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The video "Your Mass is NOT from Higgs Boson?" argues that almost all the mass that we are made of doesn't come interaction with the Higgs field, but rather that most of a nucleus's mass comes from the space between quarks (the quark-gluon plasma).

If the video is correct, then there really needs to be an easy-to-understand explanation for mass because science popularizers make us laypeople think that the Higgs mechanism is responsible for all the mass in the atoms and that would be of course very misleading.

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    $\begingroup$ The statement "The Higgs Boson gives us mass" is incorrect in two different ways. The first one is that it is the Higgs field, not the particle itself, that gives elementary particles mass. The second reason is the one that you have said- that most of the mass of atoms and nuclei are from the energy of quarks binding together, not the energy associated with the Higgs field. Here is a very good website that explains these issues more carefully than most: profmattstrassler.com/articles-and-posts/the-higgs-particle/… $\endgroup$ – Rococo May 11 '13 at 16:58
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    $\begingroup$ Thanks! I've read the link but I didn't get from it a good (for the layman) analogy as to why the turmoil inside the gluon plasma leads to the other mass (inertia). A certain particle moving through some kind of cosmic molasses is how I see a particle interacting with a higgs field and that's what gives off some mass - that's easy to visualize and the standard popsci explanation - , but what's the other working analogy for the mass coming from the gluon plasma? $\endgroup$ – alex May 11 '13 at 17:15
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    $\begingroup$ Hi alex- the answer is very simply that all energy can be interpreted as part of the rest mass of a system. This is what the famous $E=mc^2$ is really saying. Even in a hydrogen atom (for example), the mass of an isolated proton plus the mass of an isolated electron is slightly different than the mass of the two combined, because their interaction energy affects the mass of the system. In that system the change is tiny, but inside a nucleus this interaction energy, as well as the kinetic energy of the constituents, is huge and cannot be ignored. $\endgroup$ – Rococo May 11 '13 at 18:00
  • $\begingroup$ These additional links (from the same website, which I really like) might be helpful: profmattstrassler.com/articles-and-posts/… profmattstrassler.com/articles-and-posts/… profmattstrassler.com/articles-and-posts/… $\endgroup$ – Rococo May 11 '13 at 18:03
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    $\begingroup$ It is true that the "bare" mass of the valance quarks make up a small part of the mass of the nucleons. However, describing the nucleon sea as a quark-gluon plasma is simply wrong. Related: physics.stackexchange.com/q/13581 $\endgroup$ – dmckee May 11 '13 at 21:50
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Higgs mechanism is not the universal mass-responsible detail, but the ultimate. Other mechanisms could give you large quantities of mass - and in fact they do - but there is still some part which they are unable to explain. And that's why the Higgs mechanism is needed.

Numbers for you:

For the atom of hydrogen:
Total mass - about 1 GeV
Electromagnetic field - several eV (billionth parts)
Nuclear force field - none
Masses of electron and quarks - by Higgs mechanism - about 20 MeV
The rest is due to gluons (and virtual quarks) tension and motion.

For other atoms:
Total mass - about 1 GeV per nucleon (proton or neutron)
Electromagnetic field - up to keV per proton (not the field inside the nucleus itself)
Nuclear force field - up to several MeV per nucleon
Electromagnetic field inside the nucleus - up to the same as nuclear force field's part
Masses of electrons and quarks - by Higgs mechanism - about 20 MeV per nucleon
The rest is due to ... see above.

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    $\begingroup$ Sorry if I seem a bit arrogant, and excuse my layness, but there seems to be something missing from your 'answer': The answer to my question. How does the "tension and motion" of the gluons translate into the inertia that we see as a whole for the entire entire atom mass (GeVs) if it's not only the exchange of Higgs bosons between the hadrons and the Higgs field? $\endgroup$ – alex May 11 '13 at 16:52
  • $\begingroup$ A certain particle moving through some kind of cosmic molasses is how I see a particle interacting with a higgs field and that's what gives off some mass, but what's the other working analogy for the mass coming from the gluon plasma? $\endgroup$ – alex May 11 '13 at 16:59
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    $\begingroup$ Special Relativity gives you the answer. It tells (and shows how) every kind of energy can take part in the mass. For example, photon is massless. But if we take two photons flying in different directions, then taken as a whole (say, inside a box with mirror walls), they would make some mass. In a similar way, any kinematic energy of particles (quarks and gluons as well) can add up to mass. And non-zero value of some field, say, electric, also would make a box heavier. // And sorry, your image is more like tractive resistance than inertia. Hard to get an adequate image without maths. $\endgroup$ – firtree May 11 '13 at 17:53
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    $\begingroup$ The nuclear force field contribution for hydrogen is not none. The quark binding energy in a proton is quite large, and accounts for most of the proton mass. $\endgroup$ – Jerry Schirmer Mar 6 '14 at 15:01
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    $\begingroup$ @MaciejPiechotka Indeed you can use one photon, see my answer here, here and here. $\endgroup$ – WetSavannaAnimal Jun 8 '14 at 9:39
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The experimentalist's answer:

1) Experimental physics has established with very many experiments that the underlying framework of nature is quantum mechanical, and this includes special relativity, when the energies are appropriate. It is dependent on a very small number of elementary particles out of which all matter that we have observed and experimented with in our laboratories is composed.

2) The definition of mass that you are worrying about is the everyday one described well by classical mechanics, as the resistance to a force applied.

Inertial mass measures an object's resistance to changes in velocity m=F/a. (the object's acceleration).

In the regime of relativistic physics an elementary particle as seen in this table has a rest mass:
$\hspace{50px}$.

Elementary particles included in the Standard Model

They have a mass given in the table, except for the two top ones in the column in red, which are massless particles. These particles in various bound states compose the protons (quarks and gluons) and neutrons, the protons and neutrons bound make the nuclei of the atoms and gather around them the electrons and the atoms make up the solids.

If you look at the masses they could never sum up to the mass of the proton $\left(1\frac{\mathrm{GeV}}{c^2}\right).$

What happens is that the addition is not of scalar masses, but of four vectors, the three dimensional momenta that we know plus the energy as the fourth component in the special metric of special relativity. The mass, in this framework is the corresponding "length" of three dimensions and is called the "invariant mass" : For the elementary particles this "length" is identical with the mass of the table . When two elementary particles form another particle, or come out of a particle , the mass of the composite particle is a function of the four dimensional vector addition of the individual elementary particles composing it .

For example there exists a particle called pion $\left(\pi^0\right)$, of mass $135 \frac{\mathrm{MeV}}{c^2}.$ It decays into two massless photons. The two photon system has the invariant mass of the ${\pi}^0$ even though each photon has mass zero.

A hierarchy is built up then, elementary particles, (quarks, gluons) combine to compose the protons and neutrons, protons and neutrons combine to compose nuclei, electrons plus nuclei compose atoms.The composite invariant mass at one level becomes the rest mass of the next level's basic particles. Each level has less kinetic energy in the combination than the previous level , so the masses start to resemble the classical mechanics masses. When we reach solids and liquids of dimensions larger than nanometers, the relativistic effects can be ignored .

Where does the Higgs field come in, in this saga? It only affects the invariant masses of the elementary particles in the table , their rest masses. The bulk of the masses we measure macroscopically are a build up, level by level, on these elementary particles and their binding energies. The high energies that bind the under lying layers become macroscopically the classical mechanics masses.

A good point is to think of the binding energy curve and nuclear reactions where we see the opposite process: classical mass turning into energy by destroying the level of compositeness.

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  • $\begingroup$ OK, so the higgs mechanism gives rest mass to all the elementary particles in the table (except photon, gluon), with the same mechanism, same way? So the higgs mechanism for example gives rest mass to the Quarks, the same way as it gives rest mass to the W,Z bozons? $\endgroup$ – Árpád Szendrei Nov 21 '16 at 18:32
  • $\begingroup$ @ÁrpádSzendrei yes , it is only the elementary particles that get their mass from the higgs mechanism, the ones that have an electroweak coupling $\endgroup$ – anna v Nov 21 '16 at 20:11
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A particle physicist told me that Higgs fields explains just a small part of the mass, while most of the mass is due to the energy binding de protons in the nucleus (which is described using QCD).

So I think that what the video says is right.

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  • $\begingroup$ So, what is the mechanism that produces inertia from the energy (described by QCD) binding the protons in the nucleus? Quarks exchange Higgs bosons with the Higgs field so we know where inertia for particles comes from, but how does inertia from quark-gluon plasma come to exist if it doesn't exchange anything with the Higgs field? $\endgroup$ – alex May 11 '13 at 16:12
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    $\begingroup$ More likely, energy binding quarks in protons and neutrons. Nuclear energy is relatively small. (And don't fear, quark bombs and reactors are impossible - quarks are already in the least energy state.) $\endgroup$ – firtree May 11 '13 at 16:26
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    $\begingroup$ @alex energy has inertia, period. It has to, in order for GR to be consistent. Also the stuff in a proton is not the quark-gluon plasma. $\endgroup$ – David Z May 11 '13 at 19:26
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There is a clear mistake in what he says : the mass does not come from the interaction with the higgs particles in it self. In essence, for the mass due to the Higgs mechanism, the Lagrangian contains originally massless particles. This is due to the requirement of gauge symmetry. Mass terms are not gauge invariant.

The higgs mechanism is a dynamical mechanism in which originally massless fields acquire mass. The (scalar) field associated with the Higgs acquires a non zero vacuum value, as we say, by spontaneous symmetry breaking. The symmetry breaking part comes from the fact that if the vacuum state of the Higgs don't contain the same symmetry as the original, unbroken, Lagrangian then the gauge bosons will acquire a mass. The non-zero vacuum of the higgs will give the terms corresponding to a mass.

But the higgs particles, as we can produce them in the LHC, are small excitations of the higgs field. These small perturbations are done around the vacuum state of the field, and can also interact with the particles of the theory, but are not responsible for the mass.

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