16 tonnes: almost all of your weight is trapped energy

Part IWeighing yourself

Chapter 1Seventy kilograms of what?

Step on a scale and it says 70 kilograms. That is the mass of a particular collection of particles, and it is worth taking the inventory. The classic reference body of radiation protection, the ICRP's 1975 "Reference Man", is 43 kg of oxygen, 16 kg of carbon, 7 kg of hydrogen and 1.8 kg of nitrogen, plus about a kilogram of calcium, 780 g of phosphorus and smaller amounts of a dozen other elements.¹ That works out to about 6.7 × 10²⁷ atoms, 62% of them hydrogen, holding (this page's arithmetic):

2.31 × 10²⁸ protons,
the same number of electrons, and
1.90 × 10²⁸ neutrons.

Now weigh those parts separately, using the measured masses of a free proton, neutron and electron:²

Part	Count	Mass
Protons, 938.272 MeV/c² each	2.313 × 10²⁸	38.69 kg
Neutrons, 939.565 MeV/c² each	1.900 × 10²⁸	31.82 kg
Electrons, 0.511 MeV/c² each	2.313 × 10²⁸	0.021 kg
Sum of the parts		70.535 kg
You		70.000 kg

This page's arithmetic: element masses from the ICRP Reference Man (rescaled to exactly 70 kg), isotopic masses from the 2020 Atomic Mass Evaluation.³ Rows are rounded and add to 70.531 kg; the sum uses unrounded counts.

You weigh 535 grams less than your parts. The missing mass is the binding energy of your atomic nuclei. When the oxygen and carbon in you were forged inside stars, every nucleon that settled into a nucleus released about 8 MeV, and the nucleus has been lighter by that energy divided by c² ever since. Mass is not conserved when things bind; energy is. Electrons bound into atoms account for only about 9 milligrams of the deficit, and all the chemical bonds in your body for about 45 micrograms (this page's estimates). A day's food, 2,000 kcal, has a mass equivalent of less than a tenth of a microgram. On this scale chemistry is invisible.

So 99.97% of you is protons and neutrons, and the question "where does my mass come from?" becomes "where does a proton's mass come from?". This is not a small question. Einstein's E = mc² says a 70 kg body is equivalent to

E = 70 kg × c² ≈ 6.3 × 10¹⁸ J ≈ 1.5 gigatonnes of TNT About thirty times the largest bomb ever tested (the 50-megatonne Tsar Bomba), or 16 nanoseconds of the Sun's entire output.

The rest of this page is about what that energy actually is. The short answer: about one per cent of it is the mass that the Higgs field gives to the particles inside you, and almost all of the rest is quarks and gluons moving and pulling, inside volumes about a femtometre (10⁻¹⁵ m) across.

Chapter 2Adding up the quarks

Since the electron-scattering experiments at SLAC in 1967–68, we have known that protons and neutrons are not elementary. Electrons fired at them bounced off hard, point-like objects inside, as if off tiny pebbles in a cloud.⁴ These are quarks. A proton holds two up quarks and a down quark (uud); a neutron holds one up and two downs (udd).

In the Standard Model, the quarks get their mass from the Higgs field. In 1964 three groups showed how a field filling all of space could give force-carrying particles mass without spoiling the symmetries of the theory;⁵ in 1967 Steven Weinberg used the same field to give the electron its mass,⁶ and the quarks follow the same pattern. The 2012 discovery of the Higgs boson at the LHC confirmed that the field is there.⁷ Its couplings to the top and bottom quarks and the tau lepton have since been measured, and there is evidence for the muon's; those to the electron and the up and down quarks are still far too small to see. Each charged elementary matter particle has its own coupling y to the field, and its mass is that coupling times the field's value in empty space, v = 246 GeV:

m = y v / √2 The couplings range from 2.9 × 10⁻⁶ for the electron to about 1 for the top quark. Nobody knows why.

Lattice QCD calculations, combined by the Flavour Lattice Averaging Group, put the up quark at 2.14 ± 0.08 MeV and the down at 4.70 ± 0.05 MeV.⁸ (The Particle Data Group's world averages, 2.16 and 4.70 MeV, agree.⁹) Add them up:

m_u + m_u + m_d = 8.98 MeV ≈ 0.96% of the proton's 938.27 MeV For the neutron, m_u + 2m_d = 11.54 MeV ≈ 1.23% of 939.57 MeV.

For a 70 kg body, the quarks' Higgs-given masses come to 761 grams, 1.09% of you. The electrons, whose entire mass also comes from the Higgs field, add 21 grams. Total: 782 grams, about 1.1% (this page's arithmetic). The other 69.2 kilograms is something else.

Here's an odd coincidence: the 535 grams your nuclei gave away when they formed cancels about 70% of the 761 grams of quark mass. That isn't a deep fact (and nuclear binding is itself mostly a strong-force effect), but it shows how small the Higgs-given part is. A rearrangement of nuclei inside stars changed your mass by nearly as much.

Figure 1⚖️ Try it

How much of you does the Higgs account for?

Each block is 1% of you

Mass the Higgs field accounts forEnergy of quarks and gluonsAlready gone

Your weight

Put down to the Higgs

Energy of quarks and gluons

Already gone: given off when your nuclei formed

Each block is 1% of the body (700 g for 70 kg; set your own weight with the slider). The blocks fill from the feet up with the share attributed to the Higgs field under four different questions. 1%: current (MS-bar, 2 GeV) masses of the valence quarks (FLAG 2024) plus the electrons. 10%: the light-quark sigma terms σ_πN + σ_s as a fraction of the nucleon mass, 9.3–11.1% depending on the determination. 20%: adding the charm quark's sigma term (lattice QCD, roughly 70–110 MeV, so 17–23% in all). 31%: all six quarks' sigma terms, which is the Higgs–nucleon coupling f_N = 0.308(18) and equals d ln M_N/d ln v when the strong coupling at very high energy is held fixed. The dashed block is the 535 g (for 70 kg) of nuclear binding energy given off when your nuclei formed. Body composition from the ICRP Reference Man, scaled in proportion to weight; this page's arithmetic. Hover over or tap a block to inspect it.You, as 100 blocks: each is 1% of your weight (set yours with the slider). Pick a question and watch how far up your body the Higgs's share reaches. Same body, same physics: the answer depends on exactly what you ask. Tap a block to see what it is.

The 2013 Nobel citation is precise about this: the mechanism "contributes to our understanding of the origin of mass of subatomic particles".¹⁰ It gives the elementary particles their masses. Most of the mass of the things built from them, you included, comes from somewhere else.

Which quark mass? The masses above are current masses: parameters in the equations of the theory, defined in a particular calculational scheme (MS-bar) at a particular resolution scale (2 GeV). Older quark models use constituent masses of about 300–350 MeV, a third of a proton each. The difference is a cloud of gluons and virtual quark–antiquark pairs that the strong force wraps around every quark. Lattice calculations of the quark's "mass function" show it rising from a few MeV when probed at high momentum to several hundred MeV at low momentum.¹¹ That dressing comes from the strong force, not from the Higgs. Chapter 8 shows that even the current mass changes with the resolution scale, so "1%" is less fixed than it sounds.

Chapter 3Mass without mass

Einstein's second 1905 paper on relativity was three pages long and its title was a question: "Does the inertia of a body depend upon its energy content?"¹² He showed that a body emitting energy L as light loses mass L/c². In 1905 that looked like a tiny correction. For the proton it is nearly the whole story.

The theory of the strong force, quantum chromodynamics (QCD), has quarks carrying a "colour" charge and gluons carrying the force between them. Unlike photons, gluons carry colour charge themselves, so they interact with one another. The result is a force whose strength depends on the distance scale. At short distances the coupling α_s is weak, which is asymptotic freedom, discovered in 1973 (Nobel Prize 2004).¹³ At distances approaching a femtometre it grows strong. To leading order,

α_s(μ) ≈ 1 / [b₀ ln(μ²/Λ²)], b₀ = (33 − 2n_f)/(12π) μ is the energy scale of the probe, n_f the number of quark flavours light enough to matter. α_s is about 0.118 at the Z-boson mass (91 GeV) and about 0.3 at 2 GeV.

Λ, a few hundred MeV, is the scale at which the coupling becomes strong. Nothing in the theory's equations sets it: you start with a dimensionless coupling and the quantum theory turns it into a mass scale. Physicists call this dimensional transmutation. It is why the proton weighs about a GeV even though the quarks inside weigh a few MeV.

Frank Wilczek, borrowing a phrase of John Wheeler's, called this "mass without mass".¹⁴ Imagine a simplified world, "QCD Lite", with massless up and down quarks and no others. It would still have protons and neutrons, almost as heavy as ours: their mass is the energy of massless quarks and gluons confined to a femtometre-sized region. The uncertainty principle sets the scale: a quark confined within a radius R has momentum of order ħ/R, so even a massless one carries energy of order ħc/R, about 200 MeV for R = 1 fm and a few hundred MeV in models of a confined quark. Three quarks plus the energy of the field that confines them come to roughly a GeV (this page's estimate).

Lattice QCD, which solves the theory numerically on a grid of points in space and time, turned this from an argument into a calculation. In 2008 the Budapest–Marseille–Wuppertal collaboration computed the masses of the proton and its relatives starting from the QCD equations alone, using three measured particles (the pion, the kaon and the Ξ baryon) to fix the light-quark mass, the strange-quark mass and the overall scale. They found a nucleon mass of 936 ± 25 ± 22 MeV, against the measured 939.¹⁵ And if you set the up and down quark masses to zero, chiral perturbation theory says the nucleon would weigh about 870 MeV, provided the strong force's scale Λ stays the same.¹⁶ Switch off the up and down quarks' Higgs-given masses entirely and the proton loses only about 7%.

Where does the rest come from? The energy of quarks moving inside the proton, the energy stored in the gluon field, and a purely quantum effect called the trace anomaly. Chapter 7 splits it up. First, there is a vivid way to feel how much energy is involved: try to pull the proton apart.

Part IIThe rubber band

Chapter 4The sixteen-tonne rubber band

The cleanest place to see the strong force is a pair of very heavy quarks: a charm quark and its antiquark, bound into a "charmonium" meson. Heavy quarks move slowly, so their bound states can be treated almost like a hydrogen atom, with a potential energy between them. In 1975 a group at Cornell proposed a strikingly simple one and used it to predict the charmonium spectrum:¹⁷

V(r) = −(4/3) α_s ħc / r + σr The first term is like the attraction between two electric charges: it dominates at short distances, where the coupling is weak. The second grows in proportion to the distance r. σ is called the string tension.

A potential that grows in proportion to distance means a constant force. Lattice QCD calculations of a static quark and antiquark show exactly this linear rise.¹⁸ The string tension is conventionally quoted as √σ ≈ 440 MeV;¹⁹ a 2024 lattice calculation with light and strange sea quarks, extrapolated to their real masses, finds 445 ± 7 MeV.²⁰ Older estimates from lattice scale-setting²¹ and from the spectrum of rotating mesons range from about 420 to 465 MeV (this page's survey). In everyday units:

σ ≈ 0.98 GeV/fm ≈ 1.57 × 10⁵ newtons ≈ 16 tonnes-force 1 GeV/fm = 1.602 × 10⁻¹⁰ J ÷ 10⁻¹⁵ m = 1.602 × 10⁵ N, the weight of 16.3 tonnes at the Earth's surface. The range of √σ gives 14.6 to 17.9 tonnes-force, and the 2024 value, 445 ± 7 MeV, gives 16.4 ± 0.5 (this page's arithmetic).

That's the title of this page. Beyond about half a femtometre, the pull between the quark and antiquark levels off towards roughly the weight of sixteen tonnes, about 230 people of 70 kg (about 21 tonnes at half a femtometre, 17 at one), and it never drops below that as they separate, until the string starts to break a little past one femtometre (Chapter 5). A spring pulls harder the more you stretch it; a magnet pulls more weakly the further away it is. This is neither: it is like a rubber band whose pull neither fades nor grows as you stretch it.

The particle tables give an independent check. A spinning string with quarks at its ends gets heavier the faster it spins: plotted against its mass squared, its spin rises along a straight line of slope α′ = 1/(2πσ). The ρ meson and its faster-spinning relatives, the a₂, ρ₃ and a₄ (spins 1 to 4), fall on such a straight line with α′ ≈ 0.9 GeV⁻²,^9,22 which gives √σ ≈ 420 MeV, about 14–15 tonnes-force (this page's arithmetic). Patterns like this are where string theory began. In 1968 Gabriele Veneziano wrote down a formula built on such straight lines,²³ and in 1969–70 Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind²⁴ realised that it describes the vibrations of a string. QCD replaced that picture as the theory of the strong force, and the string idea went on to become string theory. The flux tube between two quarks is, in a sense, the string it started from.

The force stays constant because gluons interact with gluons. The field lines between two electric charges spread out through space, which is why the electric force falls off with distance. The colour field between two quarks can't spread out: the gluons pull its field lines together into a narrow flux tube, a fraction of a femtometre across, whose width grows only slowly as it lengthens.²⁵ A tube of fixed cross-section has a fixed energy per unit length, and a fixed energy per unit length means a fixed force. For three static quarks, an idealised proton, three such tubes meet at a junction in a Y shape,²⁶ each pulling with the same tension.²⁷

Figure 2🧲 Try it

Pull a quark

Grab the glowing quark and pull

How far you've pulled: length of the stretched tube

Drag along the graph too

Pull

That's the weight of

Energy in the stretched tube

Quarks set free so far

A static (infinitely heavy) quark–antiquark pair, or an idealised proton of three static quarks joined by a Y of flux tubes. The pull on the quark is the slope of the Cornell potential V(r) = −eħc/r + σr for a quark and antiquark at separation r, using e = 0.36 and √σ = 440 MeV (σ ≈ 0.98 GeV/fm, which is 16.0 tonnes-force); lattice calculations of three static quarks find the same tension in each leg of the Y (Takahashi et al. 2002), so the proton's pulled leg is drawn with the same curve. With light quarks in the vacuum, the "string" level crosses the "two separate hadrons" level near r_c ≈ 1.21 fm (Bulava et al. 2024, extrapolated to physical quark masses; SESAM's 2005 extrapolation gave 1.13 fm, simulations with heavier-than-real light quarks found 1.22–1.25 fm, and a 2026 preprint at physical quark masses sees hints at 0.96–1.16 fm; the shaded strip marks 1.0–1.3 fm), with a gap of about 100 MeV (this page's arithmetic from the mixing Bulava et al. find at physical quark masses; SESAM found about 50 MeV with heavier quarks), and the force falls to nearly zero. For the proton the breaking length of a leg is taken to be the same, an assumption. "Pure glue" removes the light quarks, as in lattice simulations of gluons alone, and the string never breaks. The shaded band on the Pull graph, 3.5–6 tonnes-force (0.22–0.38 GeV/fm), is the 2026 estimate of the average force on a quark in a real proton, from its gravitational form factors (Ji, Miller and Yang, published in August 2026; a follow-up preprint by Yu et al. finds about 0.3 GeV/fm); its distance scale is a transverse position in a fast-moving frame, not the separation plotted here. Illustrative parameters; this page's arithmetic.Grab the glowing quark and pull it out (or use the slider). These are heavy quarks held still, as in the supercomputer simulations. Up close the pull is even stronger; from about half a femtometre it settles towards 16 tonnes and holds there until just before the snap. The shaded band on the graph is a 2026 estimate for the light quarks in a real proton: 3.5 to 6 tonnes. Then, near 1.2 femtometres, the tube snaps into a new quark and antiquark, and you're left holding a meson instead of a free quark. Try removing the light quarks: then it never snaps.

Some numbers to calibrate the absurdity. A force of 1.57 × 10⁵ newtons on something with a proton's mass would accelerate it at about 10³² m/s². The gravitational pull between two protons one femtometre apart is 1.9 × 10⁻³⁴ N, nearly 10³⁹ times weaker. Yet because the distance is so tiny, stretching the string by a whole femtometre stores only about 1 GeV, a ten-billionth of a joule. It is an enormous force acting over an almost unimaginably small distance, and that combination is the energy scale of the proton's mass.

One caveat runs through everything in this chapter: the clean linear potential belongs to static, infinitely heavy quarks. Up and down quarks are light and move at nearly the speed of light inside a proton. Chapter 6 asks what the force is like there.

Chapter 5Snap

A rubber band that pulled with the same force at any length would let you store unlimited energy in it. Nature doesn't allow that. Once the string holds enough energy to create a light quark and antiquark out of the vacuum, it breaks: the new quark binds to the old antiquark, the new antiquark to the old quark, and you are left holding two mesons. (Pull one quark out of a proton and the proton keeps the new quark: you are left holding a single meson.) The force between the original pair drops to almost nothing. Pull harder and you get more particles, never a free quark.

Lattice QCD first saw this in 2005. With sea quarks much heavier than real ones, close to the strange quark's mass (their pion weighed about 640 MeV, against the real 140), the SESAM collaboration found the string breaking at 1.25 femtometres, and estimated about 1.13 fm for real light quarks, uncertain by about 0.15 fm.¹⁹ A 2019 calculation, with lighter but still heavier-than-real quarks (pion mass 280 MeV), found 1.22 fm for breaking by a light pair and 1.29 fm by a strange pair.²⁸ Its 2024 follow-up, with pion masses down to 200 MeV and extrapolated to the real ones, puts the breaking at 1.21 fm for a light pair and 1.34 fm for a strange pair.²⁰ A 2026 preprint working directly at physical quark masses sees hints of breaking a little earlier, between about 0.96 and 1.16 fm.²⁹ At the breaking point the string stores σr_c ≈ 1.0–1.3 GeV, about a proton's entire rest energy.

How does a pair appear from nothing? By quantum tunnelling. In 1951 Julian Schwinger worked out the rate at which a strong electric field pulls electron–positron pairs out of the vacuum;³⁰ the strong force does the same, far more easily. The Lund string model, developed from 1977 and reviewed in 1983, built this into a description of how energetic quarks turn into sprays of hadrons,³¹ and it is still the core of the most widely used simulation code. The probability falls off exponentially with the square of the quark's mass:

probability ∝ exp(−π m_⊥² / κ) m_⊥² is the quark's mass squared plus its sideways momentum squared; κ ≈ σ is the string tension.

Pair made when a string breaks	Chance, relative to up–antiup
Up or down	1
Strange	≈ 0.3
Charm	≈ 10⁻¹¹
Bottom	≈ 10⁻¹²⁰
Top	≈ 10^−200,000

The up/down, strange and charm values are the Lund-model estimates quoted in the PYTHIA 6.4 manual (PYTHIA 8 tunes strange to 0.22);³² bottom and top are this page's arithmetic with κ = 0.2 GeV², the bottom quark's MS-bar mass (4.19 GeV) and the top quark's measured mass (about 172.6 GeV). Heavy quarks are made in the hard collision or the parton shower, essentially never in the string.

The top quark escapes the string altogether. It decays in about 5 × 10⁻²⁵ seconds, several times faster than the roughly 3 × 10⁻²⁴ seconds a string needs to form (ħ/Λ), so it is the one quark that never ends up inside a hadron (this page's arithmetic). Even so, in 2025 the CMS experiment at the LHC observed an excess of top–antitop pairs made right at threshold, consistent with a fleeting, quasi-bound "toponium" held together by the short-range part of the force.³³ ATLAS reported a matching excess later that year, and its 2026 paper puts it at more than eight standard deviations.³³

You can see strings in particle detectors. When an electron and positron annihilate into a quark, an antiquark and a gluon, the particles come out in three sprays, or jets. In 1981 the JADE experiment at DESY noticed that fewer particles appear between the quark and antiquark jets than between either of them and the gluon jet.³⁴ The string runs from quark to gluon to antiquark, not directly between the quark and antiquark, and the hadrons come from where the string is. (Perturbative QCD later explained the same "string effect" through the coherence of soft-gluon emission.³⁵)

And since 2024 you can watch a string break. Teams using Google's superconducting qubits, Rydberg atoms held in laser light, and a chain of trapped ions have simulated simplified gauge theories in one and two dimensions, created a pair of charges with a string between them, and watched it break by pair creation.³⁶ These are toy theories, much simpler than QCD in three dimensions, but they make the mechanism visible, which no collider can.

Chapter 6Inside a real proton

A real proton has no static quarks and no neatly stretched string. Its quarks are light, they move at nearly the speed of light, and they are surrounded by gluons and short-lived quark–antiquark pairs. Can anything like a confining force be measured there?

In May 2026 Xiangdong Ji, Gerald Miller and Chen Yang proposed a way. Experiments that bounce electrons or photons off protons and make a single photon or meson constrain the proton's gravitational form factors: how energy, momentum and pressure are distributed inside it. From these they extracted the average force on a quark in the proton's outer region, about 0.7 to 1.4 femtometres from the centre depending on the fit: 0.38 ± 0.09 GeV/fm from fits driven by experimental data, and 0.22 GeV/fm from fits dominated by lattice QCD.³⁷ That's about six and three and a half tonnes, respectively (this page's arithmetic). The force is roughly constant across that region, as a linear potential predicts, but less than half the heavy-quark value; the authors suggest the light quarks' motion spreads the flux tube out. Treat this as an early result: it is new (published in August 2026; a July 2026 follow-up by another group, adding QCD sum-rule input, finds about 0.3 GeV/fm, about 5 tonnes, in a preprint³⁸), the "distance" is a position in a frame moving at nearly light speed rather than a quark–antiquark separation, and the answer depends on how the form factors are parameterised.

The same form factors give the pressure. In 2018 an analysis of Jefferson Lab data concluded that the quarks push outwards with about 10³⁵ pascals near the proton's centre (10³⁰ atmospheres, more than in the core of a neutron star) and that the pressure turns into an inward pull beyond about 0.6 femtometres.³⁹ A 2019 reanalysis argued that the same data, fitted more flexibly, are consistent with zero quark pressure: the uncertainty had been underestimated.⁴⁰ Those analyses saw only the quarks. In 2024 a lattice QCD calculation, with a pion only about 30 MeV heavier than the real one, computed the quark and gluon parts together. The gluons supply about two-thirds of the D-term, the quantity that sets the overall size of the pressure, and both parts agree with the experimental analyses within their large uncertainties.⁴¹ Its fits give the same picture: a push of about 10³⁵ pascals in the core, turning to a pull beyond about 0.6 femtometres (this page's arithmetic). The shape is expected on general grounds; experiments have not yet pinned down the size.⁴²

And how big is a proton? Its electric charge spreads over a radius of 0.84075 ± 0.00064 femtometres,² the smaller value that emerged from the "proton radius puzzle" of the 2010s and that most recent measurements now support.⁴³ Its mass need not sit in the same place. Photons striking protons just above the energy needed to make a J/ψ meson (a charm–anticharm pair) mostly interact with the gluons, so near-threshold J/ψ production is a handle on the gluons' share of the mass. From GlueX data, Dmitri Kharzeev estimated a mass radius of 0.55 ± 0.03 fm in 2021.⁴⁴ The J/ψ-007 experiment found 0.76 ± 0.04 fm for the gluonic part with one theoretical model and 0.47 ± 0.04 fm with another; lattice QCD gives about 0.75 fm.⁴⁵ After a factor-of-two error in the second model's formula was corrected, it gives about 0.77 fm for the whole proton and about 1 fm for the gluons alone.⁴⁶ New CLAS12 data give about 0.5, 0.7 or 1.0 fm depending on the method.⁴⁷ Most analyses put the mass at or inside the charge radius, but the answer still depends heavily on how the data are read.

Figure 3🔍 Try it

How big is a proton? Depends what you weigh it with

Radius

Average density inside it

A teaspoon of that would weigh

Nested spheres at the proton's measured radii, around three quarks shown in motion (schematic). Charge radius 0.84075(64) fm (CODATA 2022). Mass radii from near-threshold J/ψ photoproduction: 0.55(3) fm (Kharzeev 2021, using GlueX data; CLAS12 2026 data read the same way give about 0.5 fm). For the gluonic part: 0.755(35) fm with a holographic model (J/ψ-007, Duran et al. 2023; CLAS12 2026: 0.71(6) fm from its data alone, 0.70(2) fm with all three experiments combined), and 0.97(12) fm with a GPD-based model (0.77(7) fm for the whole proton, drawn dashed with the 0.55 fm reading; Guo, Ji, Liu and Yang 2023, correcting a factor-of-two error behind the original 0.47 fm; CLAS12 2026: 1.01(17) fm from its data alone). Lattice QCD gives about 0.75 fm. These are root-mean-square radii of fuzzy distributions. Densities treat each radius as a hard edge, which overstates them; "fuzzy cloud" draws the radius as a Gaussian cloud and spreads the same mass as a uniform ball with the same root-mean-square radius, which is 29% larger and 2.2 times less dense. The nucleus comparison uses nuclear saturation density, 0.16 nucleons per cubic femtometre (2.7 × 10¹⁷ kg/m³). Pressure: schematic shape of the quarks' contribution (Burkert, Elouadrhiri and Girod 2018), repulsive in the core and attractive beyond about 0.6 fm; its size from experiment is disputed (Kumerički 2019); lattice QCD with quarks and gluons together (Hackett, Pefkou and Shanahan 2024) gives the same shape, with the sign change near 0.6 fm (this page's arithmetic from their dipole fits). Drag to turn; hover over or tap a shell to pick it.A proton has no hard edge, so its "size" depends on what you measure. Its electric charge spreads out to about 0.84 femtometres; its mass seems to sit about as far out or closer in, depending on how the data are read. Tap a shell or a button to compare them, and turn the proton with your finger. Either way, a teaspoon of proton would weigh billions of tonnes.

Either way the density is extreme. Treating each radius as a hard edge, which it isn't, the proton's average density is 0.7 × 10¹⁸ kg/m³ inside its charge radius and 2.4 × 10¹⁸ inside a 0.55 fm mass radius: a teaspoon would weigh 3 to 12 billion tonnes, roughly two and a half to nine times nuclear density (this page's arithmetic). A realistic fuzzy edge lowers these numbers by about a factor of two.

Part IIIWho gets the credit

Chapter 7Slicing the proton

If the proton's mass is energy, which energy? In 1995 Xiangdong Ji wrote the proton's rest energy as the expectation value of the QCD Hamiltonian, the operator for total energy, and split it into four pieces:⁴⁸

M_p = E_{quark energy} + E_{gluon field} + E_{quark mass} + E_anomaly Quark energy is the kinetic and interaction energy of the quarks; gluon field energy is stored in the colour-electric and colour-magnetic fields; quark mass is the Higgs-given part; the anomaly term is explained below.

In 2018 the χQCD collaboration computed the quark energy, the gluon field energy and the quark-mass term on the lattice, with pion masses down to the physical one, in the MS-bar scheme at 2 GeV, and obtained the anomaly term from Ji's sum rule:⁴⁹ quark energy 32%, gluon field energy 36%, quantum anomalous energy 23% and quark masses 9% (each uncertain by a few per cent; the arXiv preprint has 33% and 37%). In a 70 kg person that's roughly 22 kg of quark motion, 25 kg of gluon field, 16 kg of quantum anomaly and 6 kg of quark mass (this page's arithmetic).

The anomaly needs explaining. Classically, QCD with massless quarks has no built-in length scale: it looks the same at every magnification. Quantum effects break that symmetry, because the coupling changes with scale (Chapter 3). The breaking leaves a term in the trace of the theory's energy–momentum tensor, proportional to β(g)/(2g) × G², where β describes how the coupling runs and G is the gluon field strength. Ji calls its contribution the quantum anomalous energy.⁵⁰ Written instead as the trace of the energy–momentum tensor, the same mass is the full anomaly plus the quark-mass term, roughly 90% and 10%:⁵² the anomaly's share depends on how you slice. Counted that way, a 2021 lattice calculation, at a heavier-than-real pion mass, found that the gluon part of the anomaly supplies most of the nucleon's mass, about 800 MeV, but only about 100 MeV of the pion's, under a third (in that calculation the pion weighed 340 MeV, not 140).⁵¹ Ji and collaborators see the anomaly as a dynamical cousin of the Higgs mechanism, a condensate that breaks scale symmetry and generates mass; Lorcé, Metz, Pasquini and Rodini argue that it is not a separate contribution to the mass at all.⁵³

Figure 4🍰 Try it

Slicing a proton

Same proton, three ways to slice it

Ji's four slices: the decomposition of Ji (1995) with lattice values from Yang et al. (2018), MS-bar at 2 GeV: quark energy 32(4)(4)%, gluon field energy 36(5)(4)%, quark masses 9(2)(1)%, and the quantum anomalous energy 23(1)(1)%, which was obtained from the sum rule rather than computed (published values; the arXiv preprint has 33% and 37%). Trace: the same mass written as the trace of the energy–momentum tensor (Shifman, Vainshtein and Zakharov 1978), the full trace anomaly plus the quark-mass term, about 90% and 10%. Quarks vs gluons: a three-term split; Metz, Pasquini and Rodini (2020) find the gluons' share between about 53% and 73% across the schemes they compare (tick marks), so the crossover can be dragged within that range. Only two terms in any such sum rule are independent; the quark-mass term (here up, down and strange) is the one free of scheme dependence. Lorcé, Metz, Pasquini and Rodini (2021) argue that the anomalous energy is not a separate contribution at all. Hover over or tap a slice for its meaning.Three ways of slicing the same proton. Tap a slice to see what it is, and switch between the ways of slicing: watch the "quantum anomaly" swing from a quarter to nine-tenths. In "Quarks vs gluons", drag the dividing line. Only one slice, the quark masses, stays about the same size every time.

So the proton is roughly a third quark motion, a third gluon field, a quarter quantum anomaly and a tenth Higgs? Not so fast. These slices are less solid than they look.

The decomposition isn't unique. Cédric Lorcé argued in 2018 that standard decompositions leave out pressure effects, that with both quarks and gluons present any split into more than two terms involves choices, and that the "quark mass" and anomaly pieces are conventional.⁵⁴
Only two terms are independent. Andreas Metz, Barbara Pasquini and Simone Rodini showed in 2020 that any such sum rule has at most two independent terms, because the relevant matrix element has only two form factors, and that the quark-mass term is the only one with no dependence on the scheme, for a given set of quark flavours (Chapter 8 shows what happens when you add the heavy ones).⁵⁵ Ji and collaborators argue that the anomaly term is scheme-independent too.⁵⁰ Across the schemes Metz and colleagues considered, the gluons' share ranged from about 53% to 73% of the proton's mass.
Two slices follow from one. In Ji's sum rule the anomaly term is ¼(1 − b)M and the quark-mass term is close to bM, where b is the quark-mass ("sigma-term") fraction of Chapter 8. So the 23% and the 9% are not separate discoveries: both follow from b ≈ 0.1. The remaining split between quark and gluon energy depends on the resolution scale at which you count momentum (this page's reading of Ji's formulas).

Underneath is a structure like the virial theorem: in Ji's sum rule the traceless part of the energy–momentum tensor contributes three-quarters of the mass and the trace part one quarter. The ¾ : ¼ split is built into Ji's way of slicing; what experiments and lattice calculations can actually pin down are the total and the sigma terms. Asking what fraction of the proton is "gluon" is like asking what fraction of a song is "bass": the answer depends on where you set the crossover.

Chapter 8One per cent, ten, or thirty

Back to the question in the title of so many popular articles on this subject: how much of your mass comes from the Higgs? There are three honest answers, because there are three reasonable questions.

Question 1: what are the Higgs-given masses of the quarks inside you?

About 1%, as Chapter 2 found. But the answer slides. Quark masses in QCD are not fixed numbers like the electron's; they depend on the resolution scale μ at which they are defined. The standard 2 GeV is a convention. Run the masses to other scales and the valence quarks' share of a 70 kg body changes: 1.43% at 1 GeV, 1.09% at 2 GeV, 0.63% at the Z-boson mass and 0.53% at 1 TeV (this page's arithmetic, using four-loop running).

Figure 5🔭 Try it

The one per cent that slides

Drag along the graph to change the zoom

Resolution scale μ: how hard you zoom in

Up quark

Down quark

Valence quarks' share of you

Running MS-bar quark masses from 1 GeV to 1 TeV (four-loop running from α_s(M_Z) = 0.1180 and the FLAG 2024 masses at 2 GeV, with quark thresholds; this page's arithmetic, interpolated between computed points, good to about 1–2%). The quark discs above the graph have areas in proportion to the masses. The valence share counts two up and one down quark per proton and one up and two down per neutron in a 70 kg body. The shaded region below about 1.5 GeV is where perturbative running becomes unreliable. The sigma-term band (σ_πN + σ_s, 9.3–11.1% of the nucleon mass) and the Higgs–nucleon coupling f_N = 0.308 do not depend on the scale.A quark's mass isn't a fixed number: it depends on how closely you look. Drag along the graph or press play: the quarks shrink as you zoom in, and "the Higgs gives you 1%" slides from about 1.4% to 0.5%. The 10% and 30% answers stay put.

Question 2: how much of the proton's mass is quark-mass energy?

The proton holds more than three quarks: it seethes with short-lived quark–antiquark pairs. The cleanest way to count all of their mass is the sigma term, how much the proton's mass changes when you change a quark's mass:

σ_q = m_q ∂M_N/∂m_q The Feynman–Hellmann theorem turns this into the quark-mass energy in the nucleon. Unlike the quark masses, sigma terms don't depend on the scheme or scale.

For up and down quarks together, the sigma term σ_πN comes from two independent routes, and they disagree. Lattice calculations with three flavours of sea quark average 42.2 ± 2.4 MeV; those that also include charm sea quarks average 60.9 ± 6.5 MeV, but that average is dominated by the one calculation that adds extra nucleon–pion states to its fits.⁸ The analysis of pion–nucleon scattering, combined with precise measurements of pionic hydrogen, gives 59.0 ± 3.5 MeV.⁵⁶ One proposed explanation is that lattice fits miss contamination from low-lying states of a nucleon plus one or two pions; including them pushes the lattice result up to about 60 MeV.⁵⁷ A 2025 lattice study traced most of that contamination to states of a nucleon plus a σ meson (the scalar resonance that, at real quark masses, decays into two pions),⁵⁸ and a 2025 two-loop chiral analysis of lattice data gets 55.9 ± 2.5 MeV and argues the gap closes;⁵⁹ neither is yet a calculation at the physical pion mass. About 3 MeV of the gap is a difference in how the two communities define the limit of equal up and down quark masses.⁵⁶ As of October 2026 the tension is unresolved. The strange sigma term is about 41–45 MeV.⁸

Put together, up, down and strange quark masses account for 9.3% to 11.1% of the nucleon's mass (this page's arithmetic). A striking way to put it: measured by how its mass responds to the light-quark masses, the proton behaves as if it held 12 to 18 light quarks, not 3. That count, the sigma term divided by the quark mass, isn't a literal number of particles, and like the masses it depends on the scale (here the usual 2 GeV), but it shows how much the sea of virtual pairs matters. Adding the charm quark's sigma term, which lattice calculations put at roughly 70 to 110 MeV,^8,60 brings the total to roughly 17–23%.⁵⁵

Question 3: how strongly does the Higgs couple to a proton?

Heavy quarks hardly appear in the proton, but they affect it anyway. Each one changes how the strong coupling runs, and so changes Λ, the scale that sets the proton's mass. To leading order, Λ depends on the heavy-quark masses as (m_cm_bm_t)^2/27. Since all three masses come from the Higgs field, so does part of Λ. In 1978 Shifman, Vainshtein and Zakharov showed that each heavy quark contributes (2/27) × (M_N − σ_light) to the nucleon's coupling to the Higgs.⁵² Adding the light-quark sigma terms gives the Higgs–nucleon coupling:

f_N = Σ_u,d,s f_q + (2/9)(1 − Σ_u,d,s f_q) = 0.308 ± 0.018 f_q = σ_q/M_N. The Higgs couples to a nucleon f_N times as strongly as it would to an elementary particle of the same mass. The value is from Hoferichter, Klos, Menéndez and Schwenk.⁶¹

Because the Higgs couples to anything in proportion to how its mass depends on v, f_N also equals d ln M_N/d ln v, provided the Yukawa couplings and the strong coupling at very high energy (above the top-quark mass) are held fixed, so that Λ shifts with the heavy-quark masses (this page's reading). In that sense about 31% of the proton's mass responds to the Higgs field: a Higgs field 1% stronger would make you about 0.3% heavier, about 216 grams. Hold Λ itself fixed instead, as Figure 6 does, and only the light-quark share of about 10% responds. The coupling f_N is also the sum of all six quarks' sigma terms divided by the nucleon mass (the heavy quarks act through the gluons), so 10%, 20% and 31% are one quantity counted with three, four and six flavours. As a response to v it is a slope, not a fixed share: the proton's mass doesn't depend on v in a straight line.

And if you switched the Higgs off?

Then the answer depends on what else you hold fixed. Keep Λ fixed, and massless up and down quarks still leave a nucleon of about 870 MeV, about 7% lighter;¹⁶ making the strange quark massless too (σ_s ≈ 40 MeV) takes off a few per cent more. Keep instead the strong coupling fixed at a very high energy, as a grand unified theory might, and removing all the quark masses lowers Λ by a factor of about 2.5 to 3 and takes away the light quarks' own mass-energy, giving a proton roughly 65–70% lighter (this page's order-of-magnitude estimate). Same question, answers from about a tenth to about two-thirds, depending on what you mean. It's the lesson of Nº 1 again: a change in a dimensionful quantity only means something once you say what it is measured against.

Chapter 9The one per cent that runs the world

If the Higgs field accounts for so little of your mass, does it matter? Enormously, because the small masses it gives out decide the details on which chemistry and stars depend.

The electron. All of the electron's mass comes from the Higgs. The size of an atom is set by the Bohr radius, a₀ = ħ/(m_ecα), so with the fine-structure constant α fixed, atoms scale as 1/v and chemical bond energies as v. Double the Higgs field and atoms shrink to half their size; halve it and they double. (Nº 11 turns a different dial, the speed of light, and watches a car battery lose most of its voltage.)

The neutron–proton balance. The neutron outweighs the proton by 1.293 MeV.² That's more than the electron's mass, 0.511 MeV, so a free neutron decays (in about 15 minutes) while a hydrogen atom lasts forever. Electromagnetism alone would make the charged proton the heavier of the two. What flips it is the down quark's extra Higgs-given mass. In 2015 a lattice calculation split the difference into +2.52 MeV from the quark masses and −1.00 MeV from electromagnetism, a total of 1.51 ± 0.28 MeV, consistent with the measured value.⁶² The margin is small, and the Higgs sets it.

The pion. The pion's mass squared is proportional to the light-quark masses,⁶³ so without Higgs-given quark masses the pion would be massless. It is the proton's opposite: by the Feynman–Hellmann theorem of Chapter 8, half of its mass, about 70 of its 140 MeV, is quark-mass energy to leading order, against a tenth for the proton, which is why the gluons' anomaly supplies a much smaller share of the pion's mass than of the proton's (Chapter 7).⁵¹ Its mass, 140 MeV, sets the range of the nuclear force: ħ/(m_πc) ≈ 1.4 fm. Heavier quarks mean heavier pions, a shorter-range nuclear force and more weakly bound nuclei.

Put these together and you can ask what happens if the Higgs field were weaker or stronger, with everything else held fixed. Figure 6 does that.

Figure 6🎛️ Try it

Turn the Higgs dial

Everything else held fixed

Strength of the Higgs field in empty space, compared with ours

Electromagnetic part of the neutron–proton difference:How much of the neutron–proton gap is electricity?

Electrons and atoms

Neutron vs proton + electron

Nuclei

You, if every atom simply scaled

The Higgs potential drawn as a surface (not to scale: depth and width are compressed); the ball marks the field's value in empty space, v. Scaling only v, with the Yukawa couplings, the fine-structure constant and the strong-force scale Λ held fixed. Electron and quark masses scale with v; the atom's size with 1/v; the pion mass (and so the nuclear force's reach) with √v. Neutron − proton = 1.293 MeV + 1.79 MeV × (v/v₀ − 1): the quark-mass part scales with v and the electromagnetic part (about −0.5 MeV) does not, as in Damour and Donoghue (2008) (who state that the gauge couplings are fixed but, like this figure, neglect the resulting shift of Λ). Boundaries: protons decay below 0.22v₀ (this page's arithmetic); hydrogen atoms capture their electrons below 0.39v₀ (Damour and Donoghue; the 2015 lattice split of Borsanyi et al., +2.52 − 1.00 MeV, would move this to about 0.5–0.6, and the Cottingham-formula estimate of the electromagnetic part by Gasser, Leutwyler and Rusetsky, 0.58 MeV, to about 0.43; choose the electromagnetic share below the dial to move this edge); the deuteron becomes unstable to weak decay at 1.2–1.4v₀, because heavier pions also loosen its binding (Agrawal et al. 1998; with the binding held fixed, this figure's inputs would delay that to about 2.1v₀, although the main solar reaction p + p → d + e⁺ + ν would stop releasing energy at about 1.18v₀, with Damour and Donoghue's split: this page's arithmetic); nuclei unbind at about 1.36 ± 0.14v₀, and by 1.64v₀ at 95% confidence (Damour and Donoghue). All of these move by 15% or more with the inputs, and holding the strong coupling fixed at very high energy instead widens the window to roughly 0.3–1.9 (below). The proton mass is a first-order estimate from the light-quark sigma terms; "you" assumes your body keeps the same atoms in the same arrangement, so its size follows the atoms' (this page's estimate). Drag the ball or the marker on the band.Drag the ball in the Higgs "hat" (or the slider) to make the Higgs field stronger or weaker and keep everything else the same. The electron's mass, the size of atoms, the neutron–proton balance and the nuclei all follow, and so would you. Our universe sits in a fairly narrow band where hydrogen, deuterium and atomic nuclei all hold together. Below the dial you can choose how much of the neutron–proton gap is electricity, and watch the hydrogen edge move.

Weaker, below about 0.4 times today's value: the neutron is no longer heavier than a proton plus an electron, so a hydrogen atom can lower its energy by capturing its electron (p + e → n + ν). Hydrogen slowly turns into neutrons. Damour and Donoghue put the edge at 0.39;⁶⁴ with the 2015 lattice split, this page finds 0.5–0.6, and with the Cottingham-formula estimate of the electromagnetic part (0.58 MeV)⁶⁵ about 0.43. The edge depends on exactly how much of the neutron–proton difference is electromagnetic.
Stronger, from about 1.2 to 1.4 times: the neutron is heavier and heavier pions bind the deuteron, a proton and neutron, less tightly, so it becomes unstable to weak decay (d → p + p + e⁻ + ν̄). Stars like the Sun begin by fusing two protons into deuterium, so that step fails.⁶⁶
From about 1.4 times: heavier quarks make heavier pions, the nuclear force's reach shrinks, and nuclei come apart. Damour and Donoghue's central estimate is 1.36 ± 0.14 times; 1.64 is their 95%-confidence upper limit.⁶⁴ (An older estimate, by a different route, put the end of all nuclei near 5 times;⁶⁶ Damour and Donoghue's bound supersedes it.)

So with everything else fixed, the Higgs field sits in a window, at most 0.39 < v/v₀ < 1.64 by Damour and Donoghue's analysis and more likely about 0.4 to 1.4, in which both hydrogen and nuclei exist;⁶⁴ the deuteron's weak decay may close it a little earlier, at 1.2–1.4. These are "if only v changed" thought experiments with Λ held fixed. If instead the strong coupling is held fixed at very high energy (the convention behind the 31% of Chapter 8), Λ itself grows roughly as v^0.22, the quark masses grow only as about v^0.78 relative to it, and the window widens to roughly 0.3–1.9 (this page's estimate). In a real theory several constants might change together, and the edges move with the inputs by 15% or more. Still, they make the point. The Higgs contributes about 1% of your mass, and that 1% decides whether you can have atoms.

Switch the field off entirely and things get strange. Chris Quigg and Robert Shrock worked out this world in 2009.¹⁶ Electrons become massless, so nothing holds them into atoms. With Λ kept at today's value, as they assume, the proton loses less than a tenth of its mass. And the W and Z bosons still get masses: the condensate of quark–antiquark pairs that QCD forms in the vacuum breaks the electroweak symmetry by itself, giving a W of about 28 MeV, roughly 3,000 times lighter than ours. The weak force becomes millions of times stronger.

Part IVWhat's left

Chapter 10What the Higgs does, and what it doesn't

"The Higgs gives everything its mass.": It gives elementary matter particles (quarks, electrons, muons and taus) and the W and Z bosons their masses. It gives none to photons or gluons. It accounts for about 1% of you, or 10%, or 30% (Chapter 8). The origin of neutrino masses is unknown (Nº 4); so is that of dark matter. Even the Higgs boson's own mass comes from the shape of the field's potential, not from "the Higgs mechanism" in the same sense.
"Each quark weighs a third of a proton.": An up quark's own mass is about 2 MeV, 0.2% of a proton. The 300 MeV "constituent" mass of quark models is a dressing made by the strong force.
"A proton is mostly empty space.": Atoms are mostly empty space; protons are not. A proton is filled with quark motion and gluon field, and its mass is concentrated within a root-mean-square radius of about 0.5–0.8 fm.
"The strong force grows forever with distance.": It doesn't. The pull is strongest at short range (although the coupling is weak there), levels off near sixteen tonnes beyond about half a femtometre, and past about 1–1.3 fm the string breaks.
"With enough energy you could pull out a single quark.": More energy makes more hadrons, never a free quark. Even in the quark–gluon plasma, above about 156 MeV (1.8 × 10¹² K),⁶⁷ quarks are freed only collectively, inside the hot plasma. The whole universe was such a plasma until it was roughly 20 microseconds old (this page's estimate).
"E = mc² is about bombs.": It's about you. About 99% of your mass is the energy of confined quarks and gluons divided by c².
"The proton is 23% quantum anomaly.": In one popular, and disputed, way of slicing. That number follows from the sigma terms, and the quark/gluon split around it depends on conventions (Chapter 7).

The heavier quarks' masses connect to Nº 0 too: the top quark's mass and the Higgs boson's mass together decide whether the vacuum we live in is stable or merely long-lived.

Chapter 11Ceilings and open questions

The page's biggest and smallest numbers in one place, then the questions nobody can answer yet.

Quantity	Value
Pull between two heavy quarks (string tension)	≈ 16 tonnes-force (14.6–17.9)
Acceleration it would give a proton	≈ 10³² m/s²
Compared with gravity between two protons 1 fm apart	nearly 10³⁹ times stronger
Average pull on a quark inside a real proton (2026 estimate)	≈ 3.5–6 tonnes-force³⁷
Stretch before the string snaps	≈ 1.0–1.3 fm
Energy in the string when it snaps	≈ 1.0–1.3 GeV
Chance that a snap makes a top-quark pair	≈ 10^−200,000
Pressure at the proton's centre	≈ 10³⁵ Pa (disputed)
A teaspoon of proton	3–12 billion tonnes
Your mass as energy	6.3 × 10¹⁸ J ≈ 1.5 Gt of TNT
Your mass as sunlight	16 nanoseconds of the Sun's output
Higgs-given mass in you (quarks + electrons)	782 g
Gluon field energy in you (one scheme)	≈ 25 kg
Quantum anomalous energy in you (one scheme)	≈ 16 kg
Mass you lost when your nuclei formed	535 g
Higgs-given share of everything in the universe	≈ 0.05%

This page's arithmetic unless cited. The last line: ordinary matter is about 4.9% of the universe's energy, and the Higgs-given part of ordinary matter (quark and electron masses) is about 1% of that. Dark matter and dark energy make up the rest, and their origin is unknown.

The open questions are sharp.

The sigma-term tension. Is the quark-mass share of the nucleon nearer 9% or 11%? Lattice and pion–nucleon scattering disagree, and the excited-state explanation has not yet been confirmed by a calculation at the physical pion mass.
Measuring the slices. The anomaly term and the mass radius are being chased through J/ψ production near threshold at Jefferson Lab and, in the 2030s, through J/ψ and Υ production at the Electron-Ion Collider at Brookhaven. A second round of the EIC's long-lead purchases was approved in February 2026 (the first came in 2024), and work to convert RHIC into the EIC, reusing its tunnel and one of its two ion rings, began in April 2026.⁶⁸
The pressure. Is it really 10³⁵ pascals? Better deeply-virtual Compton scattering data should tell.
Confinement itself. Nobody has proved it from the equations. Showing that pure Yang–Mills theory exists and has a mass gap is one of the Clay Mathematics Institute's million-dollar Millennium Prize problems.⁶⁹
The flavour puzzle. Why is the electron's coupling to the Higgs 3 × 10⁻⁶ while the top quark's is about 1? Why is the down quark heavier than the up, the fact that keeps hydrogen alive?
The hierarchy problem. Why is v = 246 GeV, so tiny compared with the gravitational Planck scale, about 10¹⁹ GeV? The window of Chapter 9 is one, contested, kind of answer.

Meanwhile the main point is not in doubt. You are made of motion: quarks whizzing about at nearly the speed of light inside regions a femtometre across, gluon fields stretched taut between them, and the quantum breaking of a symmetry of scale. The Higgs field supplies the small masses that decide whether atoms and stars can exist at all, but the 70 kilograms on the scale is, to a very good approximation, the energy of quarks and gluons held in by a pull of several tonnes (sixteen between heavy quarks) that never lets go.

Chapter 12Glossary and sources

MeV, GeV: Mega- and giga-electronvolts: units of energy, and (dividing by c²) of mass. A proton is 938 MeV/c² = 1.67 × 10⁻²⁷ kg.
Femtometre (fm): 10⁻¹⁵ metres, about the size of a proton.
Tonne-force: The weight of one tonne at the Earth's surface, 9.81 kilonewtons.
QCD: Quantum chromodynamics, the theory of quarks, gluons and the strong force.
Lattice QCD: Solving QCD numerically on a grid of points in space and time, on supercomputers.
Current and constituent mass: A quark's mass as a parameter in the theory (a few MeV for up and down) versus its effective mass inside a hadron once dressed by gluons (about 300 MeV).
MS-bar at 2 GeV: The standard scheme and scale at which light-quark masses are quoted. Quark masses change with the scale.
String tension (σ): The energy per unit length of the flux tube between a quark and an antiquark: the constant force between them at intermediate distances.
Sigma term: The part of a hadron's mass due to a given quark's mass, defined by how the hadron's mass changes when that quark mass changes.
Trace anomaly: The quantum breaking of QCD's classical scale symmetry, which contributes a term to the proton's mass.
v: The Higgs field's value in empty space, 246 GeV. Elementary particle masses are proportional to it.

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16 tonnes

70 kilograms of what?

Weighing the quarks

Mass without mass

The 16-tonne rubber band

Snap!

Inside a real proton

Slicing the proton

1%, 10% or 30%?

The 1% that runs the world

You are made of motion

Sixteen tonnes