For thousands of years, humanity would wonder just what it was — at a fundamental, elementary level — that made up everything we saw, heard, or otherwise interacted with in the Universe. Ideas ran rampant early on, ranging from the notion of elements to a fundamental single root of everything to tiny building blocks composed of a variety of geometric shapes. It was only in the 19th century that we began breaking terrestrial matter down into the microscopic constituents that compose it, like molecules and atoms, that we began approaching the problem scientifically, and scientific progress continued into the 20th and now 21st centuries.

Most of us learn in school about the existence of atoms, the different species of atom (known as elements), and the constituents of atoms: an atomic nucleus made of protons and neutrons, where the number of protons in the nucleus determines which element the atom is, and the much lower-mass electrons that orbit around the nucleus itself. But if that’s where your knowledge stops, our current understanding of what’s fundamental now goes far beyond this picture. How can you get caught up? That’s what Logical_Error wants to know, writing in to ask:

“What’s a good beginner guide to understand the Standard Model (assuming knowledge only about protons, neutrons, and electrons)? The main things I’m curious about are the properties of these particles and if we can combine them in exotic ways? Would we know the properties of these combinations?”

While there are many guides out there, they aren’t necessarily accessible to someone who only knows about protons, neutrons, and electrons. Let’s begin with only that widespread, conventional understanding, and then work our way up to today’s modern frontiers.

The scientific endeavor to understand what matter is made of began not with what we currently think of as the way to probe the structure of matter (particle physics), but with chemistry. The goal was to see how different components of matter combined together and broke apart, and it was by adding different forms of energy to a system — both chemical and thermal energy — that you could begin to isolate atoms of different species.

When we did isolate them, we found that each “species” of atom, more commonly known as elements:

• came in different weights,
• but always had the same electric charge to its nucleus,
• could exist in different stages of ionization,
• required different amounts of energy, depending on element type, to achieve that ionization,
• more-or-less readily combined with various other elements,
• and both absorbed light at certain sets of specific frequencies and emitted light at those same specific frequencies,

all dependent on which element was being examined. The atoms could exist in isolation, could combine by bonding together to make molecules, could lose or gain electrons to make ions, could have differently charged ions bind together to make salts, could dissolve in water to make acids and bases, etc. Through the countless possibilities that atoms and their constituents brought up, the entire physical world (and much of what lies beyond it) could be explained.

However, despite the name atom, which comes from the Greek ἄτομος and means uncuttable, it turns out that these entities aren’t indivisible at all.

This illustration shows 5 of the main types of radioactive decays: alpha decay, where a nucleus emits an alpha particle (2 protons and 2 neutrons), beta decay, where a nucleus emits an electron, gamma decay, where a nucleus emits a photon, positron emission (also known as beta-plus decay), where a nucleus emits a positron, and electron capture (also known as inverse beta decay), where a nucleus absorbs an electron. These decays can change the atomic and/or mass number of the nucleus, but certain overall conservation laws, like energy, momentum, and charge conservation, must still be obeyed. Beta decay always involves a neutron, whether free or within a nucleus, decaying into a proton, electron, and electron antineutrino.

The key discovery that led to this realization was radioactivity. If raw atoms themselves could emit radiation such as alpha, beta, and gamma particles (now known to be helium-4 nuclei, electrons, and photons, respectively), then atoms themselves must be made up of smaller, subatomic constituents. J.J. Thomson’s work with cathode ray tubes discovered the negatively-charged electron, and Ernest Rutherford’s gold foil experiment showed that the majority of the mass of the atom was concentrated in a positively-charged, very small region of space: the atomic nucleus. A few decades later, firing alpha particles at a sheet of beryllium produced a stream of neutral radiation, soon identified as the neutron. Protons, neutrons, and electrons seemed to be all it took to fully describe the atoms in our Universe.

But these weren’t the only particles in existence. We flew high-altitude balloons and took particle detection chambers with us; up in the stratosphere, we didn’t just see tracks consistent with atomic nuclei and their constituents and electrons, but also other types of particles:

• positrons, which had the same mass of electrons but an opposite charge,
• and muons and antimuons, which were electron-like and positron-like, but hundreds of times more massive.

Additionally, radioactive decay experiments suggested the existence of very light, neutral particles — neutrinos and antineutrinos — and if the antimatter hypothesis was correct, then protons and neutrons should have antimatter counterparts as well: antiprotons and antineutrons.

The first muon ever detected, along with other cosmic ray particles, was determined to be the same charge as the electron, but hundreds of times heavier, due to its speed and radius of curvature. The muon was the first of the heavier generations of particles to be discovered, dating all the way back to the 1930s.

One type of decay stuck out in particular to suggest that there was a substructure to protons and neutrons: beta decays. In all (regular) beta decays, the parent nucleus:

• remains at almost exactly the same mass, decreasing only very, very slightly,
• emits a fast-moving electron, close to the speed of light,
• changes its species (or element number) by moving one element “up” on the periodic table,
• and, when you add up the total energy and momentum of the emitted electron and the resulting nucleus, you find that a tiny bit of both gets lost; they aren’t conserved.

It was as though a neutron within the original nucleus had transformed into a proton, spit out an electron, and either lost energy and momentum in the process, or spit out an additional “something else” that wasn’t being seen. Other hints (ideas like baryon number conservation, lepton number conservation, the conservation of angular momentum, etc.) pointed toward what that something else might be: a light, fast-moving, neutral, antimatter version of a lepton, an antineutrino.

The big question, of course, was how was all of this happening? What was going on inside protons and neutrons to drive these processes? While the antineutrino was finally directly detected back in 1956, more than a quarter-century after it was hypothesized, a new idea came about for probing the proton and neutron for internal structures: the idea of high-energy collider physics.

The idea of a de Broglie wave is that every matter particle can also exhibit wavelike behavior, with the properties of the wave given by quantities like momentum and energy of the system. Everything, from electrons to human beings, behave like a wave under the proper conditions. The lower in momentum (i.e., the combination of velocity and mass) a particle is, the longer its de Broglie wavelength is.

There are two key aspects to understanding a particle collider.

The first is the notion of a matter wave, also known as a de Broglie wave. In quantum physics, it’s well-known that light can behave as both a wave and a particle: propagating through space like a wave, but interacting like a particle when it encounters another quantum. One key to waves — in physics — is that when the wavelength of something is longer than the thing you’re trying to interact with, the wave passes right through. (This is why interstellar dust blocks visible light, but is transparent to longer-wavelength infrared light.) Another key is that the wavelength of any wave, whether a light wave or a matter wave, gets shorter if your wave has higher energies. Therefore, to probe smaller and smaller scales, we need higher and higher energy particles.

The second is to understand Einstein’s most famous equation: E = mc². If you take two particles and collide them together, there’s going to be a certain amount of energy, E, that’s left over after you account for both the rest-mass of all of the particles and the necessary kinetic energy that’s required to conserve the momentum between all of the incoming and outgoing particles. That leftover energy, known as the center-of-mass (or center-of-momentum) energy, is available to potentially create new particles, including new particle-antiparticle pairs, as long as all of the necessary quantum properties (charge, momentum, angular momentum, etc.) remain conserved overall.

A proton isn’t just three quarks and gluons, but a sea of dense particles and antiparticles inside. The more precisely we look at a proton and the greater the energies that we perform deep inelastic scattering experiments at, the more substructure we find inside the proton itself. There appears to be no limit to the density of particles inside; it increases without bound as the collision energy rises.

It took a certain amount of energy to crack open the atomic nucleus, and reveal the individual protons and neutrons inside. At slightly higher energies, we began to crack open individual protons and neutrons: a technique known as deep inelastic scattering. Above about 200 to 300 MeV in energy — around 20% to 30% the rest mass energy of a proton — you begin penetrating inside a proton itself. The result of these experiments leads to the production of new particles: not necessarily fundamental particles, but particles of a kind that had never been seen before, mesons.

Mesons don’t live very long, but the longest lived among them are the pions and the kaons, which can live for up to a few dozen nanoseconds. When they decay, the kaons typically decay to pions, while the pions typically decay to muons (and neutrinos/antineutrinos), while the muons in turn decay into electrons/positrons (and neutrino-antineutrino combinations). Quantities that are observed to be conserved include:

• electric charge,
• lepton number,
• baryon number,
• linear momentum,
• angular momentum (including both spin angular momentum and orbital angular momentum),
• and lepton family number (where the electron family, muon family, and tau family represent the three families).

Protons and neutrons are baryons; electrons, muons, taus, and neutrinos are leptons; the mesons are neither, and particles like the photon are neither.

The particle tracks emanating from a high energy collision at the LHC in 2012 show the creation of many new particles. By building a sophisticated detector around the collision point of relativistic particles, the properties of what occurred and was created at the collision point can be reconstructed, but what’s created is limited by the available energy from the kinetic energy of the colliding particles, with new particles capable of being created from that available energy, limited by Einstein’s E = mc². The maximum LHC energies are nearly a factor of a trillion (10^12) lower than the energies present at the start of the hot Big Bang.

With higher and higher energy experiments, as well as evermore sensitive detectors, we began to create more exotic particles: heavier and shorter-lived baryons and mesons, most of which possess more complicated decay pathways than the relatively simple pions and kaons. We created neutral pions and kaons as well as the eta, eta prime, and rho mesons. We created exotic baryons like the lambdas, the sigmas, the xis, and the omega particle. We created resonance-based particles that only lived for a yoctosecond (10^-24 seconds), as well as the electron’s and muon’s even heavier sibling: the tau.

This created what was known for a long time as a “zoo” of elementary particles. There were all sorts of models that theorists were concocting to try to simplify the enormous numbers of particles that were being created by colliders. One idea was that the pions were combinations of protons, antiprotons, neutrons, and antineutrons that lost most of their mass due to binding energy: the Sakata model. Another was that the heavier baryons, heavier mesons, and heavier leptons were just excited states of the lighter particles like protons, neutrons, and electrons, but that conflicted with the “missing energy” in lepton decays and the idea of lepton family number conservation.

Finally, two ideas emerged that wound up being equivalent: the parton model for the interior of baryons and mesons, and the quark model for the substructure of those same particles.

The strong force, operating as it does because of the existence of ‘color charge’ and the exchange of gluons, is responsible for the force that holds atomic nuclei together. This force, governed by the exchange of massive gluons, is bounded by the speed of light; from inside a black hole’s event horizon, there’s no way that a force such as this can prevent any outermore particle from reaching the central singularity.

The big idea was that there are, within the proton and neutron, fractionally charged particles — up and down quarks — that move around inside, and are bound together by a new force in addition to the common gravitational and electromagnetic force: the strong nuclear force. Unlike gravity and electromagnetism, which exhibit the most forceful attractions (or repulsions) when two “charges” are closest together, in the case of the strong nuclear force, it behaves more like a spring. When two charges are close together, the force between them drops to zero, like a spring that’s completely unstretched. As the charges move farther apart, though, the force increases, and this is what keeps the quarks, particles with a new kind of “color charge,” confined inside these baryons and mesons.

In addition to gravitation, electromagnetism, and the strong nuclear force, there’s also the weak nuclear force, which is the force responsible for radioactive decays. This is the only force that allows particles (quarks and leptons) to change species from one to another. Changes include:

• transforming a down quark into an up quark, an electron, and an antielectron neutrino,
• transforming a positively-charged muon into a positron, an electron neutrino, and a muon antineutrino,
• having a neutral kaon, which contains a strange quark, decay into two pions,
• or having a negatively charged pion decay into a negatively charged muon and a muon antineutrino.

It turns out that, observationally, we have three generations of quarks and leptons (up, down, strange, charm, bottom, and top for the quarks, and electron, muon, and tau particles, plus a related neutrino, for the leptons), as well as gluons, W-and-Z bosons, and the photon for the bosons. In addition to all of those, we also have the Higgs boson: the only “spinless” particle in the Standard Model.

This chart shows the fundamental particles of the Standard Model, as well as several examples of composite particles: baryons, antibaryons, and mesons. The fundamental particles are divided up into quarks and leptons, with each quark coming in three color varieties and the leptons consisting of the charged (electron, muon, tau) varieties as well as the neutral (neutrino) varieties. Each of the quarks and leptons also has an antiparticle counterpart. The forces are mediated by bosons, which include eight gluons, the photon, the W-and-Z bosons, and also, separately, the Higgs boson. The graviton is theorized to exist, but is not typically included as a part of the Standard Model.

The most important, and not necessarily intuitive, way that particles combine in the Standard Model deals with combinations of quarks and/or antiquarks: into baryons, antibaryons, and mesons, or particles that we collectively call hadrons. Each of the quarks has a color assigned to it: think of them as red, green, and blue. If you add all three colors together, you get white, which is colorless. (That’s what baryons are, with protons and neutrons being the most famous baryons.) Similarly, each of the antiquarks has an anticolor assigned to it: cyan, magenta, and yellow. If you add all three anticolors together, you get a colorless combination also. (This makes antibaryons, like antiprotons — which were originally called “negatrons” — and antineutrons.)

And, of course, you can add a color and its anticolor together to make a colorless combination: that’s what a meson, like a pion or kaon, is. If you had the idea to ask whether you can combine:

• two quarks and two antiquarks,
• four quarks and one antiquark,
• or six quarks,

the answer is yes: these are tetraquark, pentaquark, and hexaquark states, which are theorized to exist and for which some pretty good experimental evidence now exists. The heavier your quarks and the more particles you cram in there, the shorter-lived and more unstable your composite particles are, but you can indeed build them.

This chart shows, on a logarithmic scale (with a gap to account for the extreme mass differences of the neutrinos from the other particles) all of the particles of the Standard Model. The electron is several hundred thousand times lighter than the top quark, but the neutrinos are several million times lighter than the electron is. The photon and the gluons are the only massless particles known.

That’s your introduction to what the Standard Model is! We can measure the rest masses of these Standard Model particles — and, in fact, have measured them all quite well — and there’s an enormous hierarchy there. The photon and gluons are massless, and the three species of neutrino are all incredibly light: somewhere in the ballpark of a tenth of an electron-volt (0.1 eV, in energy equivalence) each. The next lightest particle is the electron at 511 keV, followed by the up quark, down quark, muon, strange quark, charm quark, tau, and bottom quark up at 4.7 GeV. The heaviest particles are the W-bosons (80.4 GeV), Z-boson (91.2 GeV), Higgs boson (125.1 GeV), and top quark (173 GeV).

The Standard Model very well explains the fundamental particles that exist and the force relationships between them, but it doesn’t explain everything. Among the things that the Standard Model doesn’t explain are:

• why the particles have the rest masses that they do,
• what dark matter is,
• why we have dark energy at all,
• how our Universe came to have more matter (baryons and charged leptons) than antimatter,
• and how gravity fits into the big picture with the other known forces.

The Standard Model, completed theoretically in the early 1970s and completed observationally in 2012 with the discovery of the Higgs boson, is the rock-solid foundation of modern particle physics, and the most correct and comprehensive description of reality ever concocted by humanity. Someday, we hope to go beyond it, but for now, this is the up-to-the-frontier “start line” where all of our next steps begin.

Send in your Ask Ethan questions to startswithabang at gmail dot com!

This article Ask Ethan: Can you write a beginner’s guide to the Standard Model? is featured on Big Think.

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