Of Particular Significance

The Higgs FAQ 1.0

This page is out of date and superseded: please check out the Higgs FAQ 3.0 instead.

Here is the first version of the Higgs FAQ. I am sure I will add to it, and I promise over time to make some of the more obscure remarks clearer by adding pages of their own. It’s way too much to do all in one day! Sorry. Please feel free to make comments about what you find unclear or ambiguous in what I’ve said; I will use your responses to improve my answers. (That goes for my other pedagogical pages too, of course.) 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.

  • So, what’s a field?

A field is something that

  1. is present everywhere in space and time,
  2. can be, on average, zero or not zero, and
  3. can have waves in it.
  4. 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. It can also have waves — visible light is such a wave, as are X-rays and radio waves.

  • Ok, so, what is a particle?

A quantum field’s waves cannot be of arbitrary intensity. The least-intense possible wave that a field can have is called a particle, and 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 absorbs 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.

  • I kinda get it. So the Higgs particle is the smallest possible Higgs wave, and a Higgs wave is a ripple in the Higgs field.

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, at a later time.

  • 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 has a non-zero average value. 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. 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.

  • 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:

  1. 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”.)
  2. 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 electron 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?

Absolutely not! Don’t Panic!!!!!!!! Just read on, please, carefully. What we know for sure is that either

  1. there is at least one type of Higgs particle, and we will find it (or them) at the LHC, or
  2. 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! At a later time I will explain exactly how new particles and forces can make the Higgs unobservable, and why the particles we know so far cannot do so.

Either way, we learn something about what we want to know: how does the Higgs field work? The LHC was designed to be virtually certain of answering this question. So there might not be a Higgs particle, but that is perfectly ok: we will still be able to use the LHC to achieve the real goal, which is understanding the Higgs field. That said, doing so could be quite easy and start happening this year, or it could be very, very difficult and take up to a decade in the worst cases.

  • But the press — and even many physicists — say explicitly that the LHC was built to find the Higgs particle! What’s going on?

Well, what can I say? These are white lies, and 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 the Higgs particle(s), or whatever takes its (their) place, is the way to do that; and failing to find the Higgs particle or particles does not mean failure of the endeavor! It only implies that one has to find the particles and forces that make it possible for the Higgs particle to be absent. Let us not confuse the ends for the means! Understanding the field is the end goal! Finding and studying the particle is the means, and other means will do just fine at the LHC if the Higgs particle’s absence forces us to use them.

  • I’ve read that the Higgs particle will be found or excluded in the next year or two. Is that true?

Not as stated, no. What is true is that the Standard Model Higgs particle — the particle of the simplest possible Higgs field, which involves one and only one elementary field added to the other types of fields we know — will be found or excluded this year (2011) or next, barring a problem with the LHC. (Already a third of the possible mass range for the Standard Model Higgs particle has been largely excluded, using the LHC data set from the first half of 2011.) But if the Standard Model Higgs particle isn’t found, that just means that the simplest possible Higgs field is not what nature has to offer. It may then be several years more before we figure out why we didn’t find it. It could be that

  1. there is no Higgs particle (but then we know there are other discoverable new particles and forces that are responsible)
  2. there are several Higgs particles (in which case they will typically be harder to produce and take longer to find than the Standard Model Higgs particle)
  3. there’s only one Standard-Model-like Higgs particle, but it is harder to find than expected because previously unknown particles and forces cause it to behaves in unexpected ways.

In all of these cases, the world is a richer place than if the Standard Model Higgs particle is found. So don’t be disappointed if we don’t find the Standard Model Higgs particle. I won’t be! I’ll be thrilled!! Because it means that there’s more to nature’s story than just one simple new field and its one simple new particle. It will take longer, but the LHC should be able to get to the bottom of it (or, at least, well into the thick of it.)

  • 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 it. To understand the distinction between fermions and bosons is kind of off-topic. I’ll add some words about this at a later time, and on a different page.

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

Because the media thinks it sounds cool and 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.

236 Responses

  1. IMO : The speed of light is relative constant around massive objects like the earth up to a certain distance of extinction.
    So the speed of light is also constant around Venus and Mercuri.
    I.I Shapiro made radar reflection experiments and got results he did not understand.
    IMO you can understand his result if you postulate: the above assumptions and the next experiments.
    Experiments to Determine the Mass Related Lightspeed Extinction Volume.

  2. Professor,

    A wonderful FAQ written in a lighthearted fashion. But I have a question (Of course.)

    Given your explanations of how a nonzero Higgs field mixed particles I had got the impression that the Higgs particle (Or virtual equivalents) caused mass but now I think I may have to adjust my thinking. Can you tell me which (if any) of these ways of looking at things is most accurate?

    1.) Particles are constantly swapping between left and right types really, really fast so on longer timescales it looks like they are an average of the two (Much like how a proton looks elemental when seen on nuclear scales but can be seen to be composite when examined on smaller scales.)

    2.) The nonzero Higgs field allows the left and right particle fields to affect each other so that ripples in one field inevitably cause ripples in the other and vic versa. (Much like how two objects in a vacuum can’t pass (much) heat between them, but if the air pressure field’s value increases they can pass heat between each other more efficiently until eventually warming one inevitably brings both rapidly to the same temperature.)

    3.) The Higgs field causes the left and right particle fields (or particles) to become indistinguishable no matter how they are measured. (That is they are not swapping back and forth between two distinct states really quickly but the two states themselves have become indistinguishable.)

    4.) The nonzero Higgs filed causes the left and right particle fields themselves to combine so the two fields become one and the particles we know are ripples in that filed. (Not like the proton field which, though composite does not remove the quark and gluon fields from independent existence.)

  3. As an interested amateur who gained a degree in physics a long time ago, I have found your site fascinating. Thanks for all the time you have put into it.

    Two questions that have been troubling me since I started trying to understand the Higgs Field idea:

    First, how does the concept of a Higgs Field (and, indeed, the other universe-wide fields you mention elsewhere) square with Special Relativity’s equivalence of all inertial frames? Wouldn’t such a field be stationary in one frame but not in any other? Or is my ‘picture’ of a field missing something?

    Second, how does the mass resulting from particles interacting with the Higgs Field then go on to distort space-time to give rise to gravity, as per General Relativity? Is this an intrinsic part of the interaction with the field, or is it thought to be a separate process?

    1. “Wouldn’t such a field be stationary in one frame but not in any other? Or is my ‘picture’ of a field missing something?”

      No. The Higgs field is not like an ordinary medium, like air. It is stationary in all inertial frames, from the point of view of all observers… like the vacuum itself. You can think of it (and all scalar fields) as an adjustable property of the vacuum.

      Regarding mass and gravity: Newton’s theory of gravity involves mass, but Einstein’s does not.

      1) In Einstein’s theory of gravity, it is *energy* that gravitates, not mass. So gravity pulls on all energy, including the energy of massless particles, such as photons. In short, all particles gravitate whether or not they have mass. You can make a black hole out of massless particles.

      2) The Higgs field provides mass (in a way that I’m going to explain in future articles on this site) to some particles. Particles that are at rest have E = m c-squared, so for particles that don’t move much or at all (such as the atoms that make up the earth) the energy and mass of particles are proportional. That’s why Einstein’s theory of gravity gives the same answer as Newton’s, to a good approximation, for things like the earth. All the Higgs field is doing, from this point of view, is changing the energy of certain particles. This changes the details of how they gravitate. But they were already able to gravitate.

      Logically, (1) comes before (2). Gravity is universal; the Higgs field only provides mass to most known particles, and probably does not provide mass to others we haven’t discovered yet, such as dark matter.

      In fact, the Higgs field does not provide all of the mass of the Higgs particle! There is an additional source whose details are not known, but which has to be there.

  4. I found this page by asking a simple question that I’m not sure I’ve been able to find the answer to. The Higg’s Field assigns ‘mass’ to the various particles that interact with it, thus allowing structure to form as the particles come together to form heavier and heavier things, thus assigning more energy to them (atleast during their creation). But the question I actually wanted to ask was does the Higg’s Field only interact with each particle a single, distinct time, or as a continous activity that could potentionally be used to influence those particles again and again under changing circumstances.

    I came upon the question by doing a very nerdy thing of asking myself how the Higg’s Field could be used to allow us to produce larger amounts of energy with less input; and I’m kinda embarrased to admit it, rather it could be the key to creating the first conventional Faster-Than-Light means of travel. I am not that big into math and the like, though, so this was me just popping things in my head to see if they made relative sense to me.

    In any case, thank you for the great answers you’ve provided!

    1. Hmm… The Higgs field does not “assign” mass to various particles; that’s not a good term to use. The correct statement is that when the Higgs field is nonzero, as it is everywhere in the known universe, other particles, by interacting continuously with this ubiquitous field, develop a mass — and the mass is proportional to how strongly they interact with the Higgs field. So it is indeed a continuous process. One way to say it is that the Higgs field being non-zero changes the environment in which all the particles are moving around, and the shift in their masses is an effect of how they interact with the new environment.

      I’m afraid that you can prove that the Higgs field will not give you any way of beating Einstein’s speed limit. The mathematical theorems that forbid such things in Einstein’s theory are fully obeyed in the presence of an non-zero Higgs field. And the same is true for conservation of energy. [Oh yes, people certainly check such things!]

  5. Dear Mr Strassler,

    Thank you for devoting your time to answering our questions, great help!

    I am a typical lay enthusiast currently reading up on quantum theory. I would like to know if the hypothesized ‘Zero point energy field’ is exactly the Higgs field? If so, would the discovery of the Field open the door to explanations of many baffling quantum behaviours i.e. quantum entanglement ?

    Many thanks!


  6. Ah, Rahul, the big question. Think of it like this. We can think of a grain of sand, and that is certainly a particle. We can look more closely, through a microscope, and we will see that the particle of sand is in fact made up from smaller particles, called molecules. And when we look more closely at molecules, we find that they too, are made up of yet smaller particles named atoms. The name was given by aan ancient greek philosopher named Democritus, who proposed everything to be made of the smallest iriducible particle, the atom. This is where certainty becomes a strange entity, for it seems clear that atoms themselves are made up of yet smaller particlesL Lots of them.

    And they have “behaviour”. They seem able to be in two places at once in some cases, and strange agglomerations.
    The two main classes of particles are named Fermions and Bosons, together they make up “The Standard Model” which you can Google. The recent celebrations concerning the Higgs Boson concern what I have seen described as a “Sigma 5” level of certainty on it’s discovery, but some more recent statements are a bit more reserved. The truth is, it doesn’t really matter. Either way, it is a higgs like particle, and if it can be found in the collider then it’s existence in nature is not an unreasonable perspective to view backwards in time to the big bang from. The Higgs field was proposed as being neccessary for objects to have mass, and a single particle being the simplest wave, the particle was expected, but not presumed. I think. Don’t take my word for it, go and read some dummies guides and visit the CERN website. It’s all good. I sympathise.

  7. Will you please explain about what a particle is in a little simple language? I couldn’t understand it.

  8. Website-related. Not physics:

    I’ve tried to print your pages to get hard copies (I’d much rather read from paper than a computer screen). Since that didn’t work, I’ve tried to generate a pdf of the page(s) and it comes out looking the same. The whole left side (about a third or more) gets chopped off. It is also true of your “Virtual Particle” article, and perhaps others.

    Is this by design or something that should be fixed?

    Note: The brief article called, “The First Version of the Higgs FAQ” works ok.

  9. Could the reason for the uncertainty principle be that parrallel universes have stronger Higgs fields that force matter and energy through some sort of channels into this universe?

    1. The uncertainty principle is an inevitable result of particles actually being waves in quantum fields. We know why it exists and behaves as it does.

      In short, if you want to know where something (that is, a wave) is, you must stop it moving about, and the only way to do that perfectly is to bump it from all sides infinitely much, which means its speed becomes infinitely uncertain. (You can see this in a circular cup of water, tap the side right and a wave will form on the outside and move in from all directions into the center of the cup.)

      On the other hand if you want to know the speed of something you need an infinitely big space to measure it, so you can be absolutely, totally sure. (Imagine trying to measure the speed of a wave in a cup, where it is always bouncing around and hitting the sides vs measuring the speed of a wave in the ocean where it can take a long time to hit the shore.)

      Both of those examples are total lies, but they’re a nice start, you really need to understand a bit about waves and how they work before the truth of the uncertainty principle becomes obvious. (For a long time I had no idea how it worked.)

  10. Does the Higgs field’s magnitude diminish over time? Could that be why the universe is expanding so fast, but not puled apart? Again, I don’t know much, just wondering.

    1. As far as we can measure, the Higgs field has been essentially constant for several billion years, to a precision that I believe is of order one part in 10^6. Moreover, the success of the equations for the Big Bang in predicting the abundance of helium and other elements created in the early universe would suggest it has been constant even since the first few minutes of the Big Bang, to good precision (not sure how good).

      1. I’ve seen the higgs field ‘potential’ often given the analogy of the bottom of a wine bottle, with the distance from the rim to the centre being the VEV and the curvature relating to the mass of the higgs boson.

        Does your statement that the higgs field being essentially constant just refer to the value of the VEV?

        Could the mass of the higgs boson have varied over time without effecting the abundance of elements from the big bang?

        Could the actual value of the higgs field ( the particular location on the rim of the wine bottle ) slowly vary across space-time ( perhaps constrained by some global topological twist ).

        1. My statement refers to the “vev” (vacuum expectation value, i.e., what it’s doing when nothing else is going on)

          Could the mass of the Higgs have varied over time? Not likely; the mass and vev are outputs from the “wine bottle potential”, and it would be extremely challenging to make a theory where the vev would naturally be constant but the mass would vary.

          There is no possible topological twist in three dimensional space for a Higgs of the form we have in nature (a doublet of SU(2)). For some types of Higgs fields (which would predict the wrong value for the W and Z mass ratio, among other things), a twist is possible, but the variation in the field would not be slow; it would collapse to form something microscopic (a magnetic monopole.) See for example http://www.phys.ufl.edu/~fry/7097/monopole.pdf

  11. You mention that atoms and atomic nuclei would disintegrate if the Higgs field value were 0?
    Can you expand on that? Is the issue is related to mass? But protons and neutrons in the nuclei get
    mass from strong interactions rather than the Higgs mechanism. Is it related to electromagnetic forces being replaced by electroweak forces? Again would nuclei be affected?

    1. The size of an atom is inversely proportional to the electron’s mass.

      The proton is lighter than the neutron because the down quark is heavier than the up quark; if both were massless the neutron would be lighter than the proton. Many if not most important atomic nuclei would become unstable.

      The rate at which radioactivity would proceed is inversely proportional to the fourth power of the W particle’s mass.

  12. Dear Mr. Stone:

    Thank you for your kind reply. Yes, kinetic energy can be transmutated into rest mass (particle masses) in collisions. I am very pleased that you do not object to the new skewed “Stone’s symmetry” with Canada and the U.S. as everyday examples.

    The Higgs field is still very little understood. It would be great if Professor Strassler would care to help us. The most pressing point is that if the new skewed symmetry is a reality – as no one disputes following the Telemach paper which implies it –, black holes (the brain child of J. Robert Oppenheimer and my late friend John Wheeler’s) possess radically new properties that totally upset the safety equation of the admirably beautiful LHC experiment.

      1. Dear esteemed colleague:

        Would it be very demanding if I asked you to substantiate your off-hand remark. As you frequently said yourself, the simplest is sometimes the hardest to reply to.

        Thank you very much,
        Sincerely yours,
        Otto E. Rossler

    1. Dear Ottoerossler,

      Thank you for enlightening me on this topic, although this response leaves me with more questions that answers. I have read very differing opinions on the subject, when you refer to “kinetic energy can be transmutated into rest mass (particle mass) …” are you referring to relativity? Is it true that objects gain mass relative to stationary observers? I know that time and length are relative, but can not find any two things that both are comprehendable by me and have the same opinion on the topic. Is this part of the Lorentz factor, same as how length and time dilation are calculated if it is true? I guess, to sum it up- I calculated that at moving 80% the speed of light, if I had a ten foot pole, to you (stationary) it would be only 6 feet, one second to me is 1.6 seconds to you (I am not sure on this one, I am doing this off of memory) and my weight would increase from 150 to about 240 pounds. Does this increase in weight actually happen or did I do the math for not?

      Also, what are these radically new properties you speak of? What are the safety equations from the LHC? I know little on black holes, and nothing about these safety equations. (any information I know of black holes is probably from A Brief History of Time, by Stephen Hawking, although I did not read it to its entirety.)

      Finally, from your response I could not find an explanation to your previous comment, about being able to have two specimen rocks. I do not understand the concept you are trying to point out. Also, I cannot find an answer to your opinion of whether or not the higgs field being only locally universal possibly having any connection to inflation theories, nor do I know how these regions are different yet the same, and all articles retain the same mass, or how the higgs field is affected by gravity. When you referred to these things in your previous comment, could they all fit into your more recent comment in the part “The Higgs field is still very little understood.”

      May I ask what you do for a living? Are you a professor of sorts or are you a very intrigued and smart layman? Once again, thank you very much for your time, it is incredibly helpful to me and I have learned a lot!

      Sincerely, Stone Oliver

      1. My reply started with ewords: ” Dear Mr. Stone: Thank you for saying so nicely that…”
        It is probably my own fault that I cannot find it. Take care, Otto

      2. Dear Ottoerossler,

        Well, as it seems that your message is being censored… Which I can’t understand why or how, would it be possible that you could email me directly your responses, until this is sorted out? If that would be possible, my e-mail address is Oliver_s@nrevsd.com

        Thank you once again for your time.

        Sincerely, Stone Oliver

  13. In a Parallel World could there be a novel kind of physics without the Boson or Field of Higgs? What kind of world will this be? Thank you

    1. No way to know; if the parallel world (as you call it — let’s just call it a region of the universe with different physical laws) does not have a Higgs field, it also might not have any of the other forces and particles that we know about.

  14. Thank you, Sir, for your important question. I have an example using money as an analog. In two countries with different currencies, both called “dollar,” one liter of milk can cost two quarters (say) in each. This notwithstanding, one dollar in the one country may be worth only ten cents in the other, exchange-wise. (Canada has the upper hand right now, I believe.)

    In the same vein, local rest mass is everywhere the same in gravity. Nevertheless the “real value,” compared to the same body studied in flat outer space, can be arbitrarily small. The relevant factor is the redshift that is valid compared to far outside. The reason is Einstein’s principle of general covariance. It makes sure rest mass is everywhere the same locally (just like the Higgs field is). Indeed the rock will have its usual mass locally after having hit the ground, with all kinetic energy dissipated away. But this mass will only be worth half its outer mass-energy on a z=1 neutron star (say). Reason: the kinetic energy dissipated on the ground is just as high, mass-energy-wise, as the locally measurable rest mass is. So you could in principle manufacture a second specimen of the original rock down there. The two of them nevertheless must (by Birkhoff’s theorem) not have any greater gravitational influence on the outside world than the original rock had when it was still alone far outside. (To bring it back, the twin rock will need to be annihilated completely.)

    Most specialists I met get confused at this point because potential energy (and the energy of nuclear devices stemming from released potential energy) interferes in their heads. Potential energy does exist also in general relativity. However, it is advisable at high gravitational redshifts not to bring in one’s ingrained Newtonian intuitions. The notion of potential energy should be abandoned didactically at non-negligible redshifts, I feel.

    The “symmetry” you are bringing into play here is very well taken. I am afraid it represents a new type of symmetry. It will in case the above survives have to be called Stone’s symmetry.

    1. Dear Ottoerossler,

      Thank you for your response. it is enlightening, but to make sure I have understood this correctly (I am very bad in English, particularly vocabulary), are you saying as far as the whole global or universal stuff, a rock has x amount of mass, which is the same here as on a z=1 neutron star, and it gives off the same amount of kinetic energy when falling to the ground from equal distances, so it is the same, but it is a local thing because it would be much harder to pick up the rock on a neutron star, because of the differences in gravitational attraction that the Earth and a neutron star have? Is this in reference simply to the “environment” that any particles present are in? Are you simply saying that the “environment” present in a specific region has the same aspects as any other, the higgs field gives mass, gravity has effect ext., but, to use your analogy, cannot “exchange equally”? If I am correct in my comprehension, could it be possible that these differences are due to a process similar to the inflation theories proposed by Allen Guth regarding why our universe is flat? Could these fields be similar to energy in the aspect that they could form “defects”, the term used to describe trapped energy which explains the idea behind how inflation could occur?

      Also I don’t quite comprehend the part about creating a second specimen. I understand that kinetic energy, mass-energy wise is the same as the rest-mass of the object, simply because the objects kinetic energy is dictated by the mass of the object in the gravitational field it is in correct? But could you explain a bit further please?

      Finally, I would like to ask, how could there be higgs fields which are local and not universal and cannot “exchange” equally which still all give particles of the same sort the same masses? How does gravity affect the higgs field? Thank you for your time sir, it is very helpful.

      Sincerely, Stone Oliver

  15. Dear Ottoerossler,
    When you refer to being either global or universal, what do you mean? Is global referring to regions that do not causally affect other regions? When you say the higgs field is everywhere locally universal, does this mean that in regions not in causal contact, the higgs field has developed individually, possibly at different times, similar to how universal defects occur? Was there ever a time when the current higgs field configuration was not favored which may have made particles have different masses at different times, say in the early universe? If it’s possible, what kind of symmetry was present here? Thank you for your time sir.

    Sincerely, Stone Oliver

  16. Dear Professor Strassler:

    In the words of James H, I thank you for setting up such an enlightening website and your patience answering these questions is something to be admired.

    I refer to your statement “how gravity works is … not affected by the Higgs field” (March 13, 2012 at 4:08 PM). I agree.

    I would like to add that the converse does not hold true: The Higgs field is affected by gravity.

    This follows from the Telemach result ( http://www.scribd.com/doc/82752272/Rossler-s-Telemach-paper ). The math there is primitive but very geometrical. It lets a few things appear much simpler if correct; for example, Newton’s gravitational constant G is no longer a global constant while new more universal constants arise.

    The reason I mention Telemach is that the Higgs field becomes everywhere locally universal but not globally. This surprise was independently seen yesterday by a young American physicist.

    Do you think it possible that the Higgs field is only locally everywhere but not globally universal?

  17. Thank you for taking the trouble to maintain such an informative website. Reading the long discussion on this page has helped to clarify many points for me and cleared the media-fed fog of confusion. I also realise with some excitement the extent to which physics has moved on in some areas since I last sat in a lecture theatre 25 years ago.

    For some reason, I was struck by a remark that you made in a reply you gave on Nov 30 2011, in which you said “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.
    The Higgs field has a non-zero value in nature on average. (The electric field is zero on average)”.

    Why actually is the electric field zero on average? Is this a theoretical requirement or prediction? (Clearly it hasn’t been measured everywhere!). Since the electric field “is just there”, could it have any average value at all, in principle, or is there some intuitively obvious reason why it must be zero that I have forgotten in those intervening 25 years?


  18. How does the newly found Higgs particle impart mass? Does it distort the particles’ function into having mass or does it distort the space around the function? Could the Higgs particle be controlled by some kind of tensors that fight dark energy?

  19. Once more on Gravity versus the Higgs field. I am still unsure why the Higgs field would not affect gravity and thereby space curvature. If the rest mass mo and thereby the rest energy E=moC^2 is defined by the higgs field interaction with particles then would this not determine gravity and space curvature? In other words if we could somehow modify the value of the Higgs field (purely as a though experiment), would this not directly affect gravity and space curvature?

    1. The Higgs field causes mass for the known particles, but almost certainly not for all particles — in fact, the Higgs field only contributes part of the Higgs particle’s mass, the rest coming from an unknown source. Dark matter particles, if they exist, probably do not get mass from the Higgs. So the Higgs should not be thought of as THE universal mass-giver.

      Gravity, in Einstein’s theory, does not couple to mass, or to rest energy; it couples to energy. That is why it bends light. And it is completely universal, interacting with all energy the same way, no matter what particles are carrying that energy.

      So the Higgs and gravity are very, very different, and as far as any theoretical effort has ever shown, are completely unrelated.

      1. “Dark matter particles, if they exist, probably do not get mass from the Higgs” –
        Do you say this based on limits from Higgs-exchange DM scattering cross-sections?

        1. I said it because in most theories of dark matter it is not the case and because there’s no reason to expect it from any basic principle. I suspect that yes, limits on dark matter cross-sections would disfavor the possibility, though I didn’t check it — but there are assumptions that would go into those limits, so that wouldn’t disprove it.

  20. I was confused as to how the Higgs decays to 2 photons (massless particles) when I read that the photons actually come from a (Feynman) ‘loop’ of W particles? Can you elaborate?

  21. Hi Matt

    Is it correct to say that mass-energy is just interaction energy of the particle in the Higgs field – in exactly the same way as some of the energy in a proton is actually interaction energy of the quarks with the gluon field?

    If not , can you explain the subtleties of the difference between these two situations?

    1. The two issues are not the same, unfortunately. The quarks and gluons together provide the mass of the proton, and the gluon field is not a non-zero constant inside a proton or outside.

      I will try to explain the difference between these two situations someday. It isn’t easy to explain the proton mass even to other physicists — and I know it is a loose end on this website that I need to tie off.

  22. Thankyou Stone Oliver. Excellent answer. I’ve actually found the pages where I can check out the particle itself now, (day 2 onsite) so hopefuly I can answer my own questions more easily. Thanks.

  23. Dear Prof. Strassler, I am a complete layman and complete ignorant about physics. I have been very intrigued by the reporting around the Higgs particle and I have some basic questions I couldn’t get answered as it seems that the information aroun the intuition is either very incomplete or it does require anyway fundamental knowledge around particle physics. These are my stupid questions:

    1 I take it the Higgs field “gives” mass to certain particles, which would not have mass otherwise. True ? Now, if these particles don’t exist in nature in a massless state, why don’t we refer to mass simply as a property of such particles. In other words if mass derives from the interaction with the Higgs field and is not a absolute property of such particles there should be the real possibility of massless particles.

    2 I take it the Higgs bosons are a finite pack of disturbance in the Higgs field, like a wave on a surface. Is this intuitively true ? And if it is true, do these bosons exist prior to the field intercepting the other particles or they co-exist only with the particles whose mass they create and are the result of the interference itself ?

    3 if the bosons exist irrespective of the crossing of other particles, do these bosons (or waves) move on then field or they are static, if they move where do the come from and where do they go ?

    4 what does isolating a Higgs boson mean, are we decoupling it for a second from the particle whose mass it was reponsible for ? And if these bosons (or disturbance, or waves) give mass to particles, what happen to the poor particle when we isolate a boson, does it become massless ? And does the boson disappear shortly after ? If so this would intuitively tell me that the bosons only exist with the particle that is interfering with the field and that once the boson is isolate the ripple on the field, the boson itself, flattens out ?

    Sorry again for the stupid questions


    1. These are not stupid questions. You might find this article useful, not sure: http://profmattstrassler.com/articles-and-posts/the-higgs-particle/why-the-higgs-particle-matters/

      1) True. There *is* a real possibility of massless particles (and indeed, photons and gluons are massless, and there would indeed be other massless particles if the Higgs field were zero.)

      2) A wave on a surface, or even better, more like a sound wave in air — a wave in the volume. The second question I don’t really understand. The field just sits there, and we’re all within it all times; there is no “prior”.

      3) Not a meaningful question see (2) and (4)

      4) Higgs bosons are particles — they do NOT give mass to other particles (despite what you will read in the press). A Higgs boson is (as you said) a wave in the Higgs field — the “quietest” possible wave. What gives mass to other particles is the field.

      hope this helps some — feel free to ask follow-up questions.

      1. Thanks professor, also for the prompt reply. I read the article, I think I got it. The bosom is proff of the existence of the field, not the mean by which the field affects other particles. The bosom is not isolated by the experimeny but it is created by the (collision within) the experiment and then (statistically) detected. Hope this is more in line. Thank again and good luck !

  24. Thanks for this great site, I only discovered it yesterday!

    I have a couple of questions that trouble me….

    1. Why exactly is Higgs non-zero on average in empty space? Where does that energy come from?

    2. Is mass of a certain type of a particle constant in every point in space at any time because Higgs field is a scalar field? If so, is there any other scalar fields in quantum physics or Higgs is an exception?

    3. Since I’m one of those raised with term ‘relativistic mass’, I’m surprised to discover that the term has been abandoned. I know what the rest mass is and that it’s constant. However, I was under the impression that when an object asymptotically approaches c, it should appear elongated and more massive to an external observer. Does that mean that under such conditions such an object should be more inert and have increased gravity pull /spacetime distortion or not? I know gravity and mass are not necessarily related, but now I’m quite confused about the issue… is increased speed adding to gravity and not mass, to both or to none? 🙂

    4. A question on literature/further reading… I want to get more technical about modern quantum theories (meaning studying equations a bit more). Where’s a good place to start, history-wise? With old quantum mechanics (Schroedinger equations) or somwhere later? Have the descriptive methods (mathematcial models) in quantum physics changed?

    1. 1) no idea why. But no energy is needed to keep it there; it is at the (or at least, a) energy minimum [that’s why it stays there.]

      2) not really; masses are constant because the Higgs field is constant. Why is it constant? Why are all the laws of nature apparently constant over the visible part of the universe? no idea. Other scalar fields: many composite spin-zero fields are known to exist. The Higgs *might* be the first “elementary” scalar (i.e., first scalar that isn’t pretty obviously composite) ever discovered.

      3) Most of this is just semantics; it is a question about what convention you use, not what the physics is. What everyone would agree is that as an object approaches c it becomes contracted (not elongated) in its direction of motion, and its energy becomes extremely large (much larger than its rest energy). Now, whether you want to take its energy and divide by c^2 and define that as another form of mass (i.e. relativistic mass) is up to you — but notice that if you do this, photons are massive particles, because all photons have energy. Particle physicists have many reasons to dislike this convention. The convention adopted in particle physics, string theory and in mathematical branches of physics is that mass means “rest mass” and photons are massless particles.

      4) Unfortunately, quantum field theory is a huge conceptual and mathematical jump beyond quantum mechanics — the hardest jump in my own career. Few people have taught themselves the subject. You can learn a lot of particle physics without quantum field theory, however… so it depends what you want to learn. Can you give me a slightly better idea of your goals?

      1. Thank you for these clarifications.

        The reason I asked about 1) and 2) is because to my (layman) point of view these are the fundamental questions concerning
        the Higgs field. Maybe I’m wrong? I’ve read somewhere that vacuum energy (energy minimum) of our own universe could be different in another one with different laws and constants. I don’t really understand how can a field with energy above zero in every point of space exist without something pumping energy into it? Is it something that troubles scientists or is it just my limited knowledge that’s troubling just me? 🙂

        I asked 2) because it seems to me Higgs field seems more like a mathematical construct that a real-world field that could exist (constant value everywhere without fluctuations, energy dropoff etc), but then again – I don’t wield math equations to begin to understand where does the theory comes from, mathematically speaking.

        As for 3), thanks for the clarification…can you just answer if accelerated particles give rise to GR effects such as spacetime distortion around them?

        4) I’m trying to understand the concepts beyond words and verbal descriptions (such as QED, gauge theory, supersymmetry, etc.)
        I know it’s an overwhelming task, but being an engineer I always try to analyse stuff, and since physics always interested me immensely I feel quite impotent by taking pot shots with questions without understanding the math beneath it at all. I don’t wan’t necessarily to get into all the nasty details, but want to understand the basic relations that can only be expressed by studying the equation structure…I don’t know if you know what I’m trying to say… for example…if you take Maxwell’s equations for example – if you know enough about what the operators mean, you can (almost) imagine the way the EM field propagates without doing actual calculations. Just understanding the correlations/operators in an equation can give you a lot of insight. I don’t know if I’m making any sense…and even less if it’s possible given limited time and a different career path.

        1. 1) and 2) It’s indeed your limited knowledge. A field having a constant non-zero value does not mean it has energy. I realize this isn’t obvious; it is something you just have to learn.

          2) The Higgs field is constant unless you whack it, just like the density of air is constant in an empty undisturbed room until you clap your hands or do something else to disturb it. Once you whack it, it will wiggle, just like air will form sound waves if you clap your hands. That’s how you know that it is real, not some mathematical construct.

          3) Accelerated particles do not give rise to GR effects merely because of their acceleration, no.

          4) the basic equations: Schematically, the Higgs field satisfies an equation like

          (d^2/dt^2) H – (d^2/dx^2) H – A^2 H + B^2 H^3 = 0

          (actually small terms from other particles, big quantum effects — ignore them) Notice that there is a solution H = A/B which is a constant independent of time and space. There are also approximate solutions H = A/B + C cos(p c x – E t), where C is very small so that C^3 terms can be ignored, which represent a traveling wave on top of the constant field. That wave is a Higgs wave (whose quanta are Higgs particles, just as quanta of light waves are photons) and it satisfies E^2 – p^2 c^2 = m_Higgs^2 c^4 ; you can go through the exercise to calculate m_Higgs in terms of A and B and c^2.

          How does the Higgs give mass to other particles? There are equations for other particles that imply, for them, E^2 – p^2 c^2 = y^2 H^2 where y is a number that is different for each particle; then in the presence of H = 0 the particles satisfy the equation E = p c, which is the equation for a massless particle, but if H = A/B then E^2 – p^2 c^2 = (y A/B)^2, and so the particle has a mass y A / B c^2 . Thus all the particles which interact with the Higgs this way are massless if H=0, and they are massive (but with different masses, since each has a different y) if H is non-zero.

          Hope that helps. You’ve motivated me to write this up someday for those, like you, who can handle basic equations.

      2. Thanks for that equations, that’s exactly what I wanted 🙂

        I’m afraid though, I lack the knowledge to comprehend them fully…
        So H is, I suppose, the Higgs field…represented by classic f(x,t)?
        What is A and B? 🙂
        I understand the second part just fine, just lack the definition of A and B

        Last but not least, thanks for your patience!

        PS. Could not reply to original “thread” so had to reply like this…

      3. Thanks! I do hope you write a bit about basic equations, that would be great and am looking forward to it!

  25. Is the whole concept of Higgs particle or the Higgs field is with the notion that the whole Big Bang happened in the creation of this universe? If so, why always think that the universe was created from the particle of non zero mass , why not the other way round that there was huge mass already existent for some reason which got broken into tiny tiny particles say the HIggs particles.. I may be thinking crap, but i have this doubt..


    1. There’s really no connection between the Higgs particle and the Big Bang, at least as far as we know (the Big Bang isn’t something we understand in great detail, we just have the basic idea.) The equations that describe the Big Bang are mainly gravitational; the equations that describe the Higgs are the Standard Model, which includes the three non-gravitational forces along with the known particles and the Higgs. If there is a connection of a deep sort, it isn’t in our equations yet, and there’s nothing in any current data that can, as yet, suggest one.

  26. Professor Strassler, thanks for this site. They said on the news that there was a decay by the Higgs particle into two photons. Does this mean the Higgs particle is a composite particle? Sorry, proper layman here. And is it true that a super light speed nutrino has been possibly spotted? You’ll probably see I’m more of a science fictionist, but space itself is such a fascinating entity to contemplate. I hope I’m not wasting your research time. Thankyou again.
    Ali Duncan

  27. I didn’t get a chance to read all the discourse above, am not a physicist, but have a simple question. 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 it’s mass.

    Thank you in advance for addressing this
    Mike Serfes

    1. No matter how you are moving, you are not moving relative to the Higgs field. That sounds bizarre, but remember someething else bizarre: that no matter how you are moving, light is moving 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.

      1. Hi,
        Just have to comment this, because my intuition just got broken. I can understand a field in regard to which you do not move by consider it “outside space” or having the same value everywhere. I have big problems understanding a field which has different values in space and with regard to which you cannot move.
        I accept the fact that light speed is constant although my mind cannot model that intuitively.
        But then a stupid question raises: what is the speed of a photon in relation to the Higgs field ?
        Any answer that would help me patch my intuition is appreciated.

  28. Thank you for your delightfully readable review. I especially appreciate your sober comments about Dr. Lederman’s indiscretion in compromise with commerce. Your respectful chiding is balanced, consistent with propriety and scientific consensus, a trifecta of science journalism! Congratulations and thank you again.

  29. Dear Alex,

    Thank you for you reply! It is very helful to a high school kid trying to sort through all the misinformation.

    “Yes to the latter, people usually don’t include the p^2 c^4 term and thus don’t understand that the E=mc^2 formula should only used for objects at rest. However, the energy gained from the p^2c^4 part is indeed convertable to an equivalent amount of mass if you do it right”

    May I ask what you mean by “if you do it right”? To my knowledge, matter is not converted to energy, or vice versa, but a massive object contains a certain amount of energy at all times, correct? Would I also be correct in saying that if a certain amount of energy is present in a stationary form, a certain amount of mass is required? (excluding photons, because of the infinite energy problem) I also understand what you mean by
    “Yes, the author should have said energy rather than mass. In *all* modern treatments of SR, the mass of an object is defined as sqrt(E^2/c^4-p^2/c^2)” But does this pretain to what is observed? What I don’t understand is

    “that is, as a quantity equal to the rest mass and thus independent of the inertial frame of the observer.”

    While anyone can find the actual mass of the object by sqrt(E^2/c^4-p^2/c^2), is that what is observed? To say, is the extra kinetic energy also measurable as mass, to say, if I were to move at 80% of the speed of light and had a weight of about 150 pounds, would I then weigh about 240, relative to a stationary observer, or would I still be 150? Regardless of the observers capability to calculate my rest mass? I would like to think, that if an object gained momentum, it’s energy would increase, play around with the numbers enough, and I can see how mass increase with speed could work. The math being the E^2= m^2c^4 + p^2c^4, and the Lorentz equations, 1/ sqrt(1-V^2/c^2)^1/2. (If the lorentz equation is wrong, thats not why my information is wrong if it is, it’s simply because I can’t remember it offhand, and am short on time to look it up.) Thank you for your time sir.

    Sincerely, Stone Oliver

  30. Dear Alex,

    So in your response to vk, you say that “relativistic mass” is simpy the energy gained from the kinetic energy, or momentum of the object correct? I understand the concept that mass and energy are separate, I’ve seen the math and that makes sense. I just find the wording a bit odd to understand for me and would like to make sure I’m not getting the wrong idea here, so for the equation E^2 = m^2c^2 + p^2c^4, mass for the object is considered a constant as long as we always observe the same particle, and generally, people don’t understand that the energy gained from the p^2c^4 part of the equation, is not actually convertable to an equivalent amount of mass, because they think of the simplified equation, E=mc^2, and they don’t realize that E=mc^2 only applies to objects at rest? Also, regarding calculating the lorentz factor for length contraction and time dilation, I read an article that talked about how length, time, and mass can be changed, based on the observer. Would I be correct in saying that the author of the article should have said that energy, and not mass is changed based on the observer, simply because of momentum? Thank you for your time sir.
    p.s. if this comment posts at the very bottom of the higgs faq page, I was asking this question in regards to a response you (Alex) left much higher in the comments, and I can’t figure out if this is going to post as a response to your comment, or a response to the article as a whole.

    Sincerely, Stone Oliver

    1. Hi!

      “I just find the wording a bit odd to understand for me and would like to make sure I’m not getting the wrong idea here, so for the equation E^2 = m^2c^2 + p^2c^4, mass for the object is considered a constant as long as we always observe the same particle, and generally, people don’t understand that the energy gained from the p^2c^4 part of the equation, is not actually convertable to an equivalent amount of mass, because they think of the simplified equation, E=mc^2, and they don’t realize that E=mc^2 only applies to objects at rest?”

      Yes to the latter, people usually don’t include the p^2 c^4 term and thus don’t understand that the E=mc^2 formula should only used for objects at rest. However, the energy gained from the p^2c^4 part is indeed convertable to an equivalent amount of mass if you do it right, this is exactly what particle accelerators like the LHC do when they attempt to produce new particles much heavier than the protons, like the Higgs boson.

      “I read an article that talked about how length, time, and mass can be changed, based on the observer. Would I be correct in saying that the author of the article should have said that energy, and not mass is changed based on the observer, simply because of momentum? Thank you for your time sir.”

      Yes, the author should have said energy rather than mass. In *all* modern treatments of SR, the mass of an object is defined as sqrt(E^2/c^4-p^2/c^2) – that is, as a quantity equal to the rest mass and thus independent of the inertial frame of the observer. The statement that the perceived length of an object depends on the intertial frame of the observer is however correct, as well as the perceived speed of a clock.

  31. Thank you for all of your hard work on the website!

    You describe that there is certainly a Higgs field, but not necessarily a Higgs particle. Since the Higgs particle is the smallest perturbation of the Higgs field, it would seem that the lack of a Higgs particle means that the Higgs field cannot be perturbed. I assume this is false, but could you enlighten me on why?

    1. I will attempt an answer to this one, and test my own understanding after having read the FAQ.

      The Higgs field may be a composite field in which case it does not have to exhibit “a particle” – perhaps a whole slew of new particles or perhaps none at all. Also, if I understood this next part correctly – this possibility has been theorized i.e. composite Higgs field. That means if the Higgs particle is not found, the LHC has a whole bunch of other experiments lined up to investigate the composite field theory.

      I hope I got atleast some of the above right.

  32. Professor Strassler,

    I understand that the LHC is currently looking for the Higgs boson, it is seeking it at various energy levels, and there is some keen interest among members of the scientific community regarding exactly what energy/mass it will turn out to have (assuming it’s there at all). My question is: Why does the standard model not yield a prediction of exactly what energy/mass the Higgs boson will have? Is it simply a matter or our empirical uncertainty regarding exactly what the values of certain constants of the standard model are?

    Thank you in advance for any light you can shed on this question.

    1. Yes, 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 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 mass in experiment to determine the number associated with it.

      You might ask whether the Standard Model predicts anything given how 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.

  33. Prof . Strassler, you have not commented on my original question of “how” the Higgs field is supposed to impart “mass”. I would think this would be the main focus of a FAQ, yet , I see no answer. Please comment on this important aspect of the Higgs.

  34. ….Your explanations and approach are sensitive, right to the point and deep, I still gather information and have some notes and questions but for now just wanted to say thanks your blog is a pure esthetic pleasure.

  35. Sorry, another misuse of words… the word atom in the second line should be nucleus,

  36. It does, thank you, and sorry, the use of nuclei was a simple misuse of vocabulary. So the simple number of nucleons in the nucleus, affects whether or not the atom is a fermion or boson, is something interesting in itself. How come it happens to be that force carrier particles are bosons, while other elementary particles are fermions? Is there the possibility that particle spin can have an affect on particles, as far as determining whether they are bosons or fermions, as opposed to my previous assumption that the fact that a particle was a boson or fermion determined its spin? To say that to change a particles spin could change to properties of the particle? (excluding interactions with other particles) Thank you for your time professor. it is very helpful.

  37. Three things to say: This sight is great, very helpful for a young and interested high school punk, I don’t quite understand the idea of a zero and non-zero field (what are the units here, if there are any?) and I read in one of the comments that all atoms with even numbers of nuclei have zero spin, how are they then considered fermions? Given that bosons are of full integer spins while fermions are confined to fractional units of spin, true?

    1. Thanks…

      Fields have units that depend on the field itself. For instance: the wind’s velocity is a field; the wind can be calm, or it can be blowing. That’s one example of a zero field versus a non-zero field. The units are in meters per second.

      Another example: the density of air. That can be zero (in vacuum), or not (earth’s surface). The units are in number of atoms per unit volume.

      Things like the Higgs field are more abstract, because they aren’t made from any other stuff and can’t be thought of via some other type of intuition. The Higgs field has units too but exactly what units it has depends a little bit on convention. In a typical convention used in particle physics today it is given units of energy. But units are a bit arbitrary; for example, you can measure distance using meters, or you can measure distance using seconds by dividing each ruler-distance by the speed of light. (In other words, you can tell me the moon is 400,000 kilometers away, or you can say that it takes light 1.3 seconds to reach the moon; it’s the same information.)

      All atoms have a single nucleus, so clearly you don’t mean “all atoms with even numbers of nuclei have zero spin” since all atoms have one nucleus. It is true that all nuclei with even numbers of protons and neutrons automatically have integer spin, and all the stable ones have zero spin. And indeed, they are not fermions in general (not sure why you thought they were); because protons and neutrons are fermions, nuclei with odd numbers of protons and neutrons are fermions, nuclei with even numbers of protons and neutrons are bosons.

      Whether the atoms are fermions or bosons is another question. Atoms are fermions if the number of protons, neutrons and electrons is odd, and bosons if the number is even.

      Does that answer your questions?

  38. I left a reply which seems to have evaporated into cyberspace. To sum up that comment in one sentence: Bravo! You answered all my Higgs questions in your excellent FAQ. Sue

  39. Dear Prof. Strassler. I am amazed! I never imagined I could learn so much from an FAQ. I’ve found answers to just about all my questions. I am in the really unrealistic ‘place’ of trying to follow my main interests in physics: astrophysics and cosmology, without knowing much about particle physics. I certainly plan to read your article on elementary particles, but after reading this FAQ for about 2 hours, I think I’m going to take a breakfast break. The only point on which I can pat myself on the back is that it never occurred to me to try to equate gravity with the Higgs field. As you so rightly pointed out, general relativity describes space time curvature which includes bending the path of a massless photon. At least I understood something. MANY MANY THANKS FOR YOUR EXCELLENT BLOG. Sue

  40. Could you find the general rates of Dark Energy ,subtracting Electromagnetism and the Higgs field, and use this as the cosmological constant in Einstein’s field equations. The reason you would theoretically subtract them is that they are negative curvature forces, not positive curvature forces. Again, I have no idea what I’m talking about; I’m just throwing things out there and it’s not my fault if it turns out to be crap because I’m a monkey. Levity?

    1. We don’t need to.

      We already know how much dark energy there is; this is obvious by looking out at the universe and seeing how it works. (Same with dark matter, we know that if there was only normal matter galaxies would fly apart; ‘something’ has to be holding them together and extra ‘hidden\dark’ matter is a good bet.) The question is what IS dark energy? (Likewise, ‘dark matter’ may just be gravity acting wonky on a universal scale, though that possibility seems to be fading fast. (Look up MOND or Modified Newtonian Dynamics))

      The comsological constant is one of the worst predictions in physics; when you add up all the energy that empty space should have you end up with a figure far, far FAR bigger than a billion, billion, billion times what is actually observed.

      Since our results of what we calculate dark energy to be are so off the chances are that explanation is also off and pulling apart our terribly, terribly wrong result into different bits will just give us more wrong answers. When we come up with a theory for dark energy that isn’t such a horrible failure equation-wise, THEN we can start prying it apart to see what’s what.

  41. I know I really have no right to speculate without any math at all, but I was just trying to say that the Higgs field might be something that positively curves space slightly. It wouldn’t be detectable because the little amount of energy that causes the curvature would go into making energy matter. That ripple in space could compress energy into matter with mass because of the low volume of space around the particles of energy. I’m just throwing ideas to get some analytical feedback, but I’ll leave it alone, I’m not trying to antagonize with my obnoxiousness.

    1. No.

      The problem with this idea is that slight curves are large curves and the effect you want is very small (In size.) Think of the earth, it it slightly positively curved and looks flat to us. An egg is much more highly curved and is obviously curved to us. For the Higgs field to do anything like what you suggest it would have to massively curve space and this really, really doesn’t work. (Everything gets all curled up into a tiny dot.)

      As stated before, the Higgs Mechanism is a well known way to give particles mass supported by plenty of equations and predications. it doesn’t explain all mass, but it does a very good job.

  42. I meant that quarks could be held in place by the negative curvature of space, but don’t implode because of this repulsive force that keeps nuclear orbits in a happy medium and creates a distortion around bits of energy compressing them into specific orbits and create matter or fast-moving energy. I meant that the energy would just follow space’s curves, but I know it sounded crazy. This force should relate the strong force with the amount of force necessary to implode a quark orbit, somehow.

    1. I gave you some advice before. The advice remains the same. You’re stringing words together in ways that don’t make sense. You don’t know enough physics yet to realize this, so you really need to go off and learn more things, and then come back and speculate. Time is precious, especially time when you’re young; don’t waste it.

  43. Would it be mathematically possible that the Higgs boson carries a force that positively curves space and energy, then compresses the energy in between its force and the negative curvature of space?

    1. “positively curves space and energy”: Space and time are curved; energy is not something you can curve.

      “compresses the energy in between its force and the negative curvature of space”: I have no idea what this means.

      Most things you can imagine are not mathematically possible, even if they appear that they might be at first glance. They tend to be inconsistent with themselves or with other things we know. So when you ask me “is X mathematically possible?”, even if X makes sense I may not know without doing a month of work.

  44. What will be different , if the Higgs field is on average zero above the Planck scale? but not below.
    I imagine the Higgs field as and oscillating particle field, able to keep fermions spinning and converting Higgs particle by that interaction into gravitons and other photons ?

      1. The Casimir effect is acting below the Planck scale, so this could be a Higgs effects as I suggested?

  45. Well, thank you for being patient with me; I appreciate that very much. I’ll be doing a lot of research and I’m going to try and get a good question for you. Thanks again Professor Strassler.

  46. Yes, I will be going to UAB. I’ll be sure to try. So, the strong interaction can’t be explained by properties of space at all or maybe some field that attracts alike particles to each other?

    1. The strong interaction was explained in 1973 (and a Nobel Prize was awarded for that work in 2004, after three decades of testing that show that the explanation makes very accurate predictions.) The basic mechanism is very similar to the mechanism that allows photons (i.e. light) to interact with electrons. Once you take your freshman physics course you will get a somewhat better sense for why light interacts with electrons, and that will give you part of the story of why quarks and gluons interact. The very slight differences between the strong interaction and the electromagnetic interaction explain why photons operate freely while gluons end up trapped (with quarks and anti-quarks) inside hadrons.

      In case our understanding of the strong interaction needed any further testing, those tests have been going on over the past two years at the Large Hadron Collider. The extremely good agreement of theoretical prediction and experimental measurement at that machine is a testament to how well our equations for the strong interactions work. There is no obvious need for some other explanation of how the strong interaction works, and if you tried to find one you’d have to invent equations to convince people that your ideas were somehow better than the equations we have. No one’s going to pay attention to you otherwise.

      This is not to say that we understand *why* there is a strong interaction or an electromagnetic interaction. There may be deeper stories to tell about why those interactions exist at all, even though we already know how they work. But you can forget about figuring that stuff out by pure speculation before you know anything about the equations. You don’t think that’s what Einstein did, do you? He was extremely good at math, even as a child (the myth that he failed 8th grade math is just that, a myth) and knew all the math and physics equations very well by the time he started doing important work. His papers have lots of math. And today’s Einsteins need to know more math than he did, just so that their speculations aren’t wrong on line one. I cannot encourage you to make verbal speculations with no grounding in the science and math; you will waste your time, because there are a trillion trillion ways to be wrong if you have no guidance from real experiments and the mathematics of theory. A fresh and open mind is a great thing, but it has to be guided by current knowledge, even if it rejects some of that knowledge along the way.

      You should probably do something like taking Sean Carroll’s Teaching Company course. That would be more useful than speculating at this stage in your knowledge.

  47. I haven’t been taking any classes in the past month or so; I graduated early. I didn’t take a calculus or trigonometry, though. So, why do gluons and quarks interact with each other?

    1. Not sure what to tell you; if you want pedagogical advice, that advice includes basic trigonometry. Are you planning to go to college or university? I ask because your future pedagogical steps depend on whether you’ll be in a school or not.

  48. I wasn’t trying to say that gravity causes the strong interaction, but I was trying to say that it guided these gluons into place. Asymptotic freedom might hint the strong interaction is caused by the lack of energy and is possibly just a side-effect of space-time losing energy as it stretches, but you know I don’t have enough information to support these ideas. I’m really not ready for the equations, just childish imagination. I would really appreciate it if you gave me more pedagogical feedback on these speculations.

    1. I’m not responding to any idea that “gravity causes the strong interactions” either. The gluons inside of protons and other hadrons are flying around in there, and being kicked around by collisions with other gluons and with quarks and antiquarks every trillionth of a trillionth of a second. These collisions are HARD. Any gravitational effect would have no chance to guide the gluons at all, any more than a bacterium could interfere with the motion of a car on the highway. There’s just no way.

      The only way around that is to have a SPECTACULARLY HUGE gravitational effect. But you and I and the earth would notice that pretty easily. There’s no way something like that can be going on inside of hadrons. Meanwhile our theory of quarks and gluons (quantum chromodynamics) works very well for predicting the properties of hadrons; is there a clear need to modify it?

      Now, about childish imagination: The problem is that you *have* to be ready for at least SOME equations. They don’t have to be super-sophisticated equations, but you cannot do any physics at all without them… indeed, you cannot do any reasoning about the world without some basic math literacy. You cannot possibly determine whether a bacterium can affect a car unless you have a sense for the size and mass and velocity of a bacterium and the size and mass and velocity of a car. It’s not optional. It’s not that hard either; no genius is required for quantitative reasoning, once you get the hang of it.

      Learning to reason about the world in a quantitative way is the first step toward doing science. Now my job is to find you (and others like you) some kind of on-line site or course that will get you started. I don’t know of one at the moment but I am sure one exists. If readers have suggestions they should chime in.

      What are you taking as far as math and science in school right now? Will you be going to college/university soon?

      1. Possibly “Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving” depending on knowledge of maths.

  49. If you could seperate string or node particles, you could measure the dexterity of space-time and then you could measure the effects of all mater on the fabric. The equation in this should be the amount of light distortion at the edges of the universe (the angle of the gravitational wave’s incline) should be equal to how strong the fundamental particle’s bonds are. So, if you seperated a fundamental particle you could warp space and create another gravitational ripple distorting all matter within at least a 100 miles.

    1. Ok, I’m going to go easy on you because you’re 17. But I’m also going to be honest. You need to take a step back and learn more about how real physicists make progress in dealing with the real world.

      Theoretical physics is not done with words. It’s done with equations. Speculating with words will get you nowhere. If you look at physics papers, by lesser scientists or by great ones, as far back as Newton, you will find that equations are the engine that turn an idea into a research paper. Oh, that may not be obvious at first, because there are lots of words too, to explain the background, the motivation, the conclusions. But the heart of the discussion is equations… because words are ambiguous, and lack definite and clear meaning. No one gets any credit in the field for purely verbal speculations without some foundation in precise mathematics.

      Let’s look at what you’re saying carefully. “If you could separate string and node particles”; well, there’s no such thing as node particles and no experimental evidence of strings, and no meaning to separating them. So that’s the end of our discussion of this paragraph, because how can I make any sense of the rest of it when the first “if” statement doesn’t mean anything?

      If your other comment above you said “The idea of two gravitational waves moving in opposite directions and stretching space-time so that space is easily distorted by matter may explain why gluons attain mass in nucleon pairs”

      Here I can be more concrete, because the words have a vaguely sensible interpretation. First, gluons do not attain mass in nucleon pairs, so there’s nothing there than needs explaining. Second, and more importantly, the effects of gravity on the quarks and gluons in the atomic nucleus can be calculated, and they are

      100,000,000,000,000,000,000,000,000,000,000,000,000 times smaller

      than the strong-nuclear forces between the quarks and gluons. Gravity is extremely weak, and gravitational waves inside the atomic nucleus are completely, utterly and totally negligible.

      What is the moral here? You need to do less speculating and more learning. Learn what is known and solid; learn what is unknown and why; then put your speculating there, and ground it in equations before making it public. That is exactly what Einstein did, to great effect. So I would encourage you to follow his footsteps, and those of the other great physicists, all of whom have understood that equations are needed to turn vague ideas into the predictive tools that are needed for comparison of theory and experiment, without which we understand nothing about nature.

  50. The idea of two gravitational waves moving in opposite directions and stretching space-time so that space is easily distorted by matter may explain why gluons attain mass in nucleon pairs, because, before they found these nucleon bonds, they were being pulled by the trail of a gravitational wave and were basically in freefall so their mass was just hidden. The reason the strong interaction occurs might be these fighting waves causing a vortex around nodes and links.

  51. I definitely know what you mean about scales, having played guitar for over thirty years ! So I can identify with that analogy. My goals, I suppose, are to be able to read a mathematical proof of an idea and have an idea what is going on. I’m never going to work as a researcher at the LHC, I just want to understand a bit more, get to the next level. I will look into the MIT course, but also, are there any books you can think of, a bit more technical, that I can start on, the major and minor scales as a starter?

  52. Thanks Prof Strassler and TonyD, I’ll look into your suggestions. Prof, I’m sure you’ll hear more from me soon with my “lay” questions, I just want to take some time first to explore the site more fully so I don’t waste your time by asking questions that are already answered here somewhere,
    many thanks

    1. You’ll find Feynman’s book lacks too much detail, I’m afraid; it’s a good read, but I don’t think it is what you are looking for. You really have to learn to play scales patiently for a bit if you want to be able to play a Beethoven sonata, even as an amateur, some day in the future. So it really depends exactly what your goals are, and how realistic they are…

  53. I am a layman, so please bare with me asking some rather basic questions:

    I am a layman, and whilst I have read Hawking and Kaku, I don’t really understand enough of physics. I have a few simple (layman) questions, please don’t laugh!
    I see you say a photon is the particle associated with the electric field, which field is the electron associated with?
    Does a photon or electron have mass? I have always believed they do not.
    I do not have the time at this point in my life, or the money to go to university, however I am no dummy. I would desparately like to understand the maths that describes physics better, can you suggest a web site, or some books I could buy to give me an intro to what I need to know? Sorry if this last sounds like the stupidest question the physics community has ever heard, but you don’t know if you don’t ask.

    1. I don’t laugh at laypersons; the point of this site is to educate, and I never laugh at someone who is trying to understand.

      There is an electron field, and ripples in the field are electrons, in a similar vein to the way photons are ripples in the electric field. There are quark fields, and quark particles that are ripples in those fields; there are Z fields, and Z particles. There’s a Higgs field (at least one), and perhaps there is a Higgs particle; that’s one of the things the Large Hadron Collider is trying to find out.

      The photon does not have a mass, and travels at the universal speed limit (typically called “the speed of light”, but it is really the speed of any massless particle.)

      But the electron does have a mass. The mass of an electron is roughly 1/2000 the mass of a proton. Electrons in hydrogen atoms orbit the proton at the center of the atom at something like 1 percent of the speed of light.

      Learning physics is no small challenge; it really is like learning to speak Japanese fluently, or learning to be a professional musician, in that it will take years, and it is very, very difficult to do entirely on your own. However, the existence of on-line courses is making this easier. Have you looked into MITx, the courses that MIT is putting on-line? Perhaps there are groups of people like yourself who are planning to study these courses together; I would guess that some on-line searching might be able to suggest some opportunities.

      And maybe some of my readers have better suggestions; some of them may be partially self-taught.

    2. Trevor,

      You ask for recommendations of books on physics. I cannot claim expertise here because (1) I’m a lay person and, (2) I haven’t read very widely. But of the books I have read, I would recommend Richard Feynman’s “Q.E.D.” What I like about it is that Feynman seems to describe at least a small area of physics in a manner that lacks sugar-coating, hand-waiving, and confusing metaphor. He seems to tell it straight, simply leaving out the details of the math.

      I’ll close by saying that I too am interested in recommendations from others on accurate books on particle physics for lay persons. I hope that Prof. Strassler will consider writing one.

      Good luck,


  54. Also, if this has any truth to it, the stretching of space-time could cause mass by pulling space-time closer to particles and cause the interaction of space and particles that is mass. Maybe, I don’t know.

  55. I guess it doesn’t have to be waves, just two equal and opposite forces stretching space-time, creating a distortion around matter. Maybe it could explain dark flow too because the collision might create two beams of gravitational energy (like in supernovas or quasars, but with gravity waves instead) pulling galaxies in one direction in our half of this dimension and another direction in the other half.

  56. Well, the basic idea behind this misarrangement of sentences is that the dimension we live in is surrounded by a higher dimension on a sub-elementary particle level. I don’t know if I’m saying it right or not, but the smallest possible particles in our dimension are embedded in this higher dimension. I imagine the higher dimension like a bubble with intricate filamentary patterns running through it that is our dimension. Then a gravitational wave comes through this higher dimension from all angles and collides in the middle of the bubble. After that it condenses to the point where it breaks into our dimension and creates a giant gravitational wave which would cause the stretching of light in the far reaches of the universe. A smaller wave would come back towards the center and cause some particles, gluons I guess, to follow this wave and cause the strong force. The reason gravity exists might be that these gravitational waves are fighting and they cause the stretching of space-time and pulls space-time inward towards all particles. So, gould gravity be warping space-time around particles because of this stretching (caused by the fighting waves). Maybe if you took the amount of bending light waves at the edge of the universe and plugged in the strength of the strong force, it might show how much space-time is stretched? I’m sorry I don’t have any equations. I’m NOT that smart.

    1. It doesn’t make sense to say “the dimension we live in is surrounded by a higher dimension”. One dimension cannot surround others.

      But it does make sense to imagine our three-spatial-dimensions part of the universe as an extremely long “filament” inside a larger space with more dimensions. However, this “larger” space has to have very special properties to not be inconsistent with what we know about Newton’s law of gravitation (and Einstein’s extensions of it). Either in fact this space has to be very small in any new dimensions (so that your “bubble” looks like a very small tube, extremely long in one dimension and extremely short in all the others) or it has to have another very special shape, something you can’t draw but which looks something like a wedge (but very long, with us living at the very long wedge tip.) Otherwise simple tests of the 1/r^2 force law of Newton would have failed very badly, long ago.

      The notion that gravity might have something to do with gluons and the strong interactions is surely wrong. We know a great deal about the strong nuclear force; gravity is enormously weak; they are not directly related in this way.

      1. “The notion that gravity might have something to do with gluons and the strong interactions is surely wrong”.

        AdS/QCD people would disagree (of course I know what you mean, but thought I might point it out anyway). Ever considered doing a write-up of gauge/gravity basics, or is it not really suited to the goal of this website?

        1. I work in this subject myself; indeed my most cited paper is there. What this questioner asked was about gravitational waves affecting gluons. What you are referring to is the possibility that there are two different descriptions of protons and other hadrons, one using quarks and gluons, the other using strings and gravity. What you must never do, when using this “AdS/QCD” story, is talk about gravity AND gluons at the same time. It is one OR the other — two different languages to describe the same physics.

      2. Yes, I know – sorry, I was just being a little facetious (I did my PhD in the area, so I couldn’t resist an opportunity to mention it)!

  57. Sorry for being vague; I’m just trying to interpret and ,strangely, add to what Morgan Freeman said. Could you give me more detail why all of those things are wrong, and/or contradict each other, please. I’m just looking for some insight from someone that knows what the heck they’re talking about. Thank you.

    1. Ok, well– start with one thing at a time. You had dozens of things in there, all on top of one another.

      And you really have to understand that there is no way to evaluate a long string of words without precise definitions and clear presentation. If a graduate student came to me with such a string of unsubstantiated ideas I’d tell him or her to go read how the best physics papers are written: the precision, the equations, the clarity (well, sometimes clarity…) In a good physics talk, definitions are clear, equations are provided, techniques are explained in detail, etc. That makes it possible to evaluate what’s being said.

      Let’s say it this way (and it is the same with teaching) — if you can’t explain your ideas clearly, then it is possible that you don’t understand them well enough yourself.

      As for Morgan Freeman — well, with all due respect to the man, his science outreach has a rather low reputation in the circles in which I travel. Let’s just say that I run this website in part as an antidote to the amazing amount of incorrect and misleading information which the web and the airwaves seem to provide to the public.

    1. Dear Matt,
      Someone said that books, as great as they are, can never be your friends. This is because you cannot give your feedback to the book, you cannot participate in the conversation. I this context I’m considering you my friend and that’s why I’m calling you Matt instead prof. Strassler, and I hope this is OK with you.

      This is how I understand the physics science works (and this since I’ve started reading your website):
      – Based on the knowledge you accumulated, you have new questions and sometimes (or maybe all the time) new ideas (intuitions and insights).
      – Then, because the language of nature is mathematics, you have to put your ideas into equations. I understand this step (finding the right equations) is difficult and it probably gives you clearer perspective on whether your idea is good or not.
      – Once you have your equations, or even when you’re building them, you have to make sure they extend (and not contradict) the existing proven theories, and they agree with the data from the past experiments.
      – Now it’s good that you have equations because (pure coincidence 🙂 ) the language of physicists is maths too, and the next step is to publish your work, to bring it to the community attention. Your ideas are good until someone in the community finds something flawed in them or they are contradicted by some future experiment.

      As a layperson, I start the same: I have some knowledge, and I read articles. Then I have more questions and my own ideas. I can see I’m not alone here because people are throwing their ideas as commentaries on your website all the time. More, you say you get ideas, in form of equations, by mail, every day. Some people can put their ideas into equations. Good for them. I’m far from being able to do the same, so I put my ideas aside 🙂

      I am left then with my knowledge and my questions. But what do I know? Most of it is some sort of poetry combined with mental images (e.g. the image of a small ripple in a pond called Higgs field 🙂 ). So I don’t know much.

      How about my questions? Well, I would ask, for instance, how does the Higgs filed give mass to particles? Then you would probably think the language you need to explain this (which is math) cannot satisfactory be translated into English (It’s not the same as translating from Japanese 🙂 ) so you’d probably tell me you cannot explain this without using equations. Why don’t you use equations then? Probably because it would take you years to take me through all the math and physics that I don’t know and you would end up realizing I might not be smart enough to understand them anyway.

      Still, although I love reading all your articles, the most satisfying ones for me are those that have some equations in them. Like “How did Einstein do it?” Beautiful article! I can understand (or I think I can) there how things work. I can understand how Einstein extended Newton’s theory. (I still don’t understand “How did he do it?” how did he arrive to this particular trigonometric equation.) I can even understand the hint you give in another article that the right way to look at Einstein’s equations is to use hyperbolic trigonometry.

      I realize how much I don’t know (and I would like to know) and it’s very frustrating 🙂

      1. Thank you for this very interesting comment. I do think you’ve caught a lot of what I’m trying to explain, and that makes me feel that I am successfully communicating something of what we do. That said, I want to think carefully about what I might be leaving out before I say: “yes, you’ve got it.” Consider this a work in progress.

        Your wanting to see more equations instead of poetry is interesting. Obviously there are different readers on this site who have different needs, and not all of them want to see equations. And there is a limit to what I can do in this direction. It is not every day that I realize that there is a way to appeal to truly simple mathematics to explain something subtle. I will keep looking for such opportunities, however. I also plan to do more animations of my figures at some point; I think that moving pictures can help convey physics better than static ones.

        As you say, I really haven’t explained the history of how Einstein came to his particular equations. This is largely because history is always very complicated (not at all the way the textbooks say) and so I don’t know enough to write that history down yet. The equations did not all come in one step, either; I’ve conflated the history in my articles to keep things manageable. At some point I’ll try to get it right, because so many people want to know.

        1. “Obviously there are different readers on this site who have different needs, and not all of them want to see equations.” Please let me give you my perspective on this:

          Physics is the ultimate science for me (not the ultimate truth, though 🙂 ) because it’s trying to understand the fundamental building blocks of nature. I felt so disconnected with physics for so long, because I thought there is no way for me to find out (let alone understand) what are the latest news in physics. Not long ago I thought “Wait a minute, things must be different than 20 years ago. There’s Internet now, and you can find on internet articles about any subject. Surely, there must be good info about physics too”. So I’ve started searching and I ended up on a website organized in forums about physics. Most of the discussions (and arguing) over there were pure speculation. And by speculation I mean ideas put in words with not a hint of equations. I assumed those people knew what they were talking about, and that they had a common abstract language (again words not math) that they understood and I didn’t. That was scary and disappointing. Now imagine my relief when I’ve learned from you how physics science is supposed to work 🙂 (Even if that is still work in progress).

          I don’t think you have readers that don’t want to see equations. People don’t want to see things they are afraid they might not be able to understand, whether these are equations or words (poetry 🙂 ). People don’t want to feel left behind. If one takes them on a journey where things are explained clearly, then people will love both words and equations in the same way.

          These are some details of my journey so far with Einstein’s equation E2 = ( p c )2 + ( m c2 )2 (Please forgive the fact that the squares are not in superscript):

          I am reading only two websites about physics for now: Yours and a blog (recommended by one of your readers), written by Flip Tandeo, a young theoretical physicist. Initially all I knew about Einstein’s equation was E=mc2 . Then I saw the full equation in several articles on your website and understood, for instance, that the notion of “relativistic mass” was abandoned in modern physics and understood why. Then I read on Flip’s blog that this equation looks a lot like the equation of a circle. Only he writes it E2 – ( p c )2 = ( m c2 )2 and calls it a circle with “a funny minus sign”. I was thinking “It makes a lot of sense to put it in this form, cause the only constant thing there is (mc2)2. But the funny minus sign is still bothering”. Then I read your article “Mass and energy” and the circle still looks funny because I can see clearly in your pictures that the hypotenuse of that right angle triangle is not constant as I would expect from a nicely behaved circle 🙂 Then I arrive to your warning “the right way to understand Einstein’s equations is using hyperbolic trigonometry” and I have the “Aha!” moment. This is not exactly the equation of a circle but of something else I vaguely remember 🙂

          So, you see? It’s not scary anymore but rather beautiful. All it takes is someone with a deep understanding of these equations, and a deep understanding of what I don’t understand 🙂 to take me on this journey.

          Flip goes on saying (as a hint) that the equation of a circle is also a way of defining length, and as soon as you have a definition of length you have a particular kind of geometry 🙂 and if you take into account the symmetries of that particular definition of length you get… Suddenly words like “Lorentz transformations” and “Minkowski space” don’t sound so scary anymore either 🙂 For sure, now I have more confusing things in my head, but they don’t scare me. Maybe if I try to approach them by myself I will get scared again 🙂

  58. Could the Higgs field be a higher dimension that runs through the spin networks in our dimension or is that a contradiction? Also, could gravity be a wave that ran through this higher dimension to create the big bang and the reason it is so weak might be it comes from the other dimension or is that stupid? And last one, could the reason that particles have mass be that heavy particles were forced from this higher dimension at extreme speeds and lost mass, but still retained some or is that dumb too?

    1. Sorry, could the reason particles have mass be that particles forced out by the gravitational wave into our dimension and contracted the node-link structures creating a pressure from space-time curvature and a condensation of energy into matter?

      1. Well, there is extra-dimensional electroweak symmetry breaking (not quite the same thing, but related)…

  59. Oops, my bad. The idea of “no upper limit for the speed of light prior to the Higgs” is stated at the Finnish version of Wikipedia.

    Nevertheless, has the Higgs field always existed? Or did, say, the photon field come up only when the electro-weak force broke up to electro-magnetism and weak force?

    1. Hmm — that tells you the value of Wikipedia — a good place to start your research, a terrible place to finish it!

      To restate your question as I think you meant it: has the Higgs field [which, like the electromagnetic and W and Z fields, may well have always existed] 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.

  60. Dear Dr. Strassler,

    How was the very early universe like (right after the BB) before the Higgs field was established? I’ve learned there was no upper limit for the speed of light then. What does that add up to in practice? Also, did the space-time curve already before the Higgs field like it does today?

    1. I’m not sure where you learned there was no upper limit for the speed of light before the Higgs field became non-zero. That’s not true at all.

      The Higgs has nothing to do with the universal speed limit, or with space-time curvature. That’s all about space-time and gravity, which has nothing to do with the Higgs field; how gravity works is also not affected by the Higgs field. For instance, Einstein was able to write down all of his equations without even knowing of the existence of the Higgs field; all of his predictions for how space-time curves were made without knowing of the existence of the Higgs. And when Higgs and the five other people (Kibble, Hagen, Guralnik; Brout and Englert) wrote down the theory of the Higgs field, they did not refer to gravity at all; there was no need.

      As far as we know gravity and the Higgs field are two rather independent aspects of the world. There is no obvious conceptual link between them (despite attempts to think of one.)

  61. Professor Strassler,

    Firstly, I thank you for setting up such a enlightening website and your patience answering these questions is something to be admired.

    I do not have any formal education in particle/ quantum physics beyond A-level but I am doing my best to educate myself and keep up with current affairs. This FAQ has already broadened my understanding of the higgs mechanism. Until now, I was led to believe that this inappropriately-named “god” particle physically interacted with other particles to give them mass. This never did make sense, especially when it only exists for a few fleeting moments. Now I understand that the boson is a CREATION of the higgs field, rather than the CREATOR? That paparazzi analogy led me to think that massive particles had to push thier way through a sea of higgs particles (hindering thier acceleration in the process)…

    I have seen the higgs boson referred to as “scalar” i.e. no direction, is this because (or why) the rest mass of an elementary particle (of the same type) is universal? i.e. EVERY charm quark has a rest mass of 1.27Gev/C^2 and is an intrinsic characteristic of that particle. As the higgs isnt a force carrier, I assume it won’t fall into the characters of the “guage bosons”? But the graviton would? If there are other bosons mediating a particles charge and spin, it would be categorized with them? Under what “prefix”?

    1. Yes, you’ve understood: the Higgs field being non-zero gives the masses to the various other particles, while the Higgs particle is a ripple in that field, and does not itself provide mass to anything.

      The reason the Higgs boson is a scalar is that its field is a scalar; the reason the field must be a scalar is that only such a field can be nonzero and give masses to particles without huge consequences for the universe that we do not observe.

      The reason that all charm quarks have the same mass has nothing to do with this. The reason all charm quarks have the same mass is that they are all ripples in the same charm quark field. All ripples in a given field have exactly the same mass. This would be true even for fields whose particles do not get their mass from the Higgs field. Dark matter particles might be an example.

      The Higgs is not a gauge boson, and it is not what we often would call a matter particle — though the latter definition might become slippery in future. Neither is the graviton, though in certain ways it is more similar to a gauge boson. Both gravitons and gauge bosons have very strict rules which govern how they interact with other particles; Higgs bosons are much more flexible, which is why the quarks and leptons can have such different masses from one another.

      Since there’s only one thing like the graviton (the graviton itself) and so far there’s only one thing like the Higgs particle (the Higgs itself) there aren’t categories defined for them. The rest of the known particles divide neatly into the categories of force-carriers (spin-1 gauge bosons) and matter particles (spin 1/2 fermions.) It isn’t guaranteed that categorization will be useful forever.

  62. I have this notion that the Higgs field does not exist throughout 3+1 dimensional
    space. Because if it did it seems to me akin to the ether which was found to
    be superfluous.

  63. Prof. Strassler,

    I was bold enough to direct my question of December 16 directly to Weinberg via e-mail. He answered that “for a free spin 1 particle no four-vector can be constructed but an anti-symmetric tensor can be”. This means there is no problem to construct a theory for a free spin 1 particle but one has to except that gauge invariance has to be introduced.(I thought free massless spin 1 particles could not be constructed so his remark helped me a lot). For an interacting massless spin 1 particle the four-vector can be used because it is combined with a conserved current (which is also part of gauge invariance).

    So in the Standard Model we start with massless particle including gauge invariance and at that point should not care about massive particles and only talk about massive particles after the symmetry breaking. From this I get the impression that gauge invariance (which is so important in physics) cannot be explained in non mathematical terms. Do you think there is a way to explain gauge invariance in a few words? I though the fact that we can put a massive particle to rest relative to us while for a massless particles thiis is impossible had something to do with it but I am now more or less convinced that it is all a complicated mathematical consequence of the symmetry breaking.

    Thanks for your great site and all the effort you put into it!

    1. The thing you always have to remember is that gauge symmetry is a mathematical trick to make equations look nice; it isn’t physics, but technique. There is no real symmetry there, so “gauge invariance” is simply another word for “physical”.

      As Weinberg says, the theory of a spin-1 particle is that of electric and magnetic fields (combined together they form that “tensor” you referred to), and their interactions with matter. Only once you have interactions with matter do you have trouble expressing these interactions in equations that look simple. The introduction of gauge symmetry is a way of making the equations simpler. It is not, however, necessary in principle to add it in. But practically, writing things in purely gauge-invariant notation makes the equations so awful that the only way to solve them is … to introduce gauge-non-invariant quantities to make them look simpler, solve them, and then make sure you only use them to compute physical things — things that were gauge-invariant to start with.

      There are ways to explain this more conceptually but I do not have a complete and satisfactory way to do it yet… and I am afraid it is not at the moment my highest priority. But I will keep thinking about it.

  64. I thought I’d ask a simple question (hope it’s not been asked on here before). If I have a basketball in front of me, what percentage of it’s mass is due to the higgs field?

    Thanks for this great article.

    1. You thought it was a simple question. But it isn’t. You will hear people say that the proton and neutron get most of their masses from the strong nuclear force (which is true) and electrons, which get their mass from the Higgs, are 2000 times lighter than protons (also true) which means that the Higgs contributes only about 0.0003 of a basketball’s mass (which is … naively true.)

      But in fact there is an important quantum mechanical effect that this leaves out. And if you account for it, the Higgs field contributes almost all of the mass of the basketball.

      Explaining this requires a long article, possibly with one or two supplemental arguments. It’s on my list of things to do this winter… so stay tuned.

  65. On the subject of Higgs relatuionship to gravity, my naive thoughts are that if the Higgs field provides most particles with mass, and this mass makes a major contribution to the energy-momentum tensor in GR. Then surely the Higgs field is making a major contribution to the curvation of spacetime, which we observe as gravity, or have I missed something?

    1. The Einstein equations relate gravity to energy and momentum. They don’t care what the source of that energy and momentum is — whether it comes from a Higgs field’s contribution to mass or from something else. They are completely universal.

      The Higgs field gives mass to the known particles — but only partially to the Higgs particle… and many other particles may be out there that get their masses from other sources. Gravity doesn’t care.

      You will only confuse yourself if you insist on thinking that two people who both have brown eyes must be relatives.

  66. Dear Matt,

    Returning to the question of how the Higgs field induces mass, is there any similarity with effective mass in solid state physics? Here as a electron experiences the periodic potential of a crystal lattice its Energy-Momentum relationship is changed, and where there would be a rest-mass term in free space, this is modified to give a term of the same form, but which is bigger. Does the interaction of particles with the Higgs field do something vaguely similar?

  67. 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?

    1. We do. But in quantum field theory (the type of equations used in the Standard Model of particle physics) mass turns out (not obviously) to be very different from charge and spin. The charge (relative, say, to that of the electron) 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 for one type of particle 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.

      What is true in quantum field theory is true in string theory too.

      1. Thanks for the very clear answer Matt. When you say that the origin of charge and spin is very different from that of mass, are the origins of charge and spin known (albeit from a completely different framework)?

        1. Their origins aren’t known, and their details might be accidental for all we know, but there are some very clear ideas about the relationships between the charges and spins of certain classes of particles. For example, the up quark, down quark, electron and neutrino (after you pull them apart properly — see this article http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-particles-if-the-higgs-field-were-zero/ ) can be organized into two natural groupings in the context of grand unified theories (where one also tries to combine the three non-gravitational forces into one.) To say it differently, and more along the lines of your question, grand unified theories predict that there will be groupings of particles that all share the same spin and also have related charges. [The math: grand unified theories involve a Lie group, and the particles must form complete representations of the Lie group.] Even without grand unification, there are similar relations that can arise in string theory, and also other constraints that can arise from quantum consistency of the Standard Model itself. So there are partial answers, ones that do not tell us why overall we find in nature the particles we know with their charges and spins, but instead tell us that given that we find certain particles with certain charges and spins, we should not be surprised to find others with different charges and the same spins. (And if supersymmetry turns out to be correct, we will also expect new “superpartner” particles with the same charges as particles we know, but different spins.)

      2. I would add that there is also a clear sense in which mass is very different to charge and spin, in that the latter two are discretised in a way that mass is not (stemming from the fact that they can be thought as well-defined mathematical properties of the quantum fields).

        In addition, we seek a “fundamental” explanation for mass that specifically takes the form of a Higgs field, because simply putting in a mass term into our equations (without positing its origin as a Higgs field) violates an important property of the Standard Model called electroweak gauge invariance. The same cannot be said of spin or charge.

        1. I mostly agree — but I think you have to be careful on a couple of points.

          a) Spin is discretized, because of the structure of space and time in Einstein’s relativity.

          b) Charge is not necessarily discretized unless you embed electric forces into a larger structure, such as grand unification, string theory, etc. (Technical point: quantum anomalies do strongly restrict charges, however.)

          c) In the Standard Model, which has the simplest possible form of Higgs field, the non-zero Higgs field provides non-zero mass to the electron and the top quark, but says nothing about why their two masses are so different.

          d) Important technical point: Gauge invariance is a bit over-stated in the literature. One must always remember that gauge symmetry is something we put into the equations to make them easier to work with; it is not, itself, physical. All physical quantities are gauge invariant anyway. So one really needs to make statements of this sort more physically. The correct statement really has to do with charge conservation; before the Higgs field becomes non-zero, the two particles that get combined by the Higgs field into the massive electron have different charges under weak isospin and hypercharge, so they have different long-range fields and cannot be combined in any way. Meanwhile each half separately, given the long-range fields that it has, has the wrong number of degrees of freedom to be massive, so it must be massless. You notice the words “gauge invariance” do not need to appear.

  68. I had a professor tell me that Lederman answered the question of why they called it the “God particle” in an interview, and Lederman’s answer was “…because they wouldn’t let us call it the ‘goddamn particle’.”

  69. By the way, as long as you do this in the context of general relativity as an effective low energy theory below the Planck scale, the correspondence principle should hold, and gravitational and inertial mass are automatically related.

  70. Think of it this way: Einstein gravity acts on and is sourced by all forms of energy including mass. The Higgs field bestows mass upon particles, thus modifying the way they are affected by Einstein gravity in an indirect manner.

  71. Professor Strassler,

    The previous poster posed a question which is either identical to or closely connected with my own: You have stated that there is no relationship between the Higgs field and gravity. You have also stated that the Higgs field makes certain particles massive. But what is it to have mass? A particle’s having mass seems to imply two things: (1) The particle resists acceleration by certain forces to a certain degree, and (2) The particle is attracted to other particles with mass to a certain degree. Are (1) and (2) related? If so, is it correct to say that that Higgs field explains (1) but not (2)?

    Thank you for any response.

  72. Can the Higgs field not be related to gravity at all? Under non-relativistic conditions we ceratinly seem to see an equivalence between inertial and gravitational mass. I can understand that general relativity overturns Newtonian Gravitation at a fundamental level, but why do we see on a daily basis that inertial and gravitational mass are equivalent, and that hence all objects are accelerated at the same rate in free fall?

  73. Thanks for some very helpful explanations. However, the part I am still struggling with is how the Higgs field imparts mass. The celebrity analogy helps one understand how the Higgs filed could increase inertia that was already there, but where does any inertia itself come from in the first place? And secondly, how does this fit with the other aspect of mass we are all familiar with – gravitational attraction?

    1. Gravity and the Higgs field are not related at all. See the second comment and my answer in http://profmattstrassler.com/articles-and-posts/the-higgs-particle/the-standard-model-higgs/decays-of-the-standard-model-higgs/

      As for how the Higgs field does its thing: essentially, if you take a particle that can interact with the Higgs field with a certain strength, then, in a region where the Higgs field is non-zero, the particle will find its mass-energy increased by an amount proportional to that strength.

      If you ask “how does *that* work?”, I’m kind of at the stage of having to point to an equation. It’s not something for which we have natural intuition. Maybe I’ll figure out a more intuitive explanation someday. The “larger inertia” celebrity analogy is misleading in various ways, as are all the other ones that are commonly used — which is why I don’t repeat them here. It might be better, in this case, just to understand that it is a new phenomenon that you are not familiar with (and that physicists, too, were not familiar with before the 1960s.) Maybe that’s a cop-out, but I’d rather not mislead you with false analogies.

  74. Great. Looking forward to that and feel honoured! Sorry for asking this question here, I didn’t know where to go.
    If you are not already familiar with it, I would like to recommend chapter 5 of volume 1 of Weinberg, especially page 250 where he writes: we have thus come to the conclusion that no (mass-less) four-vector field can be constructed … and then introduces gauge invariance.

  75. Prof. Strassler,

    I am a theoretical physicist myself and just finished Weinberg’s books volume 1 and 2 on field theory.
    Please read my question more carefully. The whole E=mc2 was just an lose introduction. Of course I know that the full equation is E=mc2/sqrt(1-v2/c2) or even better E2-P2=m2 (c=1). Maybe it is better to read from This in turn ….
    I didn’t want to get too technical. It is related to the discontinuous solutions to the Poincare invariance, then the fact that massless spin 1 can not be constructed in a Lorentz invariant way and must be coupled to a conserved current to get rid of the non covariant contribution after a Lorentz transformation.

    Marcel van Velzen

    1. Sorry — this happens sometimes, with the wide variety of comments. When I read your question first it seemed confused, but I do see now that you were asking something sensible.

      This part of the website is really aimed at the public and not at experts. I would rather transfer your question and my answer to the “Technical Zone” part of the website.

      Meanwhile I am afraid that I do not have time to answer it today. tthe answer isn’t trivial at all, and involves a proper understanding of what gauge invariance means. Indeed I start out my second-semester quantum field theory course by answering this question carefully over the course of about half a lecture. I will try to remember to answer it over the next couple of weeks. If I forget, please feel free to ask again in the New Year.

  76. Professor Strassler,

    I would like your opinion on a deeper reason why we need gauge invariance and so need the Higgs field.
    The trouble we face in physics is already clear from E=mc2. If we put m=0 we get E=0. Now this of course is wrong (light has energy) but we could say that the formula is only valid for particles with mass. But here our troubles are not over because we would think that in the limiting case for mass to zero it would work (there is no law that says how v-> c if m->0 to be saved by the sqrt(1-v2/c2)). This in turn is related to the fact that we can always put a particle with mass to rest by running along side, while this is not possible for a massless particle. This is not continuous: it is possible or it is not possible. Now with a vector particle we get into problems, a massive vector particle has 3 polarizations (because it can be put to rest), while a massless vector boson has 2. With fermions that is not a problem because they always have only 2 polarizations and the polarizations rotate in the direction of motion if mass goes to zero. This problem that we have to get rid of one of the polarizations is at the origin of gauge invariance and gauge invariance is at the origin (among others) for the need of a higgs field. Now my question is: do you agree that gauge invariance is at the origin of the fact that we have a discontinuity between massive particles and massless particles (one can be put to rest, the other not) because you never read it in this way?

    Thanks in advance!
    Marcel van Velzen

    1. The formula E = m c2 ONLY applies to a particle that is not moving relative to you. That is why you are confused. (And it is not your fault, because this mistake — misinterpreting Einstein’s formula to apply to even particles in motion — has been made widely, and propagated even into freshman textbooks.) I have written about this in more detail elsewhere ( go to http://profmattstrassler.com/articles-and-posts/the-higgs-particle/360-2/, and search for “Alfa” in the comments, and you will see a related question and answer) and will put a more detailed article up on it someday.

  77. Thank you for your response. (Somehow the anomaly of “mass-less” photons having paths affected by passing a massive object never occurred to me.) My question concerning dark energy was prompted by some remarks of UCSD physicist Kim Griest at http://www.youtube.com/watch?v=Y-vKh_jKX7Q, from approximately 22:00 to 24:00 (and 26:30), which suggest the role of dark energy is largely to cancel the mass associated with the Higgs field.

    Also, is there any book that you would recommend on the topic of Higgs that is up-to-date, accurate, and accessible?

    Thank you.

  78. Professor Strassler,

    Thank you for your illuminating discussion. The topic is one of great current interest for a significant segment of the public. As a member of this segment, I encourage you to expand it.

    Three points of possible expansion:

    First, I was wondering if you could comment on the connection, if any, between the Higgs field and dark energy.

    Second, it is commonly said that the Higgs field’s essential function is to slow particles that would otherwise be moving at the speed of light by imparting mass to them. (If they had no mass, they would move at the speed of light.) But besides not moving at light-speed, a particle’s having mass has another important (definitional) quality, I believe: particles with mass (definitionally) attract each other. Does the Higgs field explain, or have any connection to, this feature of mass?

    Third, I found the previous question by Curious Mind concerning “how” the Higgs field imparts mass an interesting one.

    Thank you in advance for any response.

    1. Higgs field and dark energy: as far as we know, no connection. We know almost nothing about dark energy right now, and the Higgs field does not seem to have any natural way to be related to it.

      I have written elsewhere about the relation between gravity and the Higgs field (none!) Gravity in Einstein’s theory actually pulls in a complicated way on energy and momentum — and on mass only incidentally, since a massive object at rest has a “rest-energy” (or “mass-energy” as I typically call it on this site) E=mc2. This is why the sun can deflect light even though photons (particles of light) have no mass.

  79. If the Higgs particle is discovered, it seems to me, it will just ‘move the screen further’ , so to speak. We will start to explain things in terms of leptons, quarks, field particles – and the Higgs boson. Then we will say “How do we explain these particles?” And the search will continue.

    It would be very interesting and very satisfying if this particle is discovered. But even if it should be found, our limitation in finding the how and the why of things around us by experimentation, hugely expensive equipment and mathematics is limited. The popular press can miss showing this limitation.

    1. What you say is true, but it’s also obvious in a way, and I think beside the point. We’re all mortal too, but that doesn’t make life not worth living. And yes, our knowledge will always be bounded, but still it is expanding.

      One has to remember that while of course there will always be limitations, the progress in this field — going from almost complete ignorance of the weak and strong nuclear forces 70 years ago, where one could predict very little about their properties, to being able now to do high-precision calculations about them today — to the point that many hundreds of measurements at the LHC have agreed with theoretical calculations — is astonishing. There have been similar extraordinary advances in many other fields, such as the solid-state physics, astronomy and cosmology, etc. You only have to go back and look at science textbooks from 1911; then you can get a strong reminder of how far knowledge and predictive power have increased over that time.

      So it is important to find the right balance between appreciation of the limitations of human thought and knowledge, on the one hand, and celebration of what can be achieved through creative yet rigorous scientific investigation, on the other.

  80. Alex, thanks for the reply, but that reference is quite old and most of it does not currently “hold water”.

    Science’s assumed & verified results are more and more like crazy but true since fiction stories, the same argument will be valid if something goes wrong.

    In my profession I work with quite a large numbers of highly educated engineers, and would say that 90% is too young to see the results of what they are doing, and correct me if I am wrong, but it will be the same for professionals involved at the LHC.

    1. Hello Harry,

      Where do you have the information from that the LHC safety report “doesn’t hold water”?

      I have no idea what you mean about the science fiction stories.

      Actually, many, many of the people involved with the planning and building of the LHC now see the results. Obviously not those that were already really ancient when it was started, but the younger ones do of course. The LHC project was approved… like the mid 90s or so.

  81. You say that the Higgs particles are not spontaneously created. 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?

    1. 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.

      1. So if the higgs particle plays no role in the mass mechanism, then by what mechanism does the Higgs field couple to a particle like an electron? Your FAQ doesn’t appear to mention anything about “how” the Higgs field “gives” an electron “mass”. At some point, the Higgs field has to interact with the electron such that it slows its acceleration as the result of an applied force in accordance to the formula F=ma. So how does the Higgs field (regardless of what or how it is made) supposed to increase the resistance to acceleration? The only thing I can think of that an electron has that could slow its acceleration is the electrostatic force, but mass isn’t electrostaticly generated or related, is it?

  82. Good of you to take on such a range of questions, both along the half-to-wholly baked dimension and the other one that scales breadth of interest. Mine is probably low on the “baked” dimension. Its higgs-relevant score is also rather low.

    In the preceding posts, the word “mass” is thrown about as an observable: rest mass, kinetic energy mass equivalent, intertial mass, mass as a quantum observable, mass as somehow spread out but instantiated only at what we treat as symmetry-breaking loci, sort of point like but not really, really points. This has me wondering if we are not usingt he word to mean a lot of things, or to use it as wallpaper over the conceptual cracks.

    What mass “does” is threefold, I think.

    It apparently stores rest energy – another ‘everything and anything’ word – and in storing it, provides observables that characterise particles. These present seemingly unrelated values: they may align into families, but the values shown are all pretty random when viewed as a number ladder. That is, it takes on discrete, conserved but seemingly unrelated values.

    It – or that which displays it – has a relationship with spacetime that seems to have a lot to do with timelike momentum, and time like momentum with it. It – or whatever generates soem or all of what we see as “mass” – has a lot to do with what space “is”, and not merely with how things interact within it.

    Separately from the rest mass energy storage property, it also stores energy as a result of differences in momentum, with absolute properties in respect of boosts and brakes.

    These are pretty different things. I am sure that there are more categories of this sort. Are we quite clear that they are in fact ontologically the same thing, generated by the same means; or are they possibly not many faces of one thing but one face that we slap onto many things?

  83. That’s really not true. The Higgs mechanism does not require extra dimensions. There is the Higgs Hierarchy problem, but it is not entirely clear whether it’s a problem, and if it’s a problem, whether the solution is an extra dimension-

  84. So if the Higgs particle decays rapidly, 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. Do I have it backwards in that what really exists is just the Higgs field (created by some unknown process) and the Higgs particles wink in and out of existence as a kind of side effect?

    1. 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.

      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 very bad science.

      The Higgs particle is the least-intense possible wave in the Higgs field (just as any particle is a wiggle in its corresponding field; the non-zero value of the Higgs field is not important for this.)

      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 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 lake, the violin string, and the Higgs field remain behind after the vibrating dissipates.

      1. Could you go into a little more detail as to why the Higgs field (at least in its vacuum state) should not be considered a condensate of Higgs particles in the same way that the QCD (or technicolour) condensate is a condensate of q-qbar pairs? Thanks.

        1. Because the QCD condensate is not a condensate of q-qbar pairs. It is a non-zero expectation value of the q-qbar composite *field* (or “operator”, more technically speaking). Clearly there is a difference: strange quarks are unstable, but the strange-anti-strange condensate is not.

      2. The comment by James that the QCD condensate is a condensate of q-qbar pairs (rather than a non-zero vev of the composite q-qbar field) seems similar to the physical picture used in the the BCS theory of superconductivity of ordinary metals, and maybe inspired by it. In that theory, electrons are said to pair up and condense into the lowest energy state single-particle state. The non-zero expectation value is for the average . Would it be incorrect to actually say in the context of condensed matter superconductivity that “electrons pair up and condense”?
        Thanks, Prof. Strassler.

  85. Is the Higgs particle supposed to be stable? This would be a most fundamental property (stable or decays) of any particle, so please don’t ignore this fundamental question.

    1. Not stable. The Higgs field could not do what it does without coupling to ordinary matter in a way that guarantees that the Higgs particle can decay very rapidly, on extreme microscopic time scales. Typically (depending on its mass) the Higgs lifetimes is between billionth and a trillionth of a trillionth of a second.

  86. Why can a photon, particle of the electromagnetic field, have any amount of energy, but the higgs particle’s mass is fixed?

    1. You are confusing mass and energy; this is not your fault, but the fault of a major conceptual error that unfortunately runs even through freshman physics textbooks. It was caused by a wrong turn in physics concepts — one that Einstein’s original papers do not subscribe to, and that no modern professional theoretical physicist subscribes to either. Here is Einstein’s (and the modern) view.

      (1) All particles have a definite, fixed mass. This is sometimes called the “invariant mass”, but in fact it is the only thing that should be called “mass”. Photons have a mass of zero. The proton has a mass of 0.938 GeV/c^2. The Higgs has a mass of — something, guess we’ll find out soon, if it exists. A particles mass does not change as the particle moves, and all observers agree on what it is.

      (2) All particles can have any energy that is equal to or larger than their “rest energy” (or “mass energy”) E = m c^2. A particle that is moving has both mass energy and motion energy (also called “kinetic energy”), and its total energy is just the sum of the two. Unfortunately, sometimes people take the total energy, divide it by c^2, and call the result the “relativistic mass”. This is a very serious conceptual mistake which leads (as your question shows) to many confusions. Taking the energy, dividing it by a constant, and calling it a different form of “mass” is silly: one should call energy “energy”, and call mass “mass”. Unlike mass, energy depends on your point of view: if you have a proton in your hand and I am traveling past you in a car, I will see the proton as moving and say the proton has motion energy, while you will say it does not — even though we agree the proton has a mass of 0.938 GeV/c^2.

      In particular, Einstein’s theory says: E = m c^2 only for particles that are stationary!

      In short: the answer to your question is that you need to fix your definitions. A photon can have any amount of energy, but its mass is always zero. A Higgs particle (if it exists) has a definite mass M, and its energy is M c^2 if it is stationary and larger if it is moving. What is true for the Higgs is true also for a proton, an electron, and indeed any particle with a non-zero mass; its energy cannot be smaller than its mass energy, but it can be as big as you like.

  87. Prof Strassler,
    I thank you very much for the effort that you’ve put into this site, its been an enlightening read as a undergraduate physics student. I have a question as to your thoughts on a recent article that was released via arxiv as to having the gravitational field responsible for the interaction between particles that causes mass.
    The link to the paper is http://arxiv.org/abs/1111.4228 and I would very much like to hear your opinion on it, as it seems to present a logical and convincing argument.
    Thanks in advance,

    1. Any such theory would have no hope of explaining the ratio of the masses of the W and Z particles, and the strength with which the various quarks and leptons interact with the Z boson, for instance. The Higgs field is already known to exist in nature, because with it we can do a beautiful job of predicting many dozens of measurements made in the last 40 years.

      More precisely: there might or might not be a Higgs particle, and there may be one or several of them — this we do not know. But there is most certainly something playing the role of the Higgs field. Read the Higgs FAQ: http://profmattstrassler.com/2011/07/24/the-first-version-of-the-higgs-faq/ , and also the article on what the world would be like if the Higgs field were zero: http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-particles-if-the-higgs-field-were-zero/ . Gravity simply cannot rearrange the particles and forces the way the Higgs field can (and must, to agree with experiment).

  88. Very helpful site! Sorry, but I can only evaluate philosophically… I find it difficult to understand how particle mass could be continuously and dynamically assigned to atomic components (quarks and electrons) that were initially emitted billions of years ago.

    If mass was only allocated to quarks when they were initially emitted into the early universe, for example, perhaps the extreme energy density of the external spacetime into which they were emitted prevented their propagation – instead reconfiguring their kinetic emission energy as the localizing potential energy of mass.

    In this way the ‘particle selection’ function of the Higgs field is provided by the mass-energy density of spacetime, which has temporally diminished with the expansion of the universe. During most of the universe’s history emitted particles could freely propagate through low-density spacetime: their emission energy is nearly always expressed kinetically (until materially absorbed).

    In this scenario, only the exceedingly high energy density of the very early universe could allocate mass to emitted particles through reconfiguration of their kinetic emission energy. In particle collider experiments, these external fields of localized potential mass energy are dispersed along with the momentum imparted by experimental conditions, allowing composite particles to disintegrate. They may be no ‘Higgs’ particle to detect, just as there is no particles produced by the dispersion of experimentally imparted momentum.

    Sorry I can’t describe in the context of existing theory and knowledge, but might some of these ideas (properly integrated) address some of the issues with the Higgs mechanism?

  89. Thank you very much, I’m glad I found this site, already I’ve a better understanding of the Higgs field and Higgs particle’s part in nature.
    Thank you for your time.

  90. Thank you. I’m not sure my question is making sense but here goes.
    I was trying to ask what gives rise to a Higgs particle, I know it’s an excitation of the Higgs field, but what caused that excitation? In other words, is the Higgs particle/excitation a disturbance of the Higgs field caused by interactions between other particles ?
    Thank you for your time.

    1. Yes — that’s basically right. The Higgs field is just sitting there; how are we going to make it ripple? [Imagine a pond; how are you going to make ripples on it? You need a dropped stone — something with a lot of energy that interacts somehow with water. Or a silent piece of metal; to make ripples on it, you need a hammer.] The answer here that we have to get a very large amount of energy in a very small space, and we have to do it in the form of high-energy particles that interact with the Higgs field strongly enough to get it to wiggle. And that’s exactly what the Large Hadron Collider (LHC) is supposed to do for us!

      There are some surprises when we look at exactly what the best ways are to do this. In particular, the best way to make a Higgs particle at the LHC is using two colliding gluons. And that seems very counter-intuitive, because gluons do not interact directly with the Higgs field at all! They only have an indirect interaction with it, one which is really quite small. But there are so many gluons in the proton that their tiny indirect interaction with the Higgs field turns out to yield the most effective way to make a Higgs particle! (There are a couple of other good ways to make Higgs particles, involving W and Z particles, but that’s a much longer story…)

  91. First, a quick clarification: not all particles get mass from the Higgs field. Photons are particles too, but they don’t interact directly with the Higgs field, so they don’t get a mass from it. Dark matter particles (if indeed dark matter is, as many suspect, a sea of particles) probably do not get their mass from the Higgs field. So there is no statement that the Higgs field is the universal generator of mass for all types of particles; that is surely false.

    The rest of what you said is true…almost. My version of what you said would be: the important thing about discovering the Higgs particle (or particles, or whatever replaces the Higgs particles if there aren’t Higgs particles in nature) is that it/they will give us insight into the nature of the Higgs field — which we know must be there, but about which we know almost nothing. Think about how the sound of a metal pipe, if you struck it, would tell you something about the shape and material of the pipe… the ripples in the pipe [which make the air ripple too, so you can hear it] tell you something about the pipe itself.

    As for your last question: I’m not sure I understand it. Can you try to ask it again, maybe in different words?

  92. Hello, I’m finding this site very helpful.
    Reading some of the articles about the Higgs field I have become confused.
    1. The Higgs boson interacts with the Higgs field and so acquires mass.
    2. So, are there two ways particles can acquire mass? one by interactions with the field and one by interactions with the Higgs boson.
    In other words, a particle, say an electron, through interactions with BOTH the Higgs boson and the Higgs field acquires mass ?
    Is it something like, some particles interact more strongly with the boson then with the field and so have a larger mass?

    1. No particle acquires its mass by interaction with the Higgs boson. This is a misstatement you will see in the press and in some lay-person literature. The Higgs boson is another word for the Higgs particle. There are no Higgs particles in the room in which you are sitting, but your electrons have mass. What is in your room is a non-zero Higgs field. That is what gives your electrons mass.

      And it’s a good thing too, because we haven’t even established experimentally that there is a Higgs particle… only that there is a Higgs field. See http://profmattstrassler.com/articles-and-posts/the-higgs-particle/implications-of-higgs-searches-as-of-92011/ . The electron mass doesn’t care what type of Higgs particles there are in nature, if any; it only cares that there’s a Higgs field.

      Does that help?

      1. Thank you, I think that does help.
        I’m seeing it now as, particles, not photons, have mass because they are in the Higgs field, and the ‘only’ important thing about the Higgs particle is its detection (indirectly) would be our way of confirming the Higgs field idea.
        Having said that, I’m left wondering what the Higgs particle does do in its interactions? or is the Higgs particle (ripple) just the consequence resulting in the higgs field, of other particles interactions with each other ?
        Thank you for your time.

  93. One thing I do not understand about the search for the Higgs is that at the enerigies they are looking at, the Higgs particle would have to decay very rapidly. But if it decays rapidly, then how can it exist long enough to create a Higgs field which must be a long lasting stable field in order to give electrons, etc. mass. Also, if the Higgs is unstable and is constantly decaying, then by what mechanism is it being constantly being created with and where does that energy come from?

  94. Is a very light Higgs (mass < eV/c^2) ruled out by theory?

    Has a very light Higgs (mass < eV/c^2) been ruled out by experiment?

  95. Does the Higgs mechanism offer us any clue as to why gravitational mass and inertial mass are equivalent?

  96. The flip-flopping between fermion states sounds like the phenomenon of electron Zitterbewegung which is implied by the Dirac Equation.

    Could interaction with the zero-point electromagnetic field cause charged fermions to flip-flop between left and right states as well as a Higgs field?

    1. Just to give you a quick answer: first, the phenomena are in fact unrelated (the equations for zitterbewegung and for mass generation are completely different), and second, the electromagnetic field (or any other field like it) definitely cannot do what the Higgs field does. [Sociologically — if there were such a possibility, people would have studied it in great detail 40 years ago.] But I am having a little trouble writing a clear pedagogical explanation. Let me think about how I might explain it in words or a simple picture.

  97. Is it possible that the Higgs particles have been “eaten” by the W+, W- and Z particles giving them mass but leaving the fermions to pick up mass by another mechanism?

    1. Excellent question. The answer to your question is “no”. The quarks and charged leptons get their masses as described here for the top quark. Without a Higgs field, the top-quark-left and the top-quark-right particles cannot mix to form a massive top quark. So a Higgs field of the particular required type is necessary both for quark and charged-lepton masses (and neutrino masses, but it’s more subtle) and for W and Z particle masses.

      Now you might ask, couldn’t one Higgs field give mass to the W and Z and a different Higgs field give mass to the quarks and charged leptons? The answer is … “well, no, but let me explain that carefully.”

      It is possible for a Higgs field (of the required form) to give mass to the W and Z particles and give no mass to the quarks and charged leptons, but the reverse is impossible: any Higgs field that gives masses to the quarks and charged leptons will contribute some mass to the W and Z particles. [If you have two Higgs fields h and H with non-zero average values v and V, then the W and Z masses are proportional to the square root of v2 + V2 .]

      It is possible in principle for there to be, say, two non-zero Higgs fields, one of which gives mass to quarks and charged leptons and the other of which does not. Both of them will contribute to the masses of the W and Z particles.

      It would be possible, if all the charged leptons and quarks were very light, for one Higgs field to give the quarks and charged leptons all of their masses and the W/Z particles a tiny bit of their masses, and for a second separate Higgs field to give the W/Z particles most of their masses.

      But the top quark is heavy. Whichever Higgs field gives the top quark its mass must be not only non-zero but also large, and it therefore will give the W and Z particles a substantial fraction of their masses. So given how heavy the top quark is, we cannot separate the Higgs fields for quarks and charged leptons cleanly from the Higgs that gives mass to the W and Z particles.

      Since all of the charged leptons are relatively light (the heaviest, the tau, is 100 times lighter than the top quark) it remains possible that one Higgs field gives masses to the charged leptons, and another to the quarks. So that loophole remains for now. But all the mass-giving has to be done by one or more Higgs fields (of the particular required type).

  98. Hello Prof Strassler
    Thank you for the insight into theoretical particle physics. The posts are very informative.
    I would apreciate an answer to the following question.
    Is the energy of the protons not increased in proportions of E=mc^2 when protons are accelerated and have increased speed? Does such increased energy not also increase the mass of the proton and therefore the mass of the constituent quark? Is the mass of the top, bottom, charm and strange etc quark simply a result of their speed and not as a result of their interaction with a higgs field? Where else other than mass would this energy be stored?

    1. An excellent question, revealing of a widespread and profound misconception, very common at least in the United States, and even propagated by freshman physics textbooks. You ask, “is the energy of the protons not increased in proportion of E=m c2 when protons… have increased speed? Does such increased energy not also increase the mass of the proton…?” The answer to these questions is No!

      I myself partially shared this misconception until, as a first year graduate student, I witnessed a room full of professional experimental and theoretical physicists be quizzed on this question, fail to answer it correctly, and then suffer through an excellent but embarrassingly-pedagogical lecture by the great Soviet theoretical physicist Lev Okun. [By the way, the only person in the room who passed the test without any mistakes was my Ph.D. advisor, Professor Michael Peskin.]

      The correct statement, as Okun showed (obliterating the opposing viewpoint by noting several profound inconsistencies that arise if you try to argue that mass increases with speed) is that the mass m of a particle is constant and does not change with speed; that energy E and momentum p increase with speed, but the only correct relation between them is E2 – p2 c2 = m2 c4, which reduces, only for a particle at rest (which therefore has momentum p=0), to E2 = m2 c4, or equivalently E = m c2.

      Energy and momentum depend on your reference frame; if you and I are moving relative to each other, we will view the particle as traveling at different rates relative to us, and so we will assign it different values of E and p. But we will agree on its mass, m, which is the same in every reference frame.

      If you go and look at Einstein’s original paper, you will see he is most certainly not confused on this point. He states clearly that for a particle at rest, E = m c2. (Even more precisely, if memory serves, he defines E0 to be the energy of a particle at rest, and then writes E0 = m c2.)

      Since this website is intended for the layperson, I sometimes use a slightly non-standard language, and this is one of those cases. I refer to E = mc2 as a particle’s mass-energy; physicists call it rest-energy. When a particle is in motion, its energy E is larger than mc2, and I refer to E – mc2 as the particle’s motion-energy (which physicists call kinetic-energy.) There’s nothing wrong with the physicists’ language, except that it is slightly obscure at first reading, and I prefer to use more familiar words.

      So to summarize, using my language, the correct statement is the following: any particle has a definite mass m that does not change when it moves. Its energy does change when it moves (and so different observers, who will see the particle moving with different velocities, will assign it different energies, but the same mass.) It is useful to divide a particle’s energy into mass-energy mc^2 (which does not change if it moves) and motion-energy (which grows when it moves and is zero when it is not moving.)

      Does that answer all your questions in a single stroke? I think I should put this question and the answer into a sub-page for permanent reference.

      1. Prof Strassler,
        First, thank you very much for your deep enthusiasm in sharing your knowledge utilizing your ability to state things clearly.
        I have a question. Is the rest-energy (namely Eo = mc^2) of a particle all potential energy and nothing but potential energy? I raise this question because the particle gains kinetic energy when it is in motion. So, when it is not in motion, I expect it to possess just potential energy. Therefore, the question arises in me as to whether the rest-energy is just potential energy. If it is not potential energy only, what other kind(s) of energy come(s) into play here and make up the rest-energy?

        1. Rob — in freshman physics class one learns about kinetic energy and potential energy (energy of motion, and energy in the relationship between things.) But beyond freshman year one learns that this distinction has its limitations and one has to be quite careful with it.

          Rest-energy (or mass-energy, as I often call it on this site) is indeed the energy that an object has even when it is not moving.

          However, here is a complication. What is the rest-energy of a hydrogen atom? It is

          the rest-energy of its electron, plus
          the rest-energy of its proton, plus
          the motion-energy of the electron as it orbits the proton (and the little bit of motion energy of the proton too, since it isn’t quite stationary)
          the (negative) potential energy associated with the electromagnetic force as it holds the electron and proton together.

          Energy is energy, in the end, but how you break it up into types may depend on the way you describe the system that you are looking at. If you look at a hydrogen atom as a unitary whole, you will not have the same viewpoint as if you look at it in terms of its component parts.

          This is why in the end the answer to your question is not so important. What matters is that you do careful bookkeeping, and no matter what point of view you take, make sure you account for all the sources of energy in the system that you are studying, consistent with that point of view.

      2. Prof Strassler,
        I read in some places that the m in E = mc^2 is the relativistic mass. Is this wrong? Does the m always refer only to the rest mass? If the m in E = mc^2 is not relativistic mass, what is relativistic mass? Thanks in advance for your time.

        1. People do make this statement, and it has a long and sordid history, but I do not know any modern professional theoretical physicist who would make it. The modern view is that the relation E = m c2 applies only for particles at rest, and the “m” is the mass, which is the same as viewed by any observer. More generally, a particle’s mass, energy and momentum (p) are related by

          E2 – p2c2 = m2c4

          This is the fundamental relation between energy, momentum and mass; notice that for a particle that is not moving, and has therefore p=0, this reduces to E = m c2. Different observers moving relative to one another will measure a given particle to have a different energy and a different momentum, but when they use the above relation, they will always find the same mass.

          As the great theoretical physicist Lev Okun often emphasized there are many problems with defining a “relativistic mass” that is E / c-squared, and calling the “mass” I defined above the “invariant mass”. Einstein did not make any such definition!! And there were many good reasons. (For one thing, now we have two different quantities labelled “m”, which is a very bad idea.) Einstein’s statement is that particles at rest have an intrinsic rest-energy (or “mass-energy”). This is a statement with real content, because it relates two things that in general are *different*. If we define “relativistic mass” to be E/c2, such that they are always equal, we have added nothing to science, unless there is some useful consequence of this definition. As far as I can tell, the main consequence of this definition is the opposite of useful: it confuses people about whether photons do or do not have mass. (They most certainly have energy, but they most certainly do not have mass.) It confuses people about what we mean by the mass of the proton or of the Higgs particle (“but doesn’t it depend on how fast they are moving”, I am asked… the answer being no, because particle physicists always refer to the “invariant mass”, which we just call “mass”.) And whether a particle can decay to others depends in part on what their masses are, it confuses people as to why a fast electron can’t decay to a slow muon (“doesn’t the fast electron have a larger mass than the slow muon?” No, because decays are all determined by invariant masses, not relativistic masses.)

          In my view, the sooner we abandon “relativistic mass” as a concept, and return to the way Einstein described it in the first place and the way all particle theorists do it now, which is the call mass “mass” and energy “energy”, the sooner these confusions will disappear.

          Incidentally, on a website that discusses this controversy, it says that in a 1948 letter to Lincoln Barnett, Einstein wrote

          “It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than ‘the rest mass’ m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion.”

      3. I am a bit confused after reading this, given the high school physics I was taught – which is that as a particle approaches the speed of light it appears to gain mass “relativistic mass”. When did this get thrown out? And if this is not true anymore what happens if a particle with rest mass > 0 is accelerated to ~ c? No more infinite mass problem?

      4. vk,

        The name “relativistic mass” has been used a lot, in the old days in particular, but it is too misleading to keep it up, and redundant. There is already a concept that is entirely equivalent to “relativistic mass”, namely “Energy”, plain and simple. I guess people were too confused by relativity in its early days to get the nomenclature right from the beginning.
        Just substitute relativistic mass -> relativistic Energy/c^2 everywhere, and you have a more consistent picture.

        The infinite mass problem is still there, but is now more appropriately named the infinite energy problem. You would need infinite energy to accelerate a massive object to c.

        1. Alex, your last sentence is true for a single reference frame, but if the acceleration is happening in a reference frame that itself is accelerating, and both for instance are accelerating away from you can make a thing move faster than c of the original reference frame. Time/motion is relative and that is the key to understanding what I’m referring to. Very massive objects, such as a black hole, can easily accelerate massive objects to velocities beyond the speed of light of an originating reference frame.

          In my mind, there is no reason to refer to any entity that moves (and isn’t a shadow) as being massless. But physics has had a long history of not fully understanding the relativity of time and has been entangled with the idea that if it moves at the speed of light in our reference frame that it should be massless. My mentioning of the above comments, particularly with black holes, should be revealing of the inconsistency still plaguing physics theories.

  99. Very nice writeup! But one question: If the Higgs field has an VEV that is nonzero will it have gravitational implications? If so what are they? If not why not? Thanks for any response.

    1. Thanks.

      The answer to your question is complicated. On the one hand, the Higgs field being non-zero does not contribute to gravity. What contributes to gravity (or at least naively should) is the energy density of the Higgs field, which depends on its value but is not determined by it.

      [In equations: the potential energy density V(h) contributes to the cosmological constant, and depends on the Higgs non-zero value h; but V(h) is not a simple function of h… especially when you remember that this is the fully quantum corrected potential, not the simple one you write down in the classical equations. In fact, even if h=0, it may be that V(0) is positive, negative or zero.]

      So the basic answer is that the only effect of the Higgs being non-zero is on the cosmological constant (often called “dark energy”), and unfortunately the nature of that effect is not determined by the value of the Higgs field alone. And it can’t be measured independently of other contributions to the cosmological constant, so we can’t even study it.

  100. If technicolour is the answer, would we see a technipion in the place of a Higgs boson? What would distinguish it from the Higgs? (And are there composite Higgs theories that aren’t technicolour?)

    1. This is a bit more advanced as a question than I would typically want to answer in detail as a comment on this more elementary post. At some point I will have an article on various theories that propose a Higgs field that is composite (and there are many.) “Technicolour” is one example, and it predicts that there will be no observable Higgs particle. Other composite Higgs field theories, by contrast, do predict an observable Higgs particle, possibly light. There’s a long story here, and most of these theories will be ruled out within a year or two

      Regarding your other question (the “technipion”) — interactions with pairs of W particles and Z particles are the smoking gun of a Higgs particle. Other similar-looking particles — Higgs lookalikes — always fail on this measure. There are several ways to produce the Higgs particle at the LHC, and two of them involve the Higgs-W-W interaction. If these production mechanisms are not observed, the particle is not THE Higgs. (It could be part of a whole family of Higgs particles though, in which case those mechanisms might just be small and hard to measure.) Similarly, if a particle is heavy but does not decay often to W+ W- or to ZZ, then it is not THE Higgs particle.

      So there may be technipions or other Higgs lookalikes in the world, but with enough data we’ll be able to tell the difference between a false Higgs particle and a real one. It will get tricky if there are many of them. We should be so lucky.

    1. Their mechanism does not involve introducing classical fields. Black holes are not classical objects; they are *approximately* classical, meaning that their quantum phenomena are hard to observe. That doesn’t mean they aren’t quantum mechanical. You, too, are approximately classical, but your eye absorbs light one quantum at a time.

  101. A field is something that you plant corn in. Seriously, thanks for this! Looking forward to more on particle/wave. I got a little stuck on this: “The least-intense possible wave that a field can have is called a particle, and 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 particular (no pun intended), how am I supposed to figure out the “least-intense possible wave”?–“intense” seems so vague (French pun not intended) but I’m sure you mean something more specific by it.

    1. There’s nothing mysterious hidden in the word “intense”; it just means how strong the field is, in precisely the same way as saying that typical moonlight is less intense than sunlight–about a million times less intense, in fact. The light from the faintest stars you can see from a city is about a million times less intense again, and if electromagnetism were a classical field, you could keep finding light that was a million times less intense than the last example indefinitely–but it’s not; it’s a quantum field, which means that at a certain point there is beam of light which (for a given frequency/color) is the least intense beam possible: either the field contains at least one photon, or it is empty.

  102. Hi Prof. Strassler,

    that’s a very nice discussion of the Higgs field (although the “Okayyyy, let’s back up again” could potentially go on for a very long time if the listener is malicious or six years old 😉 I want to send it to my non physics family, but unfortunately I have to translate it first.

    One thing about the second half, I am not sure what to think of your take on perturbative unitarity. I’m not convinced that it is fair to say that “the theory predicts probabilities larger than one” in scattering processes, when it’s really perturbation theory that becomes unreliable. Is that really your interpretation of the maths, or is it a slight pedagogical simplification on your part? I would love to hear some more opinion of yours on what the physics significance of the breakdown of perturbation theory is in electroweak physics.

    Cheers, and thanks for the nice work on this blog!

    1. I can only answer this technically, and I assume that you have that background given your question. (Non-experts, ignore this!) It is a slight pedagogical simplification, yes. But your statement about perturbation theory, while true in a sense, isn’t really entirely right either. The Standard-Model-without-a Higgs-particle has to be defined mathematically first, before you and I can have this discussion. And you can’t define it, any more than you could define a theory of interacting pions. Either you try to hold tight to the Standard Model’s equations and you find that the theory is mathematically sick, or you have to alter it by adding new interactions, which is the same as saying that you gave up on defining it as you wanted to originally. So really the correct statement is that the theory is simply undefined. But I think it is hard to understand what this might mean if you are not an expert. The concept of mathematical inconsistency is hard to explain; phrasing it as a logical breakdown in the concept of probability is perhaps the closest approximation that I can find… it is very close to true, it emphasizes that the problem is very deep, and any more detail requires technical knowledge. I do take suggestions though if you have one!

      1. Hello, thank you for your comments.
        Yes I think I see what you mean. I admit, the negative probability argument really drives home the point that something seems wrong, almost too effectively. When we used it once in a discussion about some BSM model with astrophysicists, they looked at us like we were completely out of our minds 🙂
        Would it be an acceptable alternative to say that removing the Higgs forces us to introduce an infinite number of free parameters which are not so important at long distances, but make the theory completly unpredictive below a certain length scale? It’s not exactly the same thing as unitarity breakdown, but it should be closely related when one translates pert. unitarity violation to infinities in loops, like in the old argument by Levin and Tiktopoulos. I liked this way of seeing things because it doesn’t seem to rely so much on the peculiar limits of perturbation theory, but maybe it doesn’t entirely capture the same problems.

        As an aside, I found it interesting that some people claim that they can renormalize electroweak-like nonlinear sigma models with a finite number of parameters, though I don’t understand it at a technical level. One would still lose perturbative control, but if it’s really correct, it sounds like it would reduce the argument for a higgs to a calculational and phenomenological problem.

        1. Alex — once you’ve introduced new terms in the action, it’s not the Standard Model anymore. So again I stand by the statement — the Standard Model is not defined without the Higgs field. If you try to define the theory without changing it, you get a unitarity breakdown. If you change it, that’s fine, but you’ve introduced a new non-Standard phenomenon into the equations.

      2. Very good, I think I only now understand what precisely you meant by mathematical inconsistency in your text. I absolutely agree that strictly insisting on the SM with operators of dim<=4, it can be called mathematically inconsistent without the higgs, because they need to be generated one way or the other.

      3. Very pleased to see the discussion in relation to the breakdown of perturbative unitarity as this is something people often get very confused about. I think one of the main reasons for confusion is that a similar calculation (WW scattering) is used to interpret two different scenarios: (a) breakdown of the standard model without a Higgs field, (b) bound on the Higgs boson mass.

        In the first case I agree with your analysis that the SM without the Higgs field is inconsistent and needs a UV completion which must appear at the TeV scale. The asymptotic safety scenario (non-linear sigma model) mentioned is probably the most minimal and as far as I know not ruled out, however still requires higher order operators above TeV scale.

        However the second case is often mis-understood and may be the source of Alex’s original question. If the Higgs boson exists, the perturbative unitarity bound is not an absolute upper bound on the Higgs mass as is often stated. It simply tells us that if the Higgs is heavier than about 800GeV the W bosons become strongly coupled and perturbation theory breaks down. We would then begin to see resonances in WW scattering etc. Maybe not as exciting as other possible scenarios at the LHC but we would still see something new.

        So to summarise: in scenario (a) perturbative unitarity tells us about something fairly fundamental but in scenario (b) it is just telling us where we can use perturbation theory.

        I would be interested in your thoughts on what (if anything) rules out a heavy Higgs boson (say a few TeV), since this doesn’t really get talked about anymore. I guess the electroweak precision observables rule it out.

        1. A Higgs particle heavier than a TeV or so [if there is only one Higgs particle, mind you] has such a short lifetime that it essentially doesn’t exist as a particle. It’s an animal whose heart doesn’t even beat once.

  103. Perhaps the Higgs field exists, but is not a quantum field. Then there would be no Higgs bosons to be discovered, but the Higgs field could still be responsible for the masses of the elementary particles. The Higgs is a scalar field, after all, and a scalar particle has never been seen.

    1. Hmm. I do not understand your assertions. There are many composite scalar particles and fields known in nature. All nuclei with even numbers of protons and neutrons, including helium, have spin zero


      and are particles arising as quantum ripples in spin-zero (or “scalar”) fields. The same is true of hydrogen and many other atoms.

      Meanwhile, classical fields in nature are only approximately so; all fields in nature are quantum. Furthermore, the behavior of the top quark as it decays is experimentally inconsistent with a classical Higgs field; it decays to one, and only one, W particle, which would not occur if the Higgs field were a classical field.

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