# How does Higgs couple to mass resulting from photons or kinetic E?

1. Jul 3, 2012

### Steve Harris

The Higgs is supposed to couple to fermions but not photons. Nevertheless, photons add mass to systems in SR. Also kinetic energy (KE) of fermion motion adds inertia and mass to systems in SR theory. So, how does the Higgs field "tell" that this type of mass from photons and KE IS mass, and give it inertia?

This is a real problem. Two photons bouncing around in a container (in its COM frame) give it an extra invariant mass E/c^2 where E is the photon energy (even one photon, if trapped, will do this, but I want to make this simple--any pair of photons has invariant mass so long as they don't go in the same direction)

The same is true of the kinetic energy of any particle bouncing around in such a container. It's kinetic energy E adds to the container mass as E/c^2, since it adds energy without adding any net momentum (invariant mass is total energy/c^2 where momentum is zero, as here in the COM frame). This is most easily seen in a container of gas, where the container gets not just the rest masses of particles of gas, but mass from their total kinetic energies also.

Now, a container like this acts as a "particle" and has inertia given by the Higgs field. How does the Higgs field see the invariant mass, and particularly the parts of invariant mass that are "made" of kinetic energy and massless photons?

Clearly the mechanism works, since Higgs sees the full mass of neutrons and protons, and not just the 1% of their mass that is rest mass of their quarks. The Higgs field sees quark kinetic energies also, so it's like my bottle problem. There's something odd here, as there must be coupling between any sort of invariant mass and Higgs, and yet the invariant mass in many systems, like the kinetic energy of such a system in its COM frame, can't be "located" in space. The mass is in the system, but where is it? How does the Higgs field know?

2. Jul 4, 2012

### tom.stoer

The Higgs mechanism is responsible for masses of some elementary particles. It has been constrfucted such that it gives masses to W and Z bosons and fermions but leaves the photons and gluons massles.

The masses in SR you are talking about are typically 'invariant masses' of macroscopic systems calculated according to M=E/c² (dust, fields and their interactions, ...) and have nothing to do with the Higgs. Classical el.-mag. radiation (or a gas of massless, non-interacting photons) has a non-vanishing energy density ~ E² + B² and therefore the system has a non-vanishing 'invariant mass'. Note that this mass has nothing to do with the Higgs, simply b/c photons are massless. The masses of baryons such as protons and neutrons are due to the stroing force; with vanishing quark mass (which is due to the Higgs) the proton and beutron mass would change by a few percent only!

In SR this 'system mass' or energy (with its different contributions from kinetic energy, rest masses, interactions, ..) *can* be located, and there's no need to talk about a Higgs at all (Einstein invented SR w/o discussing a Higgs ;-) The Higgs field does not couple to this 'system mass' but to some elementary fields.

Last edited: Jul 4, 2012
3. Jul 4, 2012

### The_Duck

It doesn't. Statements you may have seen like "The Higgs field is the source of all mass" somewhat overstep the truth. For example, protons are composed of two up quarks and a down quark. The Higgs field gives each quark a mass of around 0.005 GeV. However the proton as a whole has a mass nearer 1 GeV. Most of this mass comes from the energy of the gluon field binding the quarks together. The proton would have much the same mass even if there were no Higgs field and thus the quarks were themselves massless.

However, I think you may be making a nonexistent distinction between "mass" and "inertia." Nothing "gives mass inertia" -- all mass has inertia in special relativity, and the Higgs has nothing to do with this connection. The Higgs field gives rest mass to some particles that would have originally had zero rest mass.

4. Jul 5, 2012

### Steve Harris

Okay, so you seem to say that it's no problem, as most of the mass of ordinary matter (which is NOT quark or electron rest masses) is NOT due to the Higgs mechanism. If quarks were massless, you contend that everything would "weigh" 99% as much as it does already, since we're "weighing" gluon fields inside the baryons. Does everybody else agree here? Higgs then is not responsible for most of the mass in the world (ie, ordinarly object mass).

Incidentally I thought 99% of the mass of baryons was kinetic energy of the quarks, overriding their binding energy. Any strong field interactions are attractive, and should add NEGATIVE mass like any binding energy. For example, the nuclear force results in a mass DEFECT in nuclei; the strong force should (by itself) result in a similar mass deficit inside nucleons, should it not? These forces are related and don't have the same form, but both are *attractive* in operation (the quarks stick together, after all), and thus should not ADD mass in operation, but rather subtract it.

In short, any attractive fields, including EM and gravity, subtract mass from bound systems, not add it. Why should other forces be different?

I'm afraid I cannot agree about locating the system invariant mass in SR, as it moves around according to reference frame. Kinetic energy cannot be located, but is a system property (in a 2 particle unbound system, KE is always all at the OTHER particle from the rest frame of each particle). In the COM frame, it's divided between particles, but unequally unless they have the same mass. But there's no frame preferred, as this is relativity. The system invariant mass (which includes all KE's in the COM frame) is the same in all frames (not just the COM frame).

5. Jul 5, 2012

### Steve Harris

Tom S. has said the same, so I'll ask you the same question I asked him, which was how the energy of a binding field can have positive mass. That is not the way G or EM or nuclear fields (residual strong fields between nucleons) work. Each results in a mass defect, since it is an attractive force, causing work to be done on the particles in binding-- work that must be removed. Thus, mass defect. Why should the strong/gluon force between quarks be different, if it binds them? I would have to say we're seeing the mass of the quark kinetic energy in this zero-momentum "system" that is a baryon.

Your statement that Higgs doesn't actually account for 99% of the mass of ordinary atoms, agrees with Tom's. The networks and even some physicists have gotten this wrong, if true!

The equivalence principle teaches that the inertia of objects in their "rest" frame (or really, their free-fall or inertial frame, where they float and Newton's laws hold good) is one of the ways to tell that you HAVE mass (and thus also energy). The other is being that the "thing" is a source of gravitation.

An electron and a positron in a massless bottle adds inertia to the bottle, and thus mass (and thus weight if you look to see what force is required to put it into other than its free-fall frame). It's 1.022 MeV/c^2. This is all conferred on these leptons by a weak force from the Higgs field, you say. But now, let these annihilate these into two photons in this same bottle, and look. Gravitation cannot change in the process, nor energy, nor mass, nor inertia. All remain the same, as confirmed by simple SR calculation of bottle invariant mass. But now you say that with two photons instead of two leptons, NONE of these are due to the Higgs mechanism, instead of ENTIRELY due to it. Don't you find this odd? From outside, it's the same bottle. But now its mass on the scale is due to some other mechanism or fishy behavior of the universe entirely. Where once Higgs did all the work, now it's invisible to Higgs, but looks just the same to outside observers. Say what?

6. Jul 5, 2012

### The_Duck

Someone else may have a better take on this, but: Even in electromagnetism the energy density of the electromagnetic field is everywhere positive. We speak of negative binding energies because we are referring the total energy to the case of two infinitely separated charges. Then two nearby opposite charges have less energy than this reference. Such a scheme doesn't work for the strong force between quarks, however, because the attractive force between quarks *increases* with distance and so two infinitely separated quarks have infinite energy. I'm not sure that is a complete answer, but it's something to think about.

This is not nearly as strange as you are making it out to be. Consider instead the following situation. I have only a single proton inside the bottle. Somehow I set up a spatially-varying electric potential inside the bottle. Initially the proton is in a region of extremely high electric potential, so that the proton's electrostatic potential energy makes a significant contribution to the total mass of the bottle. Some time passes and the electric field has pushed the proton to a region of zero electric potential. Energy is conserved, of course: the proton's potential energy has been converted into its now-very-large kinetic energy. An observer outside the bottle notices no change in its total mass, of course. Is this odd? Initially the bottle's mass was largely due to the electrostatic potential energy of the proton. Now the source of the bottle's mass, the kinetic energy of the proton, has nothing to do with electromagnetism at all!

I think you will agree that this is not particularly odd. The situation you describe is very similar. Energy is simply being transformed from one type to another.

If you like, you can think of the Higgs field as similar to the electric potential. In principle it can vary in space, and if it did particles that gain mass from the Higgs mechanism would feel a force similar to the electric field pushing them towards regions of lower Higgs field, because that would lower their potential energy (i.e., their rest mass). However, the Higgs field also wants to minimize its own energy, which it accomplishes by being constant throughout the universe. So it ends up just imposing a constant energy penalty for the existence of certain particles. Of course, the constant energy penalty a particle pays for its mere existence is what we call its rest mass.

7. Jul 5, 2012

### wizwom

Binding energy is NOT negative mass... its not some magical negative energy.
It is energy being used to keep the system together, which is released when the system is no longer together. It is a very real, positive, potential energy.

The article to explain the whys and wherefores of the Higgs mechanism would be Peter Higg's short article, "My Life as a Boson", Int. Jour. of Modern Physics A, 2002

8. Jul 5, 2012

### tom.stoer

Yes

Yes, nearly everything. Pions would be massless Goldstone bosons. Electrons would be massless and therefore there would be no atomic bound states, only nuclei.

Yes

I agree that simply talking about 'binding energy' and 'kinetic energy' is misleading in QCD.

The physical QCD Hamiltonian does not look like 'H = T+V'; or let's be a bit more specific, V is a very complex operator which cannot be interpreted as a 'potential well'.

b/c you reasoning relies on the above mentioned 'H = T+V' and (non-perturbative) QCD does not comply with this a simple picture.

With located or local mass I mean that in SR you can calculate the energy and momentum of a given volume V and that you can therefore attribute a mass M to this volume. For QCD the mass of a nucleon is located in a volume of ~ 1 fm³. Of course energy or mass is not located in pointlike particles

9. Jul 5, 2012

### Steve Harris

The attractive force between quarks stays constant (at long distance) and the energy therefore increases without limit. But you're still adding energy to separate the things, which means they give energy up, as they get closer. There's no getting around a negative mass, so long as the force is attractive. I'm willing to believe that there's a positive component from a repulsive potential at near distance (just as happens with the nuclear force, and indeed with the EM force between protons, where the EM potential starts to decrease the fractional mass defect for high mass nuclides (allowing fission to be net-energetic). But that's the only "out" I can see. Unlike nuclei this repulsive potential would need to be larger than the attractive one, however. That sounds unlikely. I'm more apt to believe we're "weighing" massless gluons trapped in hadrons, much as we'd "weigh" massless photons trappped in a bottle.

Okay, that's very helpful as a picture, particularly as you've said for this purpose (the Higgs interaction) we can forget the mass that massless particles (photons, gluons) add to systems. So we're "weighing" a Higgs potential here with rest masses, and that potential (the compresssed "spring" of the Higgs mechanism) is the rest mass of quarks and electrons. Cool. I get it!

You have a point that converting such a potential into kinetic energy (which also has invariant mass in the case of 2 particles, and bends space-time) is no weirder with this view of Higgs than it is for the same view of EM potential fields. I see your point. But conversion of EM field (potential) into kinetic energy is ALSO weird! Consider 2 fission fragments pushing off from each other at 180 MeV. EM potential is converted to KE. But I can point to the EM field between two charges. It's in a volume and has an energy value per volume you can calculate proportional to E-field^2. A static E field is like a bit of matter-- if it has a gravity field, you can imagine where the field originates. And you weigh the field when you weigh the atom before it fissions. It weighs 180 MeV-- as much mass as 350 electrons!

Now after fission all that field is now KE. It's still 180 MeV of mass in the COM frame, but now it's not localizable anymore. From the rest frame of each particle, it's all in the OTHER particle, and this state continues when they are light years apart. So where does this part of the mass and gravity (350 electron masses worth) now originate, then? This KE mass is sort of a property of space-time and has no location (or it's whereever you want it to be, depending on your reference frame). Look from particle 1 and it's all on particle 2, and vice versa. It's not "real" in the sense that the potential field is.

Note that if you're talking about the KE of a single particle, it's even more ghostly-- it goes away entirely, if you shift to the particle rest frame. But with TWO particles, there's some minimal KE mass that you can't get away from, and that's the KE mass that shows up as extra, in the invariant mass of the system. It's the total KE in the COM frame, but not the total KE in other frames. Nature's keeping track of energy, but now only as a sort of correlation between a pair of particles that once pushed off each other. You have to have both particles to keep track of how much energy is now stored in space-time as this new KE that came from the potential. This reminds me of quantum entanglement, but it's totally classical. Can't get my mind around it mechanistically. But you're right-- at this point it's not a Higgs problem.

10. Jul 5, 2012

### Steve Harris

Binding energy is as negative as a credit card balance-- you have to add energy to it to get zero. That's what we MEAN by "negative". A debt is negative money. Binding energy is negative mass. A deuteron has less mass than a proton and a neutron. You have to add energy (and therefore add mass) to separate them. It is not positive. The binding energy shows up as a subtraction. Which of course it is, as you've allowed energy to escape the system when the proton and neutron originally bind, so you no longer weigh it. If you could, of course, energy and mass would be separately conserved. It's that way with all binding energy-- the mass is missing only in the sense that you let it out of your system, and then didn't keep track of it.

Thanks for the ref, but it's not much help without a link. I don't have a decade of Int Jour of Modern Phys A lying around. Next time I"m in the big academic library....

11. Jul 5, 2012

### Steve Harris

I suppose. I can't imagine how a massless charged particle would interact. How can you tell how much of the electron's mass is electromagnetic, and how much is due to Higgs? Perhaps without Higgs, the electron's rest mass would only decrease by the amount of rest mass of an electron-neutrino, which presumably IS what an electron would be, without its charge. The rest of the electron's mass must be electromagnetic. But neutrinos I can see, would indeed be massless, without Higgs.

Just because pions can be neutral doesn't mean they'd be massless, as they could have a lot of stored gluon mass, just like hadrons. A pion would decrease in mass only by the amount of the rest mass of the 2 quarks that compose it.

I suppose, but a Hamiltonian is just restatement of the conservation of energy. There's a rest mass term, a kinetic term, and the rest is potential (unless you know of other kinds of energy?) Potential can be split into negative and positive potentials, I suppose, and as I said to The Duck, I can believe that the positive potential is adding mass that is weighed, if I have to. But more mass than is negative, from binding? Hard to believe. Since the thing does hold together, the net binding energy is negative, so also must be its total contribution to mass of the system. I'm betting that hadron mass is mostly massless gluons, contributing to invariant mass, as massless particles can.

But in SR you can't always calculate energy and momentum in a given volume, since this changes according to your reference frame.

If you have two particles moving away from each other, you can't say where the kinetic energy of the system is "located". You can find a frame where it is minimized (the center of momentum frame) but particularly if the particles have never interacted, that is all you can say-- you found a frame in which they had minimum energy, some of which is kinetic. But you can't say where that kinetic energy is *located*. It's a system property stored in the particles' relative velocities from each other.

12. Jul 6, 2012

### Parlyne

The issue that you're missing is that the only natural place to define a zero for potential energy of any sort is where the interaction strength falls to zero. For E&M or gravity or even the nucleon-nucleon forces, this is at infinite distance. But, the strong force isn't like this. It's (qualitatively only) more like a spring force, where the only location with no net force is at zero separation. Then, since the force is attractive, potential energy must increase with increasing separation.

13. Jul 6, 2012

### tom.stoer

The standard model fermions (quarks, electron, myon, tau and their antiparticles) would be exactly massless w/o Higgs coupling. The "self-energy" does not add a non-zero contribution to the mass.

That's not what I am saying. For massless quarks the chiral symmetry (on the level of the QCD Lagrangian) is exact, but it is broken spontaneously by the QCD vacuum state. The pions are the Goldstone bosons (excitations of the degenerate vacuum state) of this spontaneously broken chiral symmetry. For massless quarks these Goldstone bosons i.e. pions (and other mesons like Kaons) would be exactly massless, even the charged pions!

http://en.wikipedia.org/wiki/Goldstone_boson

No, it's much ,ore as you can see when studying quantum mechanical problems; it determines the (energy) spectrum of the physical states.

I am sorry, but this picture is too naive when studying non-perturbative quantum field theory.

If you like I can write down the QCD Hamiltonian. Please believe me that there are terms you can't describe by attributes like "positive" or "kinetcic energy", "negative binding energy", etc. It's much too complicated and it can be evaluated numerically only. You cannot even make a drawing of the "potential energy" in QCD (the linear rising potential for quark-antiquark pairs is an effective picture arising from lattice calculations, but this is a simplified picture, not the fundamental theory; it has nothing to say about the mass!).

I think I gave you an explicit definition of "located"; and please remember, we're not talking about particles but quantum fields.

As a summary: it is dangerous and misleading to attribute well-known words from classical mechanics (or even field theory) to problems in quantum field theory. You get confused by the language which is partially inappropriate. That's why I am saying that interpreting the nucleon mass as binding energy, kinetic energy, ... is dangerous.

14. Jul 6, 2012

### scijeebus

Photons don't have mass, but energy still distorts the fabric of space whether it's in matter or not which means photosn distort the fabric of space. How does the Higg's Mechanism cope with this? Does there need to be a separate particle for photons? Why don't Higg's Bosons couple with photons? Higg's Bosons are what give particles mass, but mass is equivalent to energy, Higg's Bosons don't attach to photons, but photons have energy, photons still exert gravitational distortion. What am I missing?

15. Jul 6, 2012

### tom.stoer

Yes, bjut this is general relativity which we do not consider here b/c it's not relevant.

b/c the SM Lagrangian has to be constructed such that the photons remain massless whereas the W- and the Z-bosons become massless.

They did not invent the Higgs w/o having something in mind. They wanted to construct a gauge theory; they wanted to construct a theory with a massless photon but massive W- and Z. They knew that the weak force had a short range and that its "force-carrier" particle must be massive.

16. Jul 6, 2012

### scijeebus

Weren't Higg's particles suppose to somehow once and for all combine QM and Relativity?
So the photon mediates a particle which carries the mass?

17. Jul 6, 2012

### tom.stoer

No. Higgs and gravity have nothing to do which each other; the Higgs does not solve a single problem regarding quantum gravity.

No. The photon mediates the electromagnetic force which is long-ranged. The weak force is short-ranged, so we don't see it in our all-days world, but it has some effects at length scales like the nucleon size. If you want to describe the weakl force like the el.-mag. force you need a heavy particle (a heavy partner of the photon) which mediates that force (high mass means short range). But the symmetry structure of the standard model (and many other similar models) definitly rules out massive force-carrier particles, so now you are in trouble! The invention of the Higgs was a trick to give the force-carriers a mass w/o destroying trhe symmetry structure.