The “traditional” beauty of theoretical physics is its equations. If we want to describe something, or the way something behaves, we can write down a relation between some properties we think that thing will obey.
The simplicity and symmetry of these equations – to someone who understands them – is amazingly beautiful.
Given the mass of a ball, the height, angle, and strength with which it is thrown, physics will tell you the path the ball with take through the air, how long it will be in the air for, and how far away and how hard it will hit the ground.
Physics can fully describe this system with just a few simple properties.
But what if you want to describe the ball itself? We could say it’s yellow and has a smiley face on it 🙂 , but what does that really mean? To describe colour you need to consider the light being reflected from the ball.
You could say the ball is made of plastic, but you need to describe the molecules, then the atoms the molecules are made of, then the subatomic particles the atoms are made of, and so on…
What theoretical physics strives towards is a description of everything, all in one place. The ultimate goal would be a “Theory of Everything” or a “Grand Unified Theory”.
The 1970s were a heady time in particle physics. New accelerators in the United States and Europe turned up unexpected particles that theorists tried to explain, and theorists in turn predicted new particles for experiments to hunt. The result was the Standard Model of particles and interactions, a theory that is essentially a catalogue of the fundamental bits of matter and the forces governing them.
While that Standard Model is a very good description of the subatomic world, some important aspects — such as particle masses — come out of experiments rather than theory.
The hunt was on to create a Grand Unified Theory that would elegantly explain how the universe works by linking three of the four known forces together. Physicists first linked the electromagnetic force, which dictates the structure of atoms and the behaviour of light, and the weak nuclear force, which underlies how particles decay. Then scientists began working to link the weak nuclear force with the strong force, which binds quarks together into things like the protons and neutrons in our atoms. (The fourth force that we know, gravity, doesn’t have a complete working quantum theory, so it’s relegated to the realm of Theory of Everything.)
The Standard Model is a kind of periodic table of the elements for particle physics. But instead of listing the chemical elements, it lists the fundamental particles that make up the atoms that make up the chemical elements, along with any other particles that cannot be broken down into any smaller pieces.
‘Particles’ are physical things that we can count. We can’t have half a quark or one-third of an electron. And all particles of a given type are precisely identical to each other: they don’t come in various colours or have little license plates that distinguish them. Any two electrons will produce the same result in a detector, and that’s what makes them fundamental: They don’t come in a variety pack. It’s not just matter: light is also made of particles called photons. Most of the time, individual photons aren’t noticeable, but astronauts report seeing flashes of light even with their eyes closed, caused by a single gamma ray photon moving through the fluid inside the eyeball. Its interactions with particles inside creates blue-light photons known as Cherenkov light — enough to trigger the retina, which can “see” a single photon (though a lot more are needed to make an image of anything).
We may be able to count particles, but they can be created or destroyed, and even change type in some circumstances. During a type of nuclear reaction known as beta decay, a nucleus spits out an electron and a fundamental particle called an antineutrino while a neutron inside the nucleus changes into a proton. If an electron meets a positron at low velocities, they annihilate, leaving only gamma rays; at high velocities, the collision creates a whole slew of new particles.
Everyone has heard of Einstein’s famed E=mc2. Part of what that means is that making a particle requires energy proportional to its mass. Neutrinos, which are very low mass, are easy to make; electrons have a higher threshold, while heavy Higgs bosons need a huge amount of energy. Photons are easiest of all to make, because they don’t have mass or electric charge, so there’s no energy threshold to overcome.
But it takes more than energy to make new particles. You can create photons by accelerating electrons through a magnetic field, but you can’t make neutrinos or more electrons that way. The key is how those particles interact using the three fundamental quantum forces of nature: electromagnetism, the weak force and the strong force. However, those forces are also described using particles in quantum theory: electromagnetism is carried by photons, the weak force is governed by the W and Z bosons, and the strong force involves the gluons.
All of these things are described together by an idea called “quantum field theory”. But we digress.
Back to the complete Standard Model of Particle Physics which took a long time to build. Physicist J.J. Thomson discovered the electron in 1897, and scientists at the Large Hadron Collider found the final piece of the puzzle, the Higgs boson, in 2012.
You can use this interactive model (based on a design by Walter Murch for the documentary Particle Fever) to explore the different particles that make up the building blocks of our universe.
There are two kinds of elementary particles in the universe: bosons and fermions. Bosons don’t mind sitting on top of each other, sharing the same space. In principle, you could pile an infinite number of bosons into the tiniest bucket. Fermions, on the other hand, don’t share space: only a limited number of fermions would fit into the bucket. The difference between bosons and fermions is just spin. But in the context of particle physics, spin is a quantum number of angular momentum. Bosons have, by definition, integer spin. The Higgs has zero, the gluon, photon, W and Z all have one, and the graviton is postulated to have two units of spin. Quarks, electrons and neutrinos are fermions, and all have a half unit of spin. This causes a huge difference in their behaviour.
Matter is made of fermions, which stack to form three-dimensional structures. The force fields that bind fermions to each other are made of bosons. Bosons are the glue holding matter together.
The leptons are a family of subatomic particles. The best-known lepton is the electron. Other leptons include heavier versions of the electron called muon and tau particles, and a group of three almost massless particles called neutrinos. Unlike some other particles, leptons don’t combine with one another; they like their personal space.
The electron powers the world. It is the lightest particle with an electric charge and a building block of all atoms. The muon is a heavier version of the electron. It rains down on us as it is created in collisions of cosmic rays with the Earth’s atmosphere. The discovery of tau in 1976 completely surprised scientists. It was the first discovery of a particle of the so-called third generation. It is the third and heaviest of the charged leptons, heavier than both the electron and the muon. Measurements and calculations in the 1920s led to the prediction of the existence of an elusive particle without electric charge, the neutrino. But it wasn’t until 1956 that scientists observed the signal of an electron neutrino interacting with other particles. The muon neutrino was first discovered in 1962. Based on theoretical models and indirect observations, scientists expected to find a third generation of neutrino. But it took until 2000 for scientists to develop the technologies to identify the particle tracks created by tau neutrino interactions. Neutrinos are all around us. They are extremely light, electrically neutral particles that only rarely interact with other matter. They are made in a variety of processes in space and on Earth. Even though they are constantly streaming through us billions at a time, we never feel a thing. Yet neutrinos seem to play a crucial role in our universe and might even hold the key to explaining why matter exists.
There are six types of quarks in the Standard Model – given the names up, down, strange, charm, bottom and top, in order of increasing mass – but of these only the two lightest (up and down) are used to make protons and neutrons.
Up and down quarks make up protons and neutrons, which make up the nucleus of every atom. Nobody knows why, but a down quark is a just a little bit heavier than an up quark. If that weren’t the case, the protons inside every atom would decay and the universe would look very different. In 1974, two independent research groups conducting experiments at two independent labs discovered the charm quark. The surprising discovery forced physicists to reconsider how the universe works at the smallest scale. The top quark is the heaviest quark discovered so far. It has about the same weight as a gold atom. But unlike an atom, it is a fundamental, or elementary, particle; as far as we know, it is not made of smaller building blocks. Scientists discovered particles with “strange” properties many years before it became clear that those strange properties were due to the fact that they all contained a new, “strange” kind of quark. Theorist Murray Gell-Mann was awarded the Nobel Prize for introducing the concepts of strangeness and quarks. The bottom quark is a heavier cousin of the down and strange quarks. Its discovery confirmed that all elementary building blocks of ordinary matter come in three different versions.
Bosons are the force! Bosons are particles that carry the four fundamental forces. These forces push and pull what would otherwise have been an unwieldy soup of particles into the beautiful mosaic of stars and galaxies that permeate the visible universe. Put differently, bosons help other particles “communicate”, and this communication is what we call a force.
The photon is the only elementary particle visible to the human eye — but only if it has the right energy and frequency (colour). It transmits the electromagnetic force between charged particles. Because photons are massless, they can travel a long way from the particle that emitted them. The gluon is the glue that holds together quarks to form protons, neutrons and other particles. It mediates the strong nuclear force. The W boson is the only force carrier that has an electric charge. It’s essential for weak nuclear reactions: Without it, the sun would not shine. The Z boson is the electrically neutral cousin of the W boson and a heavy relative of the photon. Together, these particles explain the electroweak force.
Discovered in 2012, the Higgs boson was the last missing piece of the Standard Model puzzle. It is a different kind of force carrier from the other elementary forces, and it gives mass to quarks as well as the W and Z bosons. The Higgs boson is an excitation of the Higgs field, which interacts with some of the fundamental particles to give them mass. Whether it also gives mass to neutrinos remains to be discovered.
So now we have all we need to construct matter: some fermions and some bosons. We just need to write an equation that describes everything written above in a simple, symmetrical way.
And here it is. This version of the Standard Model is written in the Lagrangian form. The Lagrangian is a fancy way of writing an equation to determine the state of a changing system and explain the maximum possible energy the system can maintain. Technically, the Standard Model can be written in several different formulations, but, despite appearances, the Lagrangian is one of the easiest and most compact ways of presenting the theory.
Makes sense, right? Thomas Gutierrez, an assistant professor of Physics at California Polytechnic State University, transcribed the Standard Model Lagrangian for the web. He derived it from Diagrammatica, a theoretical physics reference written by Nobel Laureate Martinus Veltman. In Gutierrez’s dissemination of the transcript, he noted a sign error he made somewhere in the equation. Good luck finding it!
A crash course in particle physics with Dr Brian Cox.