*Matt Strassler [October 12, 2012]*

Here is the new (and very long overdue) version of the Higgs FAQ, intended for those with little or no scientific background. *The old version (from long before the Higgs-like particle was discovered in July 2012) is HERE.*

If you have no math or physics in your background, you may also find it useful, after you read this FAQ, to read my literary article on Why the Higgs Particle Matters. Or you could read it first, if you like.

*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.

- What is the Higgs particle?

Do you know what a particle is?

- Not really.

Do you know what a field is?

- Not really.

Okay, let’s back up. The Higgs **field** is the key to the story.

- And what’s a field?

A field is something that

- is present everywhere in space and time,
- can be, on average, zero or not zero, and
- can have waves in it.
- And if it is a
**quantum**field, its waves are made from particles.

So for example: the electric field is a part of nature that is found everywhere. At any given point in space, and at any particular time, you can measure it. 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. 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”.

- Ok, so, what is a particle?

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 a “particle”. It often behave 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.)*

- I kinda get it. A Higgs wave is a ripple in the Higgs field, and the Higgs particle is the smallest — well, `dimmest’ — such wave.

You got it. Sorry for my way-too-short version of the story. *I will try to give a much more detailed and pedagogical treatment of particles and fields, with pictures and analogies and dancing bears, before the end of 2012. A version requiring a little math and physics background, such as one would get from the first few months of university-level physics, is already available here.
*

- 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, including the electron, quarks, and the W and Z particles of the weak interactions. If the Higgs field’s average value were zero, those particles would be massless or very light. 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?

Almost nothing. Mostly just that it’s there, and that it has a non-zero value. We have some limited information about how it interacts with matter, but not much. But the recent discovery of what may be its ripples — the Higgs particle — may soon give us additional insights.

- 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 (or whatever takes its place, see below) 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 the Higgs particle is the first big step 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 particle gets all the attention, while the poor 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**, though I should add comments to that “yes”. We are sure, from the results of many experiments and their successful interpretation with mathematical equations, there is **some field** that has a non-zero average value and makes the electron, the W and Z particles, and many other elementary particles massive, thus permitting our world and our lives to exist. The evidence is more than overwhelming. We call that field the “Higgs field” essentially by definition.

However there are many things we don’t know. For instance:

- There might be one Higgs field, or there might be several of them, each with its own type of particle (all collectively referred to as “Higgs particles”.)
- Or the Higgs field may in fact be an agglomeration or “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 is a composite field made from quark, antiquark and gluon fields — and we don’t know whether the Higgs is an elementary field, as is the electric field, or a composite of more elementary fields, as is the proton field.

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.

- What does elementary mean?

Sorry about this, but the answer is circular — it means “not composite”. Can’t be broken apart into more elementary pieces. Or more precisely, it can’t be broken into parts using the technology we have now. (People used to think protons were elementary. Before that they thought atoms were elementary — hence the “Periodic Table of the ~~Compo~~ Elements”.)

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

We didn’t used to be! The only reason we are almost certain they exist is from recent experimental evidence from July 2012. At that time a new particle was discovered, and all the evidence so far suggests strongly that it is a Higgs particle — but results are still not absolutely conclusive. By March 2013 we may well be sure.

In the past, what we knew for sure was that either

- there is at least one type of Higgs particle, and we will find it (or them) at the LHC, or
- Higgs particles fall apart too rapidly for us to identify them,
**but only because they are strongly affected by new particles and forces**that we will be able to discover at the LHC instead!

And now we’ve learned something: apparently, option 2 is false. Although there might *not* have been a Higgs particle in nature, it appears there is one. And now, to learn more about the Higgs field, we need to see whether this is the *only* type of Higgs particle, and what its properties are.

- The press — and even many physicists — 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 white lies, and deeply unfortunate ones. 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 us not confuse the ends for the means! ** *Understanding the field is the end goal! * Finding and studying the particle or particles is the means, and there is much left to do at the LHC as far as studying the particle that’s been found and searching for others that might be awaiting discovery.

- I’ve read that the Higgs particle has been found. Is that true?

Not as stated, no. The correct and precise statements are

- Using data collected in 2011 and the first half of 2012, a new particle was discovered at the LHC;
- This particle’s behavior is still little-studied, but it is consistent with the behavior expected of a generic type of Higgs particle;
- It is also still consistent with the behavior of the simplest type of Higgs particle — the so-called Standard Model Higgs

In other words: there’s a new type of particle that might well be a Higgs particle of some form, possibly even the only type of Higgs particle in nature, and perhaps even a Standard Model Higgs. But only additional data and study over the coming few years will clarify its true nature… and allow us to understand more about the Higgs field as a result. And meanwhile we’ll also need to keep looking for other Higgs particles that are more difficult to find; just because we’ve found one so far doesn’t mean there aren’t two or five or twelve of them!

- Are you totally absolutely completely 100% cross-your-heart sure that there is a Higgs field in nature?

Yes, yes, yes. I don’t say absolutely yes very often, but here I do. If you try to take the Higgs field out of the mathematics but keep the W and Z particles and the other heavy particles (such as the top quark) that we have **already** discovered and** know** are present in nature, you will find that the mathematics of the Standard Model simply makes no sense. You get a theory that predicts that certain processes (including ones that the LHC can study) occur with a probability bigger than one. Sorry, that can’t happen; it’s logically unsound. The probability of anything obviously cannot be bigger than one or less than zero.

It might surprise you that* it is very hard to write down logically sound theories.* Most theories that you can imagine predict negative probabilities or probabilities bigger than one. Only a very, very few make sense.

To restore the theory of the Standard Model to working order, you **must** add a Higgs field, or something like it, to the fields that we have already discovered experimentally. *But there are many possibilities as to how to do this, and the only way to figure out which one is right is to run an experiment — namely, the LHC!*

- 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 is a boson. But this isn’t actually very important for what it does or why we want to find and study it.

- 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.

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 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.

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 is **not** to 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. 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 in. You have to use something like a Large Hadron Collider 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 they might be a force carrier particle like the W for the weak force, but it doesn’t sound like Higgs particle is supposed to do this. At a recent lecture by Frank Close, I asked him about whether there are Higgs particles in the room and he mentioned that they 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 mass mechanism. It’s the Higgs **field** — in particular, the fact that its average value is non-zero — which gives mass to the various particles. 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.

The Higgs particle is a ripple in the Higgs field, and studying the Higgs particle can tell us something about the Higgs field. For more about this, take a look at my video clips on the matter, from my Secret Science Club talk: http://profmattstrassler.com/videoclips/

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/ So Frank Close wasn’t really lying to you, but he wasn’t really being clear either. What he was telling you is the standard “white-lie” most 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) so 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 meters 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!

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 problematic analogies 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.

- 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~~mass, there~~obviously must be a deep connection~~between the Higgs and gravity…~~right?~~*wrong.*

Now let me explain these corrections.

When you first learn about gravity in school, you learn Newton’s law: that the force of gravity between two objects, one of mass M_{1} and one of mass M_{2}, has a strength proportional to the product M_{1} M_{2}.

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 E_{1} and E_{2}, the gravitational force between them has a strength proportional to the product E_{1} E_{2}.

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 mass M [sometimes called ``rest mass'', but just called `mass' by particle physicists] is

- E
^{2}= (p c)^{2}+ (M c^{2})^{2}

For a slow-moving object, p ≈ Mv (where v is the object’s velocity) and pc ≈ Mvc is much smaller than Mc^{2}. And therefore

- E
^{2}≈ (M c^{2})^{2}(i.e., E ≈ M c^{2}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

- E
_{1}E_{2}≈ M_{1}M_{2}c^{4}

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 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 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 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.)

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 recently discovered new particle with a mass of 125 GeV/c
^{2}(which I will assume for now is a Higgs particle of some type)

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 that ends in a question rather than an answer. I will try to explain it someday. 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 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 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.

And black holes, which are some of the most massive objects in the universe, holding court at the centers of most galaxies, can in principle be made entirely from massless things. You can make a black hole entirely out of photons, in principle. In practise 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 guess that the Higgs has something to do with gravity is natural for a non-expert, but I am afraid it is naive; it comes from misunderstanding both

- the Higgs field, which 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,
- and Einstein’s gravity, which 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 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 is just 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.

- 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 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.

- Why do the equations of the Standard Model of particle physics not yield a prediction of exactly what mass the Higgs particle will have?

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 masses of the known matter particles. There are a few others that determine how some of those particles decay. And finally, the Higgs particle’s mass is not determined.

Although not determined by the equations, most of these numbers have been determined by experiment… obviously the strengths of the forces and the masses of the matter particles have all been measured. We’ll also have to measure the Higgs particle’s mass in experiment (assuming we find it) to determine the number associated with it.

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 then the Standard Model makes 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 matter 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 thousands (probably 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 or 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 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.

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I might suggest that you move the long response as to why the Higgs field and gravity are essentially unrelated to the *end* of the FAQ. Folks who might otherwise balk at reading the lengthy explanation or stop at the introduction of some mathematics will miss the excellent questions that follow …

Great FAQ, BTW, although I think it will still leave the novices scratching their heads over just what a field actually *is* — the details here are still somewhat abstract.

Matt – thanks a lot. The explanation seems to be a little convoluted, but of course this is very much a work in progress. A question of my own: Does the mass of electrons and muons come mostly from the Higgs field, and can we derive the relationship of these two masses?

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I need to start with thank you for all the effort and time you have put into this web site, Thank you.

And there is a very good chance I should not even comment on this site. However , I have read page

after page and so have a lot of other people. One is lead down this path. Again before D and E are

true you need to be sure A,B and C are. Before you can have a field , you need a derivitive, and for

that you need continous time. Can anyone prove time is continuous ? There is a simple story that

shows it is discrete. I apologize if this is inappropriate here.

The equations we use do not require that time be continuous, only that the discreteness of time (if any) be in steps that are short compared to 10^(-26) seconds or so. All evidence from experiments (such as the LHC) indicates that time is approximately continuous down to those time scales. For instance, that is about how long it takes for a Z boson to decay. These experiments do *not* prove time is continuous at shorter time steps. If time was discrete in steps of 10^(-43) seconds, for instance, we wouldn’t know it from current experiments.

When we derive the equations of quantum field theory, we often do (as a crutch) first assume time and space are discrete. We then make the discreteness smaller and smaller, just the way mathematicians do in defining an integral from a serious of rectangular areas. So the derivatives we use are in fact obtained by first taking a discrete version of the theory. Because we use this technique, we can (and do) explicitly check that discreteness in time doesn’t cause a measurable change in the physics equations

as long as the discreteness of time is short enoughcompared to the time scales of the physics processes we are measuring in our experiments.Great post. Thank you. What implication does the recent LHC discovery have, if any, on string theory? e.g. for super-symmetry?

on string theory? none, except for people have a very strong prejudice about how string theory relates to supersymmetry.

on supersymmetry? considerable, but unfortunately very complicated and detailed. Many simple variants of supersymmetry are ruled out, but other simple variants and many slightly more complex variants are still allowed by this data. It would probably be better to wait until we have more data from LHC so that more easily interpretable statements can be made. Maybe middle of next year.

I haven’t heard of a proton field before. Are there quantum fields of more complex compound entities? A gold field, an ethanol field, a DNA field, a VW Beetle field?

The answer is “yes, but”. The concept of a quantum field is something we find useful when calculating quantum phenomena, and if there aren’t any interesting quantum phenomena going on, it’s extra unnecessary baggage that doesn’t help you predict or think.

The art of being a scientist is knowing when a concept, though available in principle, will waste your time in practice; so it is with a quantum field for DNA or VW Beetles, and even for ethanol under most circumstances.Already when we do atomic physics of, say, hydrogen, the notion of an electron field and a proton field, though available, are mostly useless, unless we are doing extremely precise calculations, in which case the electron field becomes needed. But the electromagnetic field [which holds atoms together, and whose particles are photons] must be treated as a field; again it can often be treated as a classical [i.e. non-quantum] field for some purposes, but if you want to understand the light emitted from glowing gasses or hot rocks, you need to use the fact that the electromagnetic field is a quantum field.

This light-footedness on the part of scientists is something that often seems surprising to non-scientists. But for instance we may treat the earth as a point when we try to understand how it orbits the sun; we can’t treat it as a point but may treat it as a perfect sphere when we want to make rough estimates of how much light it absorbs from the sun; but we treat must treat it in great detail as slightly-pear-shaped if we want to correctly predict orbits of commercial satellites. In truth the earth has lots of mountains and valleys, but we don’t need to know those details for most purposes. And yes, a VW Beetle is a quantum mechanical object, just like you, but this does not in the slightest affect most physical processes, and there’s no benefit in thinking about it.

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All we know is referred in the context of the speed light.

observations happen beyond this speed could explain maybe much more!

Such as dark energy or dark matter.

The whole fundamental theory of all(i think) cannot be proven if you consider the speed of light as the limit!

for example: partilcles or detecting energy cannot be observed further more with the assumption that the speed is the limit. I think that E=mc2 is valid within the bounderies of our capabilities of observing thing(entities). Quantum mechanics is a way to assume to predict an observation. But if one dares to exlpain dark energy or particles, maybe one needs to explain dark matter or energy leaving the speed of light.

Thank you for your effort, it was very helpful for me, but I have some questions;

- Do antiquarks have mass?

- If quarks get their mass from Higgs field, and and protons are made from quarks, antiquarks, and gluons, how come protons don’t get their mass from Higgs field?

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Prof Stassler.

As a non scientist, non mathematician I must start by saying thanks for your efforts to make complex ideas understandable to people like me.

It took me some time to get my head round the idea that the speed of light was invariant, now you say that ” No matter how you are moving, you are not moving relative to the Higgs field”. Please could you apply one of your “low-tech” explanations to this concept.

Well, think about ordinary empty space for a minute. If you were out floating in empty space, far from the earth, could you tell if you were moving through it? No. Empty space — vacuum — is as close to nothing as you can imagine. It doesn’t make any sense to ask if you are moving relative to it; there’s no experiment you could do to even ask this question. You can only ask if you are moving relative to physical objects. Even if you and I are moving relative to each other, there is no experiment that we can do which will be able to ask whether one or the other of us is stationary with respect

to space itself.What the Higgs field does is change some of the underlying properties of empty space. But it doesn’t turn empty space into a physical object, and there’s no meaning to asking whether you are moving relative to it.

This is in contrast to what would happen if you filled empty space with, say, air. Now you’ve got

stufffloating around in empty space — and you can ask if you are moving relative to that stuff. If you are, you’ll feel a wind, because the air — its physical molecules — will be bumping into you.There’s no such “stuff” corresponding to the Higgs field, so even if you and I are moving relative to each other, neither of us will feel any Higgs wind — nor is there any experiment that we can do which will be able to ask whether one or the other of us is stationary with respect to the Higgs field. Under normal circumstances, it’s as unmeasurable as space itself.

In fact, the only thing that we can do to really make sure that it is there at all is make it ripple — whack it and see if it wiggles — and that’s what we’re doing at the Large Hadron Collider, where the proton collisions “whack” the universe, and the Higgs particle is a resulting ripple in the Higgs field.

Thanks for that. I have a particular fascination with the idea of infinity, so I have done quite a lot of thinking about empty space. Your illustration makes sense to me, as far as that part goes, but applying the same thinking to the Higgs field seems like saying that the Higgs field is “is as close to nothing as you can imagine”.

I’m fine with the idea that I cannot know if I am moving relative to the Higgs field, because I don’t react with it. However, elementary particles react with it, so should it not be possible to know if they are moving relative to the Higgs field?

On the contrary, you are made from elementary particles, so you DO react with it.

But you (and all elementary particles) interact with it the same way no matter how you are moving. The presence of the Higgs field is NOT like having air in a room. It changes the

propertiesof space; it does not fill space withstuff. The latter provides a notion that you could be moving relative to the stuff; the former does not change the fact that there is no meaning as to being in motion relative to space.This is probably a naive question, but I’m going to ask it, anyway.

You say that a field can be measured as zero or non-zero. If it is measured as zero, in what sense can you be said to be measuring anything? How can you be sure the field is actually there?

You can look for ripples in the field. For example, even in a room where the electric field and magnetic field are zero, the passage of radio waves (or light or microwaves or any other wave in the electric and magnetic fields) through the room proves the electric and magnetic fields exist; an electrically charged object or a magnet will wiggle back and forth as the wave passes — and indeed our radios use this fact.

I came up as Shoogis16, there. Why? I have no idea. I think I can safely blame my wife. :)

In case the same thing happens again, I am Bill Stidwill.

? weird…

I guess I had the idea that if waves could be measured in a field, the field measurement would be non-zero.

I believe I stated the field could be zero or non-zero ***on average***. At some points in the text I may have dropped the “on average” modifier, but where I introduced the idea, the “on average” comment clearly appears.

You are absolutely right, of course, you did say “on average”.

At 72 I am experiencing the excitement of trying to grasp concepts I wish I had had a chance to learn about several decades ago – and never let anyone tell you you will have plenty of spare time when you retire. So please be patient if penetration takes a while.

So far, what I think I have is that fields permeate the cosmos. (Is this theory, or is there any way in which it has been/could be established?)

On average, fields may be measured as zero or non-zero, at any point in space. (Is that their energy?)

We detect fields by observing disturbances in them.

I assume this also applies to the gravitational field, because, although gravity waves have not yet been observed directly, we can detect it only because it is disturbed by the presence of matter and/or energy.

The normal form taken by disturbances is that of waves.

You say that in a quantum field the waves are [also] particles. Are there any fields that cannot be described as quantum fields?

All particles are associated with fields, but only at quantum level is this of significance in the present state of our knowledge.

I would appreciate your comments/corrections – with or without your red pen. :)

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Thanks for your simplified explanation of how everything can be stationary relative to the Higgs field. That makes perfect sense – even to me.

It does leave me wondering about one thing, though: all the explanations I have seen for how the Higgs field gives mass to fundamental particles involves these particles moving relative to the Higgs field.

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I think, through posts on this site, and in other places, I may have answered my own question; both as to why descriptions of how the Higgs field gives mass to elementary particles always involves motion, and how this can work without motion relative to the Higgs field.

William Waldgrave, science minister in John Major’s Government, needed a layman-level explanation of the Higgs mechanism in order to make a case for continued funding for the CERN project. He offered a bottle of Champagne to the physicist who could provide the best explanation in plain English, on one sheet of paper. David Miller won with an analogy that involved Margaret Thatcher walking through a room full of party workers.

How, then, can we visualise the mechanism by which the Higgs field gives mass to elementary particles, such as the electron? We will try to visualise it, first, by thinking of a more familiar field, the electromagnetic (EM) field. It too permeates space, where, on average, its value is zero; only locally is it non-zero. At a time and place at which it is non-zero it may have visible effects, for example, a person’s hair might stand up. Thus we can think of the EM field as being turned on (non-zero) or turned off (zero).

The Higgs field, on the other hand, is, on average, non-zero throughout space. In other words, it is permanently turned on. Those things which react with it, react with it all the time simply by being in its presence. No motion is necessary.

Criticism invited, please.

All of your criticisms of the existing analogies, and your statements about the Higgs field, are correct. The analogies are wrong, because as you say, they involve motion, whereas clearly what the Higgs field does to particle masses can’t have to do with motion, since an electron gets its mass from the Higgs field even when it is standing still. The only thing missing is that what you’ve said still begs the question: “yes, but how does the Higgs field, when it is “on”, give certain particles mass?”

I do plan to write an article soon saying much of what you just said and trying to answer the question of how the Higgs field does what it does, in layperson’s terms and without math. I gave a public talk last week in which I gave this a try, and it seemed to work pretty well.

Thanks for the comments. I didn’t attempt the last question; I don’t have the physics.

I look forward to your “layperson’s” article.

Thanks for a great site, where even an old codger can learn lots. Helps to fend off dementia, so they tell me. :)

Can you explain the relationship between the smallest wave in the higgs field and a particle that you can find in the LHC? You said the smallest wave in the Higgs field moves like a particle – is this this that wave/particle duality? Is this something like pair production where you eject positrons/electrons particles from empty space by sending in gamma ray waves? I can only think of a wave, moving as a wave and would never end up being detectable as a massive particle. Can you explain?

The relationship is *identity*: the smallest wave (meaning the wave of smallest height, or amplitude) in a quantum field

isa “particle.” A better term than “a particle” is “a quantum”. It behaves like a particle because (a) it is indivisible and unbreakable; (b) you can have one, or two, or three, or four of them, but not 23.45 of them or 0.26 of them; (c) it carries energy and momentum and tends to travel in a straight line just like a particle; (d) when it is absorbed or emitted or bounces off of something, it does so as a whole, just like a particle. And yet it remains a wave, too; it vibrates, and it can interfere with itself and with other Higgs particles.Part of the conceptual problem here is the word “particle”; it is misleading. A Higgs “particle”, like a photon or electron or indeed any elementary “particle”, really is a “quantum”; it is particle-like in some ways, wave-like in others, but in some ways it violates our intuition for particles and in some ways it violates our intuition for waves. But to my own mind, a quantum isn’t

bothparticleandwave; it is somewhere inbetweenparticle and wave. (Not everyone you talk to might share this way of talking about it.) The term “wave/particle duality” is unfortunately ambiguous, so the answer is “kind of”: yes, this is one of the things people mean when they speak of “wave/particle duality”.This is not a trivial thing to visualize, indeed I do not know anyone who can visualize it. I certainly can’t. Yet it lies at the heart of why quantum field theory (which is naturally about things that wave) is used to describe “particles”. And the match between the predictions of the theory and the measurements we make can’t be ignored, of course… even though what the mathematics suggests is happening can’t be visualized.

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Going a bit deeper into this idea of a “quantum”, there still seems to be a disconnect between the idea that there is this quantum which is really neither wave or particle and the idea that you can go look for a real tangible particle at the LHC with a mass of ~126 GeV. There is a chasm between what you are explaining from a Higgs field perspective (the quantum) and the actual search for a tangible Higgs boson (reconstruct decays to something with a mass of 126 GeV which poke up in the data). Can you bridge this chasm?

A quantum *is* a thing that has energy, momentum and mass; the real tangible “particle” is a real tangible quantum of a Higgs wave. I’m not sure if the problem you’re raising regards the

wayI explained it (so that it wasn’t clear that quantum=particle) or whether the chasm you’re worried about is the conceptual challenge of understandingwhyquantum=particle.To explain that conceptual issue better will indeed require some more work on my part. I figured out last fall how to explain this using freshman-level math, http://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/. I’ve recently figured out how to explain it, a little less thoroughly of course, without using math, but I haven’t written it down yet. So that chasm, at least, will be bridged this spring.

Following along your math links to the formula mc^2 = hv, we can solve for v if we know the mass of the Higgs particle they found at 120GeV which translates into about 2.139 x 10^-22 Kg. So v = mc^2/h = 2.139×10^-22kg * (2.9×10^8)^2/6.62×10-34 = 27173700906344410876132930513 Hz.

That seems to be an awfully high frequency for it to be a “minimum” frequency for the Higgs field. Is this correct and why would we think it would have such a high minimum frequency? Why couldn’t the minimum frequency be something like 10 hz?

Mr. Strassler you did not comment on whether I correctly interpreted the minimum frequency for the Higgs Boson. 2.71 x 10^28 does seem insanely high. Is this correct and does it make physical sense?

Now that we’ve found this Higgs boson, what exactly does that tell us about the Higgs Field other than it has a really high frequency? It would seem that the existence of the Higgs boson confirms the existence of the Higgs field, but we are no closer to having an inution about how this field interacts with things like electrons.

If I were to make a laser like thing out of higgs bosons and zap it at a photon, what would happen?

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At one point you give the speed of light as “300,000 meters per second”. Of course you meant to say either 300 million meters per second, or 300,000 kilometers per second, but as you well know it’s just a bit less. Might I suggest “just under 300 million meters per second” as an alternative? It avoids confusing the issue with a lot of digits (299,792,458), and yet doesn’t shade the truth. Thanks again for your wonderful web site.

I think this Higgs FAQ has been very useful in understanding the Higgs particle and I thank you for providing answers and incorporating them into your new 2.0 FAQ, but it still left me unsatisfied because there are still a lot of unknowns, like what is the Higgs field “built” out of and what provides mass to the HIggs particle itself and protons and neutrons. That would seem to leave out a lot of important stuff. I am concerned with explaining physics concepts to laypeople and so I “made up” my own models of how things like mass, charge, magnetism and gravity work. I was most concerned about how the describe the Higgs field as being made out of actual physical particles we are familiar with and make it provide the mass of all particles. Since I “made it up” without reference to any existing theories, this might be considered a work of “science fiction” rather than of science, but I thought that readers of this FAQ may be interested in alternate models that a layperson could easily understand. The short 4 page paper can be found at this link:

http://vixra.org/pdf/1305.0075v1.pdf

I referenced and used what I learned from this FAQ to write the introduction to this paper, but after that, the rest is speculation. While it is wild speculation, it manages to unite mass, inertia, and magnetism under the same physical mechanism which only includes positrons and electrons. I would be interested in your thoughts.

(1) The Higgs field is not (in current understanding, which may not be complete) built from anything. Electric fields aren’t built from anything either, nor are up quark fields or W fields. The elementary fields of nature are the fundamental ingredients of the universe out of which everything else is built; the Higgs is one of them.

The Higgs field’s interaction with itself provides its particle with mass, but that interaction is itself very poorly understood as it is very sensitive to subtle effects. At this point you should consider this question only partly answered.

Proton mass: http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-structure-of-matter/protons-and-neutrons/

(2) You are welcome to write science fiction, as long as you are very clear about what science involves. Science is not done by speculation. Speculations have to be turned into precise equations with clear predictions that (at least in principle, if not in immediate practise) can be tested by careful experiments; only at that point, the discussion becomes science.

[quote=Matt Strassler] Speculations have to be turned into precise equations with clear predictions that (at least in principle, if not in immediate practise) can be tested by careful experiments; only at that point, the discussion becomes science. [/quote]

Whilst in no way disagreeing with the above quote, I would be fascinated to know how many (and which) of the following you would consider to be science.

Dark matter.

Dark energy.

Multiverse.

Rolled up dimensions.

Singularities.

Future directed time travel.

Could you please add “Higgs field” to the list ?

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Prof Stassler,

You said the Higgs field (unlike most of the elementary fields of nature) has a non-zero average value throughout the entire universe. Can this field be a potential candidate for Dark Energy ?

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I’ve been trying to figure out an appropriate analogy to describing the interaction of particles with the Higgs field that results in mass for some particles, without drawing the analogy of moving through a crowded room. This is what I came up with:

There is a room full of magical fat that coalesces onto people who exists in the room. A person X exists in this space, and he coalesces a light amount of magic weight on from the air; he can move around lightly. A person Y also exists in this space, and in his existence, he coalesces a lot weight on him; he moves around less lightly. A person Z exists in this space, but he is special and coalesces no magical fat on him at all, and he is able to zip about at speeds unthinkable to X and Y. The encumbering of the coalesced magical fat on the persons are the given mass to particles. Thus, X has less mass than Y, and Z, akin to the speed of light, and having no magical, cumbersome fat on him at all, is mass-less.

Would this be a suitable layman’s analogy to explain the Higgs field on particles?

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Can the VEV of the Higgs field be interpreted as the average of a large number of measurements made on an ensemble of identically prepared states?

More generally, can the eigenvalues of $\phi(x)$ (maybe integrated over a smooth function centered on a particular point) be interpreted as the possible outcomes of some measurement?

My background: graduate student in physics, have taken courses on QFT and the Standard Model.

Thanks!

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Can it be that through this, the concept of mass and energy seem less distinct? “Mass” as such always seemed to be a mysterious property that made everything “solid”. When you look at it from the perspective as “just” an interaction with the higgs field, perhaps the term mass is incorrect in a way.

Isnt it more the interaction between fundamental fields (higgs and weak force for example) that results in the rise of the gravitational force (“mass”) in the gravitational field. Also, is it the rise of gravity that warps spacetime, or is it the warping of spacetime due to higgs field interactions that originates the gravitational force?

And is it a coincidence that the same properties of “matter” particles (ie half integer spin) that cause them to clump together (higgs interaction, mass, gravity), but also keep them from occupying the same space (pauli excl.), so forming 3d structures?

A further hint towards a theory of QG perhaps? I mean, there was always a gut feeling that relativity was not a fundamental theory, but a derivative, a large scale approximation, of some more fundamental phenomenon.

1) ““Mass” as such always seemed to be a mysterious property that made everything “solid”. When you look at it from the perspective as “just” an interaction with the higgs field, perhaps the term mass is incorrect in a way.”

The notion that “mass is what makes things solid” is really inherited from what mistaken intuition learned in chemistry and first-year physics class. But mass is *not* what makes things solid. Solidity of things has to do with the structure of ordinary matter and how it is formed. The mass is just stored inside those things, but has nothing to do with the solidity at all.

Mass has to do with the energy required to have an elementary particle, or to stick elementary particles together. Elementary particles are really ripples in fields. The mass of an electron is simply the energy required to make a stationary ripple in the electron field (i.e., make an electron), divided by c^2. The Higgs field gives mass to electrons by making the electron field “springier”, and thus forcing you to use more energy to make an electron.

There’s no connection at this stage with gravity. Even if there were no gravity, what I just stated above in the previous paragraph would be true.

Gravity is a response of space-time to the presence of energy. Energy stored in mass of objects is the most familiar source of gravity in nature — the energy stored in the mass of the earth distorts space-time, and the moon responds by moving in orbit.

There’s no connection with quantum gravity here.

[quote=MS] Mass has to do with the energy required to have an elementary particle, or to stick elementary particles together. Elementary particles are really ripples in fields. The mass of an electron is simply the energy required to make a stationary ripple in the electron field (i.e., make an electron), divided by c^2. The Higgs field gives mass to electrons by making the electron field “springier”, and thus forcing you to use more energy to make an electron.[/quote]

This is a naïve interpretation, so I need to check it, please.

Elementary particles are ripples moving through fields, but they are not actually particles unless they stop moving.

The eventual mass of a particle is proportional to the energy needed to stop it moving.

Without the Higgs field a wave can be stopped, and a particle formed, with relatively little energy,

The Higgs field changes the electron field such that more energy is needed to stop a wave and form a particle.

This seems to say that without the Higgs field an electron would have mass, but it would be somewhat less than it is in the presence of the Higgs field.

1) Elementary particles are ripples at all times, whether stationary or not. A stationary ripple is a particle that is not moving (it is rippling in place, like a wave on a violin string.) A moving ripple is a particle that is moving.

2) The mass of a particle is proportional to the energy that was needed to create the stationary ripple — and since moving ripples have more energy, this is the *minimum* energy required to create a ripple, stationary or not.

3) There’s no issue with stopping the wave; the problem was creating it in the first place. For the known particles this takes arbitrarily little energy without the Higgs field, but the amount required goes up once the Higgs field’s average value isn’t zero.

4) The Higgs field changes the electron field so that more energy is needed to create a ripple in the electron field.

5) Without the Higgs field it would require arbitrarily low energy to create a ripple in the electron field, and you can’t create a stationary one at all — which is the statement that the electron would be massless without the Higgs field and would move always at the speed limit (c, the speed of light). Just like the massless photons that make up light, a massless electron could never be stopped or slowed.

Thanks for the prompt clarification. The confusion arose because I interpreted “stationary ripple” as a wave that had been stopped, rather than as a standing wave, which would have made more sense.

This is just another example of the gap between what experts say and what “hitch-hikers” hear.

It needs pictures and animations. I have a Fields and Particles (with freshman-level math) section which has a lot of the animations that you might want. Following that there’s a “How the Higgs Field Works” section. I’m planning to update it for a non-math audience, but that will take a good month of work, and I haven’t had the time.

There’s that shoogis 16 again, sorry, I’m not really pretending to be someone else :)

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Hi,

I have spent many hours recently on this blog and I am sure I will spend many many more. It’s simply fantastic! My physics is on level of basic engineer physics course, but I would like still to put some questions (I guess I am at the level, the blog is addessed).

1. So I noticed that Higgs field has a very interesting property that you cannot move in reference to it. It’s a bit analog (but a reverse situation) to light in special relativity, which always moves at constant speed from you. It might be that it’s just as counter-intuitive as with special relativity, but my thinking is that it implies actually Higgs field to have a constant value in the universe, because if it wasn’t constant, then by measuring it’s value we could have detected our motion by detecting a change in the field value.

I don’t remember enough to know if such field must have potential energy or not, but it seems to me it could have any arbitrary value?

2. Relativistic fields don’t have constant values: mass (or strictly speaking energy) influences gravity, electric charge electromagnetic field etc, but if Higgs field is “flat” then there is nothing equivalent? OK, I know that we have no idea about Higgs field nature yet, but anyway… I agree that knowing the nature of this field is more interesting that the boson itself.

1. Your guess that “It might be that it’s just as counter-intuitive as with special relativity” is correct. The special thing about a Higgs-like field is that even though if it has a constant non-zero value, it maintains special relativity as it was before. If it wasn’t constant — say it changed gradually from one place to another — then yes, that would define a direction and a frame of reference with respect to which we could define our motion. But not being constant would also cost energy, so the field would settle back to being constant if it could.

The field does have potential energy, which varies as a function of its non-zero value, and its non-zero value lies at the minimum.

If you took physics once upon a time, and it sounds like you did, you might want to read my series

http://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/

and

http://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/

which require only first-semester undergraduate physics and have lots of diagrams and simple equations that illustrate many of these points.

2. The Higgs field can be non-constant in principle; the Higgs boson is in fact a ripple in that field. But the energy required to make the Higgs field be non-constant, non-rippling and with a value significantly different from usual in a large area is so enormous that even around black holes the gravitational effects on the Higgs field are extremely tiny. You’d need to be microscopically close to a place where Einstein’s gravity goes singular (the central core of a black hole) before you’d see any effect. Similarly electromagnetic effects are always tiny. One place where the Higgs field could in principle have a little dimple in it is right around a particle that it makes heavy… such as a top quark. But even there, this is an ultra-microscopic effect and unobservable.

Finally, if a top quark and top anti-quark are close enough, there is a non-constant Higgs field between them, over a distance of about 10^(-17) meters, something like the 1/r^2 electric field between an electron and a proton, but falling off exponentially after 10^(-17) meters. This effect MAY be observable in the next 30 years, as a small shift in the production rate for top quarks. I actually wrote my first particle physics paper about this: http://prd.aps.org/abstract/PRD/v43/i5/p1500_1

Thank you for your kind answer. Actually, reading the maths pages helps a lot with understanding it. Furthermore, it answered more questions I have had. I have noticed that some people like to have their own “theories” because they don’t understand math at all, and take the analogies you provide as actual physical link between different phenomena. I’d say that thanks to some math this is the best science web page I have ever found.

I’d like to ask an additional question:

Since all quantum fields “fill in” the whole time-space, which is still constantly expanding, and vacuum has its zero-state energy, that would imply a constant increase in the whole universe total energy, unless it’s compensated by an equal growth of negative energy (like gravity potential). Is this how it is currently understood?

I hope you have one or two more questions.

Greetings professor Strassler, thank you for this amazing faq, really helpful for non-scientists like me :)

A question:

If i understood correctly: By “giggling” the space at a certain point (by smashing particles) we can see a higgs particle appearing, which appearance show us the presence of the non-zero value Higgs field. If i understand correctly Higgs Field is everywhere, a characteristic of how the (our;) Cosmos works.

I wanted to ask: You said about that field having (non zero) values. Can we make a “map” of that field? I want to say that for example I can make a 3D map of the “electric field of my room”. The x-y-z points inside the room walls where the electric cords are, will have a big value of 220v (assuming a device is plugged), where as the x-y-z above my head has 0v. Does Higgs field have the same characteristics (bound to x-y-z and/or time) and if so, can we cartograph the Higgs field values in space around us (then we wonder if there is a place somewhere where Higgs field is 0? -well if Higgs field is essential for matter to exist there should not be such a “place”?) and would that mean different Higgs field values in places across space, different effects of Higgs field onto the other particles? (even if variation of Higgs field values goes very far away to change even slightly -so around the earth/solar system/galaxy/whatever that field feels like a “constant” but actually is not?)

So can i sale my old house and put the price a little higher by saying my house has nice view, parking, and the strongest Higgs Field in the area for all the family to enjoy?

Thank you!

Dimitris

please excuse any grammar mistakes -non native English speaker

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