out to be of a very different nature from the question where the charges and spins come from.

## Fundamentals

• Has the Higgs field always been non-zero?

This depends on the history of the universe, which we don’t know well enough yet. It is quite possible that there was an extremely short time when the universe was very hot and the Higgs field’s value was close to zero; it is even possible there was an extremely short time when all of the fields we know about were rearranged beyond recognition (as might happen in a different vacuum of the landscape of fields, sometimes called the “string theory landscape” but this need have nothing to do with string theory.) Or maybe it was a long time. The history of the universe before the Big Bang became hot may have been very short, or it may have been very long; we really have no idea.

However, the Higgs field has been non-zero ever since the current universe-as-we-know-it has been cooler than a few million billion degrees… since a tiny fraction of a second after the current Big Bang is naively thought to have begun.

There are a number of unknown constants that appear in the Standard Model’s equations. These include the strengths of the electromagnetic, weak nuclear and strong nuclear forces, and the numbers that (after the Higgs field becomes non-zero) determine the various rest masses of the known particles. There are a few other numbers that determine how some of those particles decay. And finally, the Higgs particle’s mass is not determined. Although not specified by the equations, most of these numbers have been learned though experiment… obviously the strengths of the forces and the masses of the various particles have all been measured.

You might ask whether the Standard Model predicts anything, since so much has to be determined by experiment. The answer is: “Oh my goodness, yes!!!!” We do have to measure about 20 numbers first, but once that is done, the Standard Model makes tens of thousands of successful predictions, for a huge diversity of experiments over many decades. For instance: it predicts the W and Z particles masses, and how often they are produced at experimental facilities such as LEP, Tevatron and the LHC; it predicts how quickly and to what particles they decay; it predicts how all the other particles decay, in great detail; it predicts the magnetic response of the electron to 12 decimal places and that of the muon to 8 or so; it predicts how often top quarks are produced and how, in detail, they decay … I think I should stop here.

To get tens of thousands (perhaps more by now) of successful predictions out of 20 measured inputs is a huge success. But of course we do very much want to know where these 20 or so inputs come from, and we hope the LHC and other ongoing experiments will give us clues. One must also keep in mind that the Standard Model contains the simplest possible version of the Higgs field, and that may well not be what nature actually possesses. So we’re not just interested in the Higgs boson’s mass; we need to check how it behaves.

See http://profmattstrassler.com/articles-and-posts/the-higgs-particle/the-standard-model-higgs/ and the various articles to which it links.

### 3 Responses

1. Bob Schwerzel says:

Matt, thank you very much for your explanation of how the Higgs field works, and how particles/wavicles interact with fields. This has all been very helpful to me! I’d like to ask, though, if you could dive a bit deeper into the other properties of particles some time when you have a chance? For example, if the fundamental particles like electrons and quarks are actually standing waves of their respective fields, how do they get their properties like charge, spin, or angular momentum? And for that matter, how does a wave develop angular momentum unless it’s somehow spinning in the first place? Are the waves that comprise these particles somehow “compactified” into little spinning vibrations?

1. I can answer a few of these. I have expressed the wavicles (whether standing or not) as though they were given by functions of a single real variable: e.g. F = cos (t), where t is time. That is strictly only appropriate if the particle is described by a single real field.

But intrinsic spin and charge have to do with the fact that many particles/wavicles are waves in a set of fields which may be real or complex. This allows for more complicated waves. For instance, the spin of a photon is already encoded in first-year physics; in an electromagnetic wave, the electric and magnetic fields both oscillate, but with the possibility of circular polarization, which means they are out of phase. That out-of-phase-ness — the circular polarization of the wave — gives the wave angular momentum, in that if it hit something lightweight enough, it could cause it to rotate. Careful calculation of the intrinsic angular momentum of a photon — its spin — shows it is equal to +hbar or -hbar. (Other forms of angular momentum are not intrinsic to the particle and depend on the presence of other particles, so we can’t speak about them in a general way, only in specific cases.)

Similarly, the spin and charge of an electron are encoded in the fact that four complex fields are needed to describe the electron wavicle and positron wavicle. As with a photon, the waves excite all the fields, and their relative phases determine things like spin and charge.

I haven’t gone through the exercise of figuring out the easiest way to show these things explicitly. I’ll put it on my list of potential things to do… but I’m not sure I could present the details any more easily than the first chapters of a Quantum Field Theory textbook.

1. Bob Schwerzel says:

Thanks very much, Matt – this actually helps quite a bit. I had struggled to see where angular momentum came from, but the “out-of-phaseness” of interacting waves and fields gives me an intuitive picture to hang onto, even if I don’t have a firm grasp of the underlying math. And the concept of electrons and protons interacting as waves also helps explain something else I’ve wondered about over the years – why molecular rotations (like a methyl group spinning on a larger molecule) were quantized (and accessible via microwave radiation). I could visualize electronic transitions (visible/UV/x-ray) as stepping between quantized energy levels and molecular vibrations as quantized anharmonic oscillators, but I had no good mental picture for rotations. However, thinking of the atoms in that ethyl group as a collection of out-of-phase waves interacting with the waves and fields of the rest of the molecule, somewhat analagous to the circular polarization you mentioned for photons, helps me see how quantized rotation (at rf frequencies) could arise. I’m sure this is by no means a rigorous picture, but it’s helping me fill in the gaps in my knowledge that have arisen since my grad school days in the late 60s!

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## Buy The Book

A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC