Core Concepts
In this article, you will learn what fundamental particles are, how they were discovered, and where the next frontiers of this field of science are.
The Fundamentals of the Fundamentals
What makes a particle fundamental or elementary? Fundamental means not able to be broken down any further into smaller constituent pieces. In the case of chemistry and particle physics, fundamental particles are the smallest pieces of matter that can be broken down, and each “copy” of a given particle is exactly identical.
Let’s briefly think of how the human body is organized. You are an organism. Your body can be broken down into a bunch of different organ systems. Within each organ system, each organ is composed of tissues, and each of those tissues is composed of cells. Those cells, in turn, consist of organelles, which we can simplify even further into various biomolecules like proteins, lipids, and DNA. We can even reduce these molecules into smaller pieces (the individual atoms that make them up).
Believe it or not, we can even break down atoms into smaller pieces: the electrons and nucleus. While electrons cannot be broken down further (our first fundamental particle!), we can simplify the nucleus into nucleons (protons and neutrons). Finally, we can reduce nucleons further, forming quarks. We’ll discuss these specific particles later in the article. For now, let’s discuss how we learned that these tiny, invisible entities exist in the first place.
The process of breaking things down into their smallest pieces and understanding their organizational structure is very difficult. It requires infrastructure the size of a large city, such as the Large Hadron Collider (LHC) in Geneva, Switzerland. As such, for the majority of human history, we did not have the means to break things down to their smallest levels, nor did we know how small the smallest pieces of reality are.
A particle accelerator like the LHC helps us achieve these efforts. Its large scope, which spans 27 km across, is underground to help shield experiments from the effects of cosmic radiation. The LHC is essentially a long tube in which scientists accelerate particles to 99.9999991% of the speed of light (or 266,593,900 meters per second). Here, they crash into one another, and sensors detect the resulting materials. This enables researchers to study how particles behave and interact with each other.
So, how did we discover the smallest of particles? What are the fundamental particles? Why are these discoveries important, and what do they mean for the future?
The History of Particle Physics: Discovering the Rules of Matter
Particle physics is an ongoing field of study that draws from millennia of scientific inquiry. In this section, we’ll cover some of the most groundbreaking milestones in developing our understanding of particles.
Atomic Theory (320 BCE – 1803 CE)
The idea that smaller pieces form the structure of matter goes back to ancient Greek philosophy, where Democritus and Leucippus proposed atomos, indivisible units that make up everything. At the same time, Aristotle suggested that matter consisted of earth, air, fire, and water. This view dominated for centuries, despite lacking experimental support.
In the late 1700s, Antoine Lavoisier demonstrated the law of conservation of mass, showing that matter obeys measurable rules. Later, in 1803, John Dalton proposed that each element is made of identical atoms that combine with each other in simple, whole-number ratios. This became the first scientific atomic theory and, for nearly a century, defined atoms as being fundamental.
Nuclear Theory (1897 CE – 1932 CE)
It was in 1897 that J. J. Thomson discovered the electron using a cathode ray tube. This revealed a huge finding: that the atom contains smaller, negatively charged particles. In light of this discovery, Thomson posited the plum pudding model, wherein the atom is a sphere of positive charge, with those smaller negative particles sprinkled throughout it.
Not long after, in 1911, Ernest Rutherford’s gold foil experiment proved Thomson’s model wrong. Instead, it showed that almost all of the atomic mass and positive charge are concentrated into a small point, while negatively charged electrons occupy the surrounding space. This starkly contrasted the plum pudding model’s suggestion that the electrons are scattered throughout the atom’s positive portion.
Finally, in 1932, James Chadwick discovered the difference between the proton, a positively charged particle in the nucleus, and the neutron, a neutrally charged particle in the nucleus. This also explained isotopes and how atoms of the same element can have different masses. With these findings, people gained a fairly strong understanding of atomic structure, with these three particles (the electron, the proton, and the neutron) considered fundamental. But, yet again, this was not the end of the search for answers.
Quantum Theory (1964 CE – Present)
Equipped with the basics of nuclear theory, scientists began observing cosmic rays interacting with the atmosphere. This led them to start building the first particle accelerators. Particle accelerators offered high-tech tools for researchers to discover a myriad of new particles: muons, pions, kaons, hyperons, and so many more. This vast quantity of particles, the particle zoo, prompted the idea that maybe all of these particles are not fundamental.
In 1964, Murray Gell-Mann and George Zweig individually proposed forms of the quark model. The quark model implied that many of the particles in the particle zoo could consist of different combinations of up, down, and strange quarks. Over the years, experiments confirmed quarks’ existence and revealed the particles that carry the fundamental forces of the universe. With all of this new information, a new model emerged into view: the Standard Model of elementary particles.
Quantum Theory and the Standard Model of Elementary Particles
The Standard Model of elementary particles is the set of building blocks of which all other particles are composed. These building blocks are the smallest particles that can no longer break down into tinier constituent pieces.
We can organize the Standard Model into two major types of particles: fermions and bosons. Fermions are the three generations of matter particles, ordered mainly by decreasing stability with each subsequent generation. It’s possible to further subdivide fermions into leptons and quarks, which we’ll discuss in more detail soon. Bosons carry the fundamental forces of the universe: gravity, electromagnetism, strong nuclear force, and weak nuclear force. In essence, bosons represent the methods by which particles interact with each other. For instance, our familiar proton and neutron both consist of quarks surrounded by electrons, with bosons as their medium of interaction.
As we move through our discussion of the different particles and some simple quantum reactions, another important thing to note is that we measure mass in a unit called electron volts per c2 (eV/c2) where c is the speed of light. This derives from the relationship between matter, energy, and momentum. Einstein’s mass-energy equivalence equation, E = mc2, describes this relationship. In the equation, energy is proportional to the amount of mass times the square of the speed of light. Rearranging the equation reveals that m = E/c2, which is how scientists represent particles’ mass.
For the countless quantum reactions that don’t seem to follow the law of conservation of mass, this relationship allows conversions of momentum and energy that transfer from parent particle to daughter particles. For simplicity, this article will not discuss the calculations and will instead focus on some key members of the particle zoo and Standard Model.
Fermions
One of the defining characteristics of fermions is their half-integer spin (1/2, 3/2, 5/2, and so forth). This means that they follow the Pauli exclusion principle. The Pauli exclusion principle states that two particles may not occupy the same quantum state. Because of this, fermions must organize themselves into discrete energy levels and multiple spin states, like the different electron orbitals and nuclear energy shells in the nucleus.
We can break down the fundamental fermions into two smaller groups, leptons and quarks, which can also exist as antiparticle versions of themselves. Antiparticles have the same mass as their particle counterparts, but are otherwise opposite in every other property. When an antiparticle interacts with its particle counterpart, they explode and cease to be. This event, annihilation, involves converting all of their mass into energy. For example, an electron and positron would undergo annihilation with one another.
Since chemistry is mainly about the study of the interactions of the most famous lepton, the electron, we’ll start there.
Leptons
The leptons are a tight-knit family that includes our familiar electron, as well as the muon, tau, electron neutrino, muon neutrino, and tau neutrino. Each of the leptons has one of those six flavors, or quantum identities. We can further subdivide the leptons into the electrically charged leptons and the uncharged neutrinos.
Charged Leptons
The charged leptons are the electron, muon, and tau. Each has a charge of -1, or +1 for their antiparticle versions. Since they have a half-integer spin of 1/2, they follow the Pauli exclusion principle.
Electron
The electron is the main subject of chemical reactions and the most stable of the charged leptons. Electrons have a charge of -1 and a rest mass of 0.511 MeV/c2. Rest mass or invariant mass is a particle’s mass or momentum when in its lowest quantum energy state.
Electrons organize themselves into discrete energy levels, allowing for complex chemical reactions that transfer charge without changing an atom’s nuclear identity. Its antiparticle counterpart is called the positron. Electrons are symbolized by a e– while the positron is symbolized by e+.
Muon
The muon is the electron’s larger, more unstable cousin. It has a charge of -1 and a rest mass of 105.66 MeV/c2. Muons only exist for a fraction of a second, and organize themselves into discrete energy levels similarly to the electron, though with much smaller orbitals.
Due to the muon’s short-lived nature, it does not perform well chemically in the same way that electrons do. However, cosmic ray collisions in the upper atmosphere constantly create them, with a miniscule fraction of them even making it all the way through to Earth’s crust. Muons are symbolized by the lowercase Greek letter μ– (mu), or μ+ for an antimuon.
Tau
The tau is the even larger cousin of the electron and muon. As such, it’s even more unstable, decaying in femtoseconds (1 femtosecond = 1×10-15 seconds). Due to this, taus are unable to form orbitals like electrons and muons do.
Taus have a charge of -1 and a rest mass of 1.777 GeV/c2. We symbolize them with the lowercase Greek letter τ– (tau), or τ+ for an antitau.
Neutrinos
In the lepton family tree, neutrinos are the much smaller, uncharged cousins of the charged leptons. For a long time, no one even knew they existed, due to how tiny they are. For reference, the electron, at 0.511 MeV/c2, is about a million times larger than the electron neutrino, at 0.8 eV/c2. Also, since they have no charge, neutrinos are not electromagnetically attracted to the positively charged atomic nucleus, and thus do not form orbitals. Because of this, neutrinos barely interact with normal atomic matter, so they’re very hard to detect and study.
Similarly to the charged leptons, the neutrinos get larger with subsequent generation, with the muon neutrino and tau neutrino being 0.17 MeV/c2 and 18.2 MeV/c2, respectively. All neutrinos are represented by the Greek letter ν (nu), with a subscript featuring their respective flavor. We also represent antineutrinos with ν, but with a bar above it. Since neutrinos already have no electric charge, antineutrinos also have no electric charge. In this sense, their only difference is that they have the opposite flavor.
Example: Muon Decay
To see some neutrinos in action, let’s use the muon as an example of decay. The muon decays into an electron, muon neutrino, and anti-electron neutrino. One particle enters, while two particles and one antiparticle exit, so the net number of particles is the same. Muon flavor is not destroyed, but transferred to the muon neutrino. The muon’s electric charge transfers to the electron. As the electron appears, its anti-flavor particle, the anti-electron neutrino, is also born. Finally, the muon’s mass converts into the mass and momentum of its daughter particles. Ultimately, there is no net change in the properties of the universe; as such, all is conserved.
Since neutrinos are so difficult to detect and study, there is still a lot we need to learn. Some theories suggest that there may be a flavor-changing phenomenon associated with neutrinos. This is because the reactions producing them, primarily inside stellar bodies like our Sun, should only produce electron neutrinos, yet scientists have detected all three types. This has led to theories about neutrino oscillation, where neutrinos change their flavor as they move through space. However, the mechanism is not well understood.
Now that we’ve met all of the leptons, let’s move on to our other fermions: the quarks.
Quarks
Quarks are some of the main constituents of the nucleons, helping to form the nucleons’ identities. All quarks have an electric charge, rest mass, a spin of 1/2, and one of six quark flavors: up, down, charm, strange, top, and bottom quarks. Just as we can classify fermions, we can similarly organize quarks in a few different ways. One possible way is by charge, but it’s generally more relevant to organize quarks by generation.
First-Generation Quarks
The first-generation quarks are the up quark and the down quark. Their names arose because they were originally thought of as spinning up and spinning down, respectively. They are the smallest, most stable quarks that make up the entirety of known atomic matter.
Up Quarks
Up quarks have spin-1/2, a charge of +2/3, and a rest mass of 2.16 MeV/c2. They are the smallest of the quarks and are sometimes thought of as the basic, most stable ground state of matter.
Down Quarks
Down quarks have spin-1/2, a charge of -1/3, and a rest mass of 4.7 MeV/c2. They are the second-smallest type of quark. In some fascinating nuclear reactions, a down quark can decay into an up quark.
First-Generation Quark Combinations
Together, the first-generation quarks make up all protons and neutrons. Other combinations of first-generation quarks exist, but they decay very quickly into protons and/or neutrons. Any particle made of more than one quark is called a hadron: this includes mesons (particles comprised of two quarks) and baryons (particles made of three quarks).
Protons are baryons consisting of two up quarks and one down quark. Together, the sum of these charges is as follows: (+2/3) + (+2/3) + (-1/3) = (+3/3) = (+1). Since the overall sum of the charges is a positive value, it makes sense that protons have positive charge. However, a proton’s mass, 938.272 MeV/c2, is much greater than the sum of the quarks’ masses, indicating that there is something else contributing to the proton’s mass.
Neutrons, which are also baryons, are fairly similar to protons. They consist of one up quark and two down quarks. The sum of these charges is actually zero: (+2/3) + (-1/3) + (-1/3) = 0. This explains why we consider neutrons to have no charge, or to have neutral charge. The mass of a neutron is 939.565 MeV/c2, which is, again, much greater than the sum of its quarks’ masses.
In addition to the mass discrepancies, you may have noticed another curious detail in this dynamic. There are two up quarks in a proton, and two down quarks in a neutron, which we expect to repel one another via electromagnetic force. Why don’t they? What are we missing from the picture?
Basic RGB Color Theory for Elementary Particles
To understand the mass and charge discrepancies we’ve noted, we have to take a brief detour into the more artistic side of science. Quantum chromodynamics (QCD) is a theory that addresses the concept of strong nuclear force and how quarks join together to craft nucleons.
The word “chromodynamics” comes from Greek root, “chromo-“, meaning color, and “dynamics,” referring to forces and motion. The notion of color as a facet of force or motion arose because quarks have a property called color charge. This naming convention came about not because the quarks have an actual observable color, but because it’s a good analogy to red green blue (RGB) color theory.
Under RGB color theory, in the context of particle physics, a quark can be red, green, or blue. Likewise, an antiquark can be antired (or cyan, C), antiblue (or yellow, Y), or antigreen (or magenta, M).
According to RGB color theory, red, green, and blue are the primary colors. (Fun fact: tiny red, green, and blue lights are also how digital screens, like the one you’re reading this article on now, present color output!) Every other color is some mixture of the three primary colors. Note that, in the diagram above, each primary color has an “anticolor” which is located directly across from the primary color. When we mix all three primary colors, or a primary color and its anticolor, in equal amounts, white is the end result.
Quantum Color
This idea translates well for quantum color, too. Unlike charge, which is a dichotomy with two possible axes, color charge is a trichotomy. Recall that negative electric charges and positive electric charges attract each other in an attempt to reach electric neutrality. Analogously, the three colors in color charge attract one another in an attempt to reach color neutrality. This is basically how the quarks are attracted to each other in the proton and neutron, despite being similarly electrically charged.
Below is an image of deuterium, the second-most common isotope of hydrogen. It contains one proton and one neutron, with gluons between the quarks of each individual nucleon. We’ll discuss gluons in more depth soon, but for now, you should understand that a gluon is the mediator of the strong nuclear force. This deuterium image represents the electron by both the particle and the cloud around the nucleus, indicating the 1s electron orbital. Importantly, note that each quark in a nucleon is a different color, with the goal of attaining color neutrality.
Second-Generation Quarks
Advancing with our exploration of quark types, the second generation encompasses the strange quark and the charm quark. Like the second-generation leptons, the second-generation quarks are larger and less stable than their first-generation versions. Second-generation quarks decay into the first-generation quarks and either a W boson or Z boson, which we’ll talk more about later. First, let’s learn more about the second generation of the quark family tree.
Strange Quark
The strange quark got its name because larger particles containing it were “strangely” more stable than scientists had predicted. Before they discovered and confirmed the strange quark’s existence, scientists described “strangeness” as a quality of some particles.
The strange quark has spin-1/2, a charge of -1/3, and a rest mass of 93.5 MeV/c2. Although it is relatively stable, particles containing strange quarks are still unstable. Due to their instability, they decay in about 10-8 to 10-10 seconds, which is fairly long-lived for unstable particles. Because of this quirk, strange quarks are arguably among the most interesting of quarks due to their relatively prolonged stability. Some theories posit that certain combinations of strange quarks might be the most stable form of matter there is.
Charm Quark
As you may have noticed already, particle physics relies on many aspects of math and symmetry. The charm quark‘s discovery was “charming” because it made all of this math and symmetry work out very neatly. A charm quark has spin-1/2, a charge of +2/3, and a rest mass of 1.273 GeV/c2. Just like strange quarks, charm quarks are also unstable. However, they decay much faster, in only about 10-12-10-13 seconds.
Third-Generation Quarks
The rest of the quarks, bottom quarks and top quarks, are even more unstable than the members of the first two generations. As a consequence of their instability, they typically decay into the second-generation quarks and a W or Z boson. Alternatively, on rare occasions, they decay directly into first-generation quarks and a W or Z boson.
Originally, the top quark and bottom quark used the names “truth” and “beauty,” which somewhat reflect the other whimsical quark names. Later, scientists scrapped these names because “truth” sounded a bit philosophical and confusing. But since the initials had already stuck, they used “top” and “bottom” to align with “up” and “down.”
Bottom Quark
The bottom quark has spin-1/2, a charge of -1/3, and a rest mass of 4.183 GeV/c2. Scientists discovered it after the charm quark and, again, identified some interesting qualities. For example, particles containing the bottom quark were more stable than originally thought, decaying in about 10-12 seconds. This allowed scientists to study some of the symmetry violations of the universe and pinpoint the slight differences between a particle and its antiparticle. As such, the discovery of the bottom quark aids in our understanding of why matter, rather than antimatter, has dominated the universe.
Top Quark
The top quark has spin-1/2, a charge of +2/3, and a rest mass of 172.57 GeV/c2. It also makes highly unstable particles, decaying almost instantly, in only 10-25 seconds. Because of this, we can grant the top quark bragging rights for being the largest and most unstable of all quark types.
Bosons
Remember that bosons are force carriers that govern how particles interact. We define bosons by their integer spins (0, 1, 2, 3…), as opposed to the fermions’ half-integer spins, and their ability to disobey the Pauli exclusion principle. Since bosons don’t have to adhere to this principle, they can occupy the same quantum states and spin states.
Elementary bosons are the force carriers of the fundamental forces of the universe. The fundamental forces in order of weakest to strongest are: gravity, electromagnetism, weak nuclear force (weak force), and strong nuclear force (strong force). These forces are subject to the influence of specific boson types. Photons mediate the electromagnetic force, W and Z bosons mediate weak nuclear force, and gluons mediate strong nuclear force. The Higgs field is responsible for the phenomenon of rest mass, which is not the same thing as gravity. Scientists have not definitively observed a quantum particle associated with gravity, though they’ve hypothesized that the graviton exists as a spin-2 particle.
Elementary Bosons
Higgs Boson
The Higgs field is what gives fundamental particles their mass. When there is a “ripple” or disturbance in the field, we attribute that to the Higgs boson particle. A Higgs boson has a spin of zero, indicating that, regardless of how you rotate the particle, its mass’s quantum state does not change. An up quark’s rest mass (invariant mass) will always be 2.16 MeV/c2.
Photon
The photon is a quantum excitation of the electromagnetic field, which is responsible for all interactions (both attraction and repulsion) between electrically charged particles. Photons themselves carry no electric charge, meaning they do not directly interact with each other under normal conditions. The photon has a spin of 1; in other words, its quantum state returns to itself after a full 360° rotation. This is a signature of spin-1 vector particles that arise from directional fields like electromagnetism.
W Boson and Z Boson
The W and Z bosons are the spin-1 mediators of the weak nuclear force, which govern nuclear decay processes. The weak nuclear force is the only way we know of by which particles can change their flavor. Therefore, the W and Z bosons help with balancing charge, flavor, and momentum.
The W boson got its name from the fact that it is the mediator of the weak nuclear force. It can either be negative or positive, has neutral flavor, and has a rest mass of about 80.369 GeV/c2. An unstable atom can emit a W boson via beta decay, where it only exists for about 3×10-25 seconds before decaying itself. The W boson decays into a similarly charged lepton antineutrino pair or antilepton neutrino pair.
By contrast, the Z boson got its name because it carries zero electric charge. It is electrically uncharged, unflavored, and has a rest mass of 90.188 GeV/c2. Similarly to the W boson, the Z boson also decays very quickly, but instead into a particle-antiparticle pair. Reactions that produce Z bosons are more rare.
Gluon
The gluon is the spin-1 mediator of the strong nuclear force and is the largest component of QCD. It has no electric charge, no flavor, and no rest mass. Instead, it has the property associated only with quarks: color charge.
However, unlike with electromagnetism (where the photons carry no electric charge), the gluons themselves have a dual color charge. Red quarks will emit red-cyan gluons, blue quarks will emit blue-yellow gluons, and green quarks will emit green-magenta gluons. A green quark can absorb a blue-magenta gluon and become a blue quark. A blue-yellow gluon can decay into a blue-cyan gluon and a red-yellow gluon.
In this way, gluons do interact with one another. These interactions exhibit a constant exchange of color, similar to chemical equilibrium. This constant exchange and tangling of color is what makes the strong nuclear force so strong. It is also what gives nucleons all of their extra mass!
The final important thing to note about gluons and the strong nuclear force is how their strength changes with distance. Unlike the infinite ranges and weak power of electromagnetism and gravity, the strong nuclear force’s range is very small yet very powerful. This means that, the farther apart two quarks are, the more attractive force exists between them. The closer they are to each other, the weaker the force gets. This allows the quarks to move freely, but only in the small region of space that a nucleon takes up, a phenomenon we call confinement.
Internuclear Attraction
The graph below shows the force that exists between nucleons. The y-axis represents the force, in units of 104 Newtons, with the negative y-axis representing attractive forces and the positive y-axis representing repulsive forces. The x-axis represents the distance between two nucleons. You’ll notice the repulsive force starting on the left, as two nucleons can’t occupy the same space being fermions. Then, moving rightward, the graph quickly drops to below zero, indicating the change in repulsion to attraction. The peak of attraction occurs at just beyond one femtometer, where about 2.5 × 104 Newtons of force pull the two nucleons together; this force is about the same as the force of gravity acting on a pickup truck. After the peak, the attractive force tapers off, approaching zero, exemplifying how nucleons are attracted to one another.
This helps account for why the heavier an element is, the more unstable it becomes. Heavier elements have more nucleons, and as the number of nucleons increases, the distance between them increases. As protons stack in the nucleus, the repulsive positive charges will eventually overcome the attractive forces between nucleons. This is why certain elements, like uranium, which has 92 protons, are unstable and go through decay.
Quark-Gluon Interactions
This also means that, the farther apart two quarks move, more and more energy will be required to separate them. Even if we apply enough energy to fully separate a quark from its hadron, the attractive force of the other quarks will pull a new quark-antiquark pair out of the gluon field energy. As a result, quarks cannot be outside of a hadron unless there is a substantial amount of energy in the system, like in the very beginning of the universe or in theoretical quark stars.
The animation below shows how the quarks inside nucleons interact with one another via gluons and the strong nuclear force, shifting the color charge around. It also shows how gluons can decay into quark-antiquark pairs that fill any color absences in the hadron. In this interaction, a neutral pion (denoted π0), made of a blue down quark and a yellow antidown quark, acts as a mediator between the down quarks of a proton and a neutron. Since the spins of fermions add up to a full integer, the neutral pion is actually acting as a boson of the strong force, though not fundamental. This is only one of many different kinds of mesons that can be created.
Conclusion
These topics are just the tip of the particle physics iceberg, with many more discoveries waiting to be made. Quantum interactions and the fundamental forces of the universe dictate how different pieces of the universe move and exist with one another. Together, these properties give rise to the particle zoo and the Standard Model, where quarks, leptons, and bosons all play distinct roles. A particle’s electric charge, color charge, quantum flavor, quantum spin, and mass determine not just what it is, but how it interacts, transforms, and persists in the universe. The Standard Model organizes the particle zoo, but cannot fully explain dark matter, neutrino behavior, nor the universe’s matter-antimatter imbalance. Questions about mass hierarchies, force unification, and quantum gravity hint that deeper structural layers may lie beyond our current understanding. Who knows what new discoveries about the properties of our universe are lying just around the corner?
