From quarks to the Higgs

Foundations

The picture that will not die

Every textbook cover shows it: a nucleus in the middle, electrons whizzing round it in neat elliptical orbits, like a tiny solar system. It is a hundred years out of date, and it is wrong in a way that matters.

Electrons do not orbit. They are not little balls with positions and paths. What an atom actually looks like, as closely as the question can be answered, is a dense nucleus surrounded by a cloud of probability, a standing wave whose shape depends on the electron’s energy. Those shapes are what lesson 3.4 called orbitals, and their geometry is what gives carbon its four bonds at their particular angles. Chemistry is quantum mechanics, and the solar-system picture cannot explain a single chemical bond.

So this lesson goes underneath the chemistry: what matter is actually made of, and what holds it together.

Three particles

Everything in this chapter, every element, every molecule, every rock and every living thing, is built from three particles.

Two of them are quarks, called up and down. Three quarks make a proton (two up, one down) or a neutron (two down, one up). The third is the electron. That is the whole inventory of ordinary matter. Add the photon, the particle of light, and you can build the universe as it appears in the rest of this course.

Nature also provides a great deal that is not needed. There are six kinds of quark, not two, and three kinds of electron-like particle, and three kinds of neutrino, arranged in three families of increasing mass. The heavier families exist only briefly, made in collisions and in cosmic rays, and decay within fractions of a second. Nobody knows why they exist at all. The physicist Isidor Rabi, on being told of the discovery of the muon, a heavier cousin of the electron, asked “Who ordered that?” Sixty years later there is still no answer.

Four forces

Four forces govern everything.

The strong force binds quarks into protons and neutrons, and binds those into nuclei. It is the strongest by an enormous margin, and it behaves unlike any other force: instead of weakening with distance, it holds firm. Try to pull two quarks apart and the energy needed keeps rising, until it becomes cheaper for the universe to create a brand new quark and antiquark from that energy. You end up with two particles instead of one free quark. This is why no one has ever isolated a quark and no one ever will.

It also explains something surprising about you. The quarks inside a proton account for only a small fraction of its mass. The rest is the energy of the field binding them, converted to mass by the most famous equation in physics. Almost all of your weight is not stuff. It is the energy of the strong force doing its job.

Electromagnetism acts between charged particles and is carried by photons. It holds electrons to nuclei, binds atoms into molecules, and is therefore responsible for the entirety of chemistry, all of biology, every material, and the light by which you are reading this.

The weak force does something none of the others can: it changes one kind of quark into another. That is what makes radioactive decay possible, and, crucially for lesson 2.2, it is what lets a proton turn into a neutron so that two protons can stick together. That is the first step of the Sun’s fusion chain, and the slowest, and it is why the Sun burns for ten billion years instead of exploding. A universe without the weak force would have no shining stars.

Gravity is the odd one out. Between two protons it is about a million billion billion billion times weaker than electromagnetism, so weak that it is irrelevant to everything in this chapter. But it has no opposite charge to cancel it, so it accumulates. Put enough matter in one place and gravity beats everything, which is chapters one, two and four. It is also the one force the standard theory cannot accommodate.

Where mass comes from

By the 1960s the theory of the weak force worked beautifully except for one thing: it predicted that its force-carrying particles should be massless, like the photon, and they plainly were not. In 1964 several physicists, including Robert Brout and François Englert in Brussels and Peter Higgs in Edinburgh, proposed a way out. Suppose space is filled everywhere by a field, and suppose particles acquire mass by interacting with it. The stronger the interaction, the heavier the particle. A photon ignores the field and stays massless; a top quark interacts strongly and is heavier than an atom of gold.

The idea explained the observations, but it made a testable prediction: if such a field exists, it should be possible, by putting enough energy into a small enough space, to make a ripple in it, and that ripple would be a new particle. Finding it took forty-eight years, a tunnel twenty-seven kilometres round beneath the French-Swiss border, and about ten thousand people. On 4 July 2012 the two big experiments at the Large Hadron Collider, working independently and blind to each other’s results, both announced a new particle at about 125 times the mass of a proton. It was the Higgs boson.

What the Standard Model is, and is not

Put the particles and the first three forces together and you have the Standard Model. It is the most precisely tested theory in science: some of its predictions match experiment to twelve decimal places. Every particle it predicted has been found. Nothing found in a laboratory contradicts it.

It is also, certainly, incomplete. It says nothing about gravity. It contains no candidate for the dark matter of lesson 1.7, and nothing to explain dark energy. It does not explain why matter outnumbered antimatter in lesson 1.2. It does not say why particles have the masses they have, which are simply measured and typed in, or why there are three families rather than one.

A theory can be right and unfinished at the same time. That is where particle physics has been sitting for fifty years, waiting for an experiment to show it something it cannot explain.

Deeper

From the particle zoo to quarks

Through the 1950s, accelerators produced a proliferation of strongly interacting particles with no obvious organisation. In 1961 Gell-Mann and Ne’eman independently noticed that they fell into geometric patterns of eight and ten, and in 1964 Gell-Mann and, separately, Zweig proposed that the pattern followed if all of them were built from three constituents with fractional electric charge. Gell-Mann initially treated quarks as a mathematical convenience. The 1969 deep inelastic scattering experiments at SLAC, which fired high-energy electrons at protons and found them bouncing off hard point-like objects inside, changed that: the proton had structure, and the structure had the properties predicted.

Asymptotic freedom and confinement

Quantum chromodynamics, the theory of the strong force, has a property no other force shares: its coupling grows at low energy and shrinks at high energy. Gross, Wilczek and Politzer showed in 1973 that non-Abelian gauge theories behave this way, which explained both why quarks inside a proton behave almost as free particles when probed at high energy and why they cannot be extracted at low energy. The potential between a quark and an antiquark rises roughly linearly with separation, at about one giga-electron-volt per femtometre, so separating them by a nanometre would require enough energy to create a billion new pairs. What emerges instead is a shower of ordinary particles, a jet, which is what detectors actually see.

Mass without matter

The up and down quarks have masses of a few mega-electron-volts each; a proton is 938. Adding the three quarks accounts for about one percent of the proton. The remainder is the energy of the gluon field and the kinetic energy of the quarks, converted to mass by E = mc². Lattice calculations, which solve the equations numerically on a grid of spacetime points, now reproduce the proton’s mass from first principles to a few percent. The statement that ordinary matter is mostly binding energy is not a metaphor; it is a computed result.

The Higgs mechanism

The electroweak theory unifies electromagnetism and the weak force, but gauge invariance forbids explicit mass terms for the force carriers. The Brout-Englert-Higgs mechanism introduces a scalar field with a potential minimised at a non-zero value, so the vacuum is not empty but permeated by a constant field. Three of the field’s four components are absorbed to give mass to the W and Z bosons; the fourth remains as an observable particle. Fermion masses arise from Yukawa couplings to the same field, with each coupling a free parameter. The mass of the Higgs boson itself was not predicted, which is why it took so long to find: experiments had to sweep the possible range.

The 2012 discovery

ATLAS and CMS both reported excesses in the diphoton and four-lepton channels at about 125 GeV, each at the five-sigma level required for a discovery claim, in analyses kept blind from one another. Subsequent measurements have confirmed the particle’s spin, parity and couplings as consistent with the Standard Model prediction, with the couplings to top quarks, bottom quarks and tau leptons now directly observed. Englert and Higgs received the Nobel Prize in 2013; Brout had died in 2011.

The Standard Model’s known gaps

Neutrino oscillation, established by the experiments of lesson 2.2, requires neutrinos to have mass, which the original Standard Model did not include. Dark matter has no Standard Model candidate. The observed matter-antimatter asymmetry exceeds what the model’s CP violation can generate by several orders of magnitude. Gravity has no quantum description that works at all energies. And the model contains at least nineteen free parameters, including all the particle masses, which are inputs rather than outputs.

Frontier

Nothing new, so far

The Large Hadron Collider was expected by many to find supersymmetric partner particles or other new physics alongside the Higgs. It has not. Searches have pushed the possible masses of many proposed particles above several tera-electron-volts, excluding the versions of these theories that were most popular in the 1990s. The absence is itself information, and it has shifted effort toward precision measurements of Higgs couplings, where a small deviation from prediction would be the first crack.

Where the answers might come from

Neutrino experiments, measuring the mass ordering and whether neutrinos are their own antiparticles; precision measurements of rare decays; direct dark matter searches; and cosmological observations that probe energies no accelerator can reach. The next collider, if built, would study the Higgs boson to far greater precision. The open questions of lesson 1.7 and those of this lesson are, increasingly, the same questions.

Transcript and shot list

Target runtime about 8 minutes. Built as going underneath the chemistry: inventory the particles, then the four forces in order of how much of your life each runs, then the field that supplies mass, then what the theory still cannot do. Shot types: ANIM is rendered from code with Manim, AI is a generated shot from Higgsfield with the shared style reference, REAL is agency imagery with credit, CAM is the narrator.

[00:00] S01 · ANIM · The classic textbook atom: nucleus with electrons on elliptical orbits; it dissolves into fuzzy probability clouds in the shapes of real orbitals.

Almost none of your weight is made of stuff. The quarks inside a proton account for about one per cent of its mass, and the rest is the energy of the field holding them together. I’ll come back to that. But to get there we have to go underneath chemistry, and the first thing to drop is the picture on every textbook cover: a nucleus with electrons whizzing round it like planets. It’s a hundred years out of date, and it’s wrong in a way that matters. Electrons don’t orbit. They aren’t little balls with paths. An atom is a dense nucleus surrounded by a cloud of probability, a standing wave, and the shapes of those waves are exactly what gave carbon its four bonds at their particular angles in the last lesson. Chemistry is quantum mechanics. So let’s go underneath the chemistry.

[01:06] S02 · ANIM · Cosmic calendar; a marker at the first millionth of a second; a second marker in the last flicker of 31 December for 1964 to 2012.

The particles have existed since the first millionth of a second. The theory that describes them was assembled between 1964 and 2012: the last flicker of the cosmic year.

[01:19] S03 · ANIM · Two up quarks and a down quark forming a proton; two downs and an up forming a neutron; an electron; then a molecule, a rock, a hand.

Everything in this chapter, every element, every molecule, every rock and every living thing, is built from three particles. Two quarks, called up and down: three of them make a proton, or a neutron. And the electron. That’s the entire inventory of ordinary matter. Add the photon, the particle of light, and you can build the universe as it appears in the rest of this course.

[01:50] S04 · ANIM · Three generations laid out; the second and third flash into existence and decay; a caption: “Who ordered that?” Rabi, 1936.

Nature also supplies a lot that isn’t needed. There are six kinds of quark, not two. Three kinds of electron-like particle. Three kinds of neutrino. Arranged in three families of increasing mass, and the heavier ones exist only briefly, made in collisions, decaying in fractions of a second. Nobody knows why they exist. When the muon was found, a heavier copy of the electron, the physicist Isidor Rabi asked, “Who ordered that?” Ninety years later there’s still no answer.

[02:26] S05 · ANIM · Two quarks pulled apart; the energy between them rises linearly; at a threshold, a new quark-antiquark pair appears and two particles result.

Four forces run everything. The strong force binds quarks into protons and neutrons, and it behaves unlike anything else. Instead of weakening with distance, it holds firm. Pull two quarks apart and the energy keeps climbing, until it’s cheaper for the universe to create a brand new quark and antiquark out of that energy. You end up with two particles. Never one loose quark. That’s why nobody has ever isolated one, and nobody ever will.

[03:01] S06 · ANIM · A proton opened up: three small quark masses; a vast field of gluon energy; a bar chart showing about 1 percent quarks, 99 percent binding energy; a bathroom scale.

It also explains something surprising about you. The quarks inside a proton account for about one percent of its mass. The rest is the energy of the field binding them, turned into mass by E equals m c squared. Almost all of your weight isn’t stuff. It’s the strong force, doing its job.

[03:25] S07 · ANIM · Electromagnetism holding electrons to nuclei, then atoms into molecules, then a whole chemistry set; a photon travels to an eye.

Electromagnetism acts between charges and is carried by photons. It holds electrons to nuclei, binds atoms into molecules, and is therefore responsible for all of chemistry, all of biology, every material, and the light you’re seeing this with.

[03:43] S08 · ANIM · The weak force converting a proton to a neutron; two protons then stick; the Sun’s fusion chain starts; a clock showing a billion years for one proton’s turn.

The weak force does something none of the others can: it changes one kind of quark into another. That’s what makes radioactivity possible. And it’s what lets a proton turn into a neutron, so that two protons can finally stick together. That’s the first step of the Sun’s fusion chain, and the slowest, and it’s the reason the Sun burns for ten billion years instead of going off like a bomb. Without the weak force, no star would shine.

[04:19] S09 · ANIM · Gravity between two protons, 10³⁶ times weaker; charges cancelling; mass accumulating; a planet, a star, a galaxy.

And gravity, the odd one out. Between two protons it’s about a million billion billion billion times weaker than electromagnetism. Utterly irrelevant to anything in this chapter. But it has no opposite charge to cancel it out, so it accumulates. Pile up enough matter and gravity beats everything. That’s chapters one, two and four. It’s also the one force this theory can’t handle.

[04:48] S10 · ANIM · A field filling all space; particles moving through it, some slowed heavily, some passing free; photon massless, top quark heavier than a gold atom.

Then there’s mass itself. By the 1960s the theory of the weak force worked beautifully except for one thing: it said the force carriers should be massless, like the photon, and they clearly weren’t. In 1964 several physicists, including Brout and Englert in Brussels and Peter Higgs in Edinburgh, proposed a way out. Suppose space is filled everywhere with a field, and particles get their mass by interacting with it. Interact weakly, stay light. Interact strongly, become heavy. A photon ignores it entirely. A top quark is heavier than an atom of gold.

[05:31] S11 · REAL · The Large Hadron Collider tunnel and a detector event display (CERN; confirm licence and credit). S12 · ANIM · 4 July 2012; two independent bumps at 125 GeV appearing side by side.

That idea made a testable prediction: put enough energy into a small enough space and you should make a ripple in the field, a new particle. Finding it took forty-eight years, a tunnel twenty-seven kilometres round under the French-Swiss border, and about ten thousand people. On the 4th of July 2012, the two big experiments, working independently and deliberately blind to each other’s results, both announced a new particle at about a hundred and twenty-five times the mass of a proton. The Higgs boson.

[06:10] S13 · ANIM · The Standard Model chart complete; then a list of things it cannot explain appears beside it: gravity, dark matter, dark energy, matter-antimatter, the masses themselves.

Put the particles and three of the forces together and you have the Standard Model. It’s the most precisely tested theory in science: some predictions match experiment to twelve decimal places. Every particle it predicted has been found. And it is certainly incomplete. It says nothing about gravity. It has no candidate for dark matter, nothing for dark energy, no explanation for why matter beat antimatter, and it can’t say why the particles have the masses they do. Those are typed in by hand.

[06:49] S14 · ANIM · Labels: ESTABLISHED for the particles, the forces and the Higgs; OPEN QUESTION for the masses and the generations; ACTIVE RESEARCH for what lies beyond.

The scorecard. What ordinary matter is made of, how the forces work, and that the Higgs field is real: established, to twelve decimal places in places. Why there are three generations and why the masses are what they are: open. And whether anything lies beyond the Standard Model: active research, with fifty years of looking and, so far, no crack.

[07:17] S15 · AI into ANIM · A hand; zoom in through skin, cells, molecules, atoms, nucleus, quarks; then back out; the calendar returns.

So: three particles, four forces, one field that gives things mass, and a theory that is both spectacularly right and obviously unfinished. Which leaves one question for the end of this chapter. You’ve now met every ingredient. Where did yours actually come from? Next lesson: are you really made of stardust?

Shot list

One AI shot, thirteen code-rendered shots, one CERN image. Estimated Higgsfield use: 2 to 4 generations including retries.