In the last article we saw that light has a lot in
common with matter. Despite this, we don't
usually refer to light as "matter". In fact, as
Faraday realized, light is related to the *electromagnetic
force*. The electric field (which
makes like charges repel and opposite charges
attract) and the magnetic field (which makes
like magnetic poles repel and opposite magnetic
poles attract) are in fact parts of a single
field, the *electromagnetic field*, and light consists
of waves in this field.

Iron filings scattered around a bar magnet arrange themselves along field lines.

This unified description of light and electromagnetism is extremely successful, and you directly rely on it every time you use a mobile phone or any other wireless gadget. In this description, the electromagnetic field affects, and is affected by, charged particles like the electron. Matter, consisting of particles, interacts with forces, represented by fields.

But how do we square this with the view
of light as consisting of photon particles? As
we shall see in a moment, *quantum field theory*
provides the answer, and will somewhat blur
the line between forces and matter.

Apart from electromagnetism, it has turned
out that there are only three other forces in
nature: the *strong force*, the *weak force* (both
terrible names) and gravity. The strong force
holds protons and neutrons together in the
nucleus, and also the quarks inside those protons
and neutrons. The weak force is involved
in radioactivity and is the main way stars
produce energy. I will keep using electromagnetism
as my running example, but the
story is similar for the strong and weak forces
(gravity is the odd one out).

### Quantum fields

If you have read anything at all about modern
physics, you will have heard countless testimonies
about the incredible strangeness of
quantum mechanics, the physics of the very
small. This article will be no exception. In
fact, taking the principles of quantum mechanics
(originally formulated for tiny pointlike
particles) and applying them to fields
(like the electromagnetic field) makes ordinary
quantum mechanics seem like a breeze,
and kept even the most brilliant physicists
banging their heads against various walls for
decades. Luckily for us, their struggles have
left us with a marvellous theory, *quantum field
theory* (QFT), which is currently the language
of all our physical laws (except gravity). (Professor David Tong has given an excellent public
talk about QFT at the Royal Institution; this was part
of the inspiration for this article. You can also read more in *A brief history of quantum field theory*.)

QFT makes sense of our confusion about whether light consists of waves or particles. In very simplified language, the essence is this: quantum mechanics says that waves in a field can't be arbitrarily weak. Instead, you create a large wave by adding together a large number of tiny, indivisible waves. A particle is, more or less, the weakest such allowed wave, as shown in image below.

A particle is the weakest possible wave in a field—the central idea of quantum field theory. (Image: Elias Riedel Gårding)

QFT also explains, in a unified way, many of the science fiction-sounding concepts that are a big part of the allure of physics. For example that some particles have an antimatter partner (just a different type of wave in the same field) and that particles can be created and destroyed, turning into other types of particles (a wave in one field can be transferred into waves in some other field).

### The fields of our universe

Let us consider the table of known fundamental particles in the light of quantum field theory.
Instead of seventeen fundamental *particles*,
we now have seventeen fundamental *fields*,
for example the electromagnetic field (also
called the photon field), the electron field, the
up-quark field, the muon neutrino field, the
Higgs field, and so on.

The known fundamental particles (Image MissMJ)

Viewing the particles in terms
of fields makes it a lot easier to quantitatively
describe how the particles behave, by means
of an equation (called a *Lagrangian*, $\mathcal{L}$). For example, to describe the
physics of photons, we must first write down
the equation governing the electromagnetic
field. This equation has long been known to
physicists, and it reads

Don't worry about what the symbols in this equation mean; I am just including it to illustrate that this very short equation captures everything we know about electromagnetism and light.

We play a similar game when we want to describe other particles. For example, the equation for the electron field is called the Dirac equation and reads

The equations for capturing the behaviour of a particle field are remarkably simple. But you can also bring these together to describe how two types of particles, such as electrons and photons, interact:

In fact, you can capture *all the known interactions between
all the known fields* in just one, admittedly more complicated, equation:

The equation for the *standard model*. It encodes all known particle interactions.

Defining all the symbols in this equation is a bit messy and might take a few pages, and learning exactly how to interpret them would take you the better part of a year at university or, depending on the level of detail you are aiming for, a research career in physics.

(Suffice it to say that some of the symbols represent the actual fields: $\phi$ is the Higgs field, the $L^i$ and $R^i$ represent the lepton fields, $Q_L^i$, $u_R^j$, $d_R^j$ and $q^f$ all represent the quark fields in various ways, $W^{\mu\nu}_a$ and $B^{\mu\nu}$ represent the electromagnetic (photon) field as well as the $W$ and $Z$ boson fields while $G^{\mu\nu}_a$ represents the gluon field, and that the appearance of the letters $L$ and $R$ refers to left-handed and right-handed particles (in a certain sense spinning clockwise and counterclockwise, respectively) which, in a strange twist, Nature treats very differently from each other.)

But, together with the list of
particles in table above, this equation is known
as the *standard model* of particle physics. If
you find it daunting, you are not alone. But
considering that this single equation captures all the
known laws of nature, except – again – gravity,
it really isn't all that bad!

*Find out how physicists use pictures to do their calculations in the next article*.

### About the author

Elias Riedel Gårding grew up in Stockholm and chose physics instead of programming for his undergraduate degree because his secondary school physics class was frankly not very good, and he wanted to see what he was missing. He has always been interested in the most basic laws of nature – those of fundamental physics – but it wasn't until his master's degree in theoretical physics that he got to study them properly. He thinks quantum field theory, the basic paradigm of particle physics, deserves to be more widely known, hence this article series.