Chapter I: The Physics of Dirt I The Physics of Dirt
The wizard, Veryan, whispered into her crystal the familiar incantation as she clambered through the cold, dark cavern. With a puff of breath, as if to release the seeds of a dandelion, she awakened in the stone a dazzling red light that illuminated the moss-covered rocks around her.

After walking for some time, she found herself at an entrance. Her passage was barred by a vast wooden door held together with wide iron joists. Working in the harsh light of the crystal, she felt her way to the door’s handle, a thick, black iron ring. She pulled, but the ring held: the door was locked. Finding the edge of the wood, she pressed her fingers into the small gap between the door and its surrounding and found the door’s bolt, made of the same rough iron as the handle.

She spoke again to the crystal in her practiced, quiet tone and it gradually dimmed. After a few seconds, she found herself once again in perfect darkness. Positioning herself in front of the bolt, she rested the crystal flat on her palm, offering it to the door like grass to a horse and uttering a few syllables of the old tongue, more sharply this time. The light returned as an intense red heat, a focused, narrow beam. Piercing the gap, the stream of light cleaved through the bolt, leaving in its wake the red-orange glow of molten iron, the noxious smell of the blacksmith’s forge cutting through the air. The light vanished as quickly as it had appeared. She pulled again at the ring; with effort, the door eased open. As it did, light and life began to seep in through the widening crack from the dry stone staircase on the other side. Her task was about to begin.

This is a book about wizardry. It will reveal the secret ways of the wizard’s art, and how you, too, can learn to follow them. It is also a history of magic, telling how, by a process of observing the world, wizards deduced the spells they cast—and how modern wizards continue to develop new magic to transform the world before our very eyes.

The modern name for magic is “physics,” and the name for a wizard’s magic is “condensed matter physics.” Before we discuss what these names convey, you must understand that this book comes with a warning. Once you have learned how a spell is cast, the effect of the spell will cease to appear to you as magic. It will become mundane. Everyday. Boring. This is the cost of magical knowledge. It will take a great deal of practice, and patience, for you to regain the sense of wonder you had when the magic was first performed for you.

Throughout most of history—even within living memory—the story you just read would surely have been the stuff of fantasy. If you could produce from your pocket a crystal able to light a cavern at your request, then magic must be at work, and you must surely be a wizard. Yet these days such an action is mundane: an LED, a light-emitting diode, is a crystal, and by passing electricity through it you can cause it to light at the flick of a switch. A laser diode, also a crystal, creates an intense light that, when focused, can cut through solid metal. Now you probably feel cheated. There’s no magic in using an LED flashlight. Using an LED flashlight is boring! Magic requires a certain incomprehensibility and unfamiliarity. LED flashlights are boring because they’re familiar, and because, at one level or other, you understand how they work. But if you showed the flashlight to someone in the Middle Ages, they would certainly think it was magical because its technology would be unfamiliar. With enough time you could explain it to them. As you did, and as they gained familiarity, it would cease to appear magical. But would it really have lost its magic? Or is that just an illusion?

It takes work to see the magic in the familiar, but it’s there. Physics is a program to rationalize and understand the world. Many things that would once have been considered magic are now routine. Yet our understanding tends to advance in increments, building on existing knowledge. You may find a joke funny forever, but you can only “get” it once. But understanding the joke allows you to perform it for others. With skill in the telling, and a little luck, a joke will have on others the effect it once had on you. So it is with magic. The secret to learning the world’s magic—to learning physics—is to laugh continuously at the cosmic joke. It’s the difference between seeing a conjurer perform a trick and having the trick explained. Hopefully, when you first meet some of the ideas in this book, they may invoke in you that sense of magic. And hopefully, when you’ve read the book, you will understand where those ideas came from, and they will seem more natural. You may have to work to maintain the sense of magic they once held, but by learning a spell you can cast it to the benefit of others.
The Rules of Wizardry
Now that you’re heeding the warning, let’s talk about wizards. When I refer to wizards, I’m thinking, like, classic wizards. People who do magic.I I’d say the defining characteristics of a wizard are something like this. We can call them the Rules of Wizardry:

1. A wizard studies the world.
2. A wizard understands that they are a part of the world they are studying.
3. A wizard’s understanding leads them to see hidden patterns and connections that others do not.
4. A wizard’s knowledge is of a practical, hands-on kind.
5. A wizard can cause changes to the world, but they make such changes sympathetically (see Rule 2).

Sometimes a wizard’s study is academic, like Harry’s and Hermione’s at Hogwarts. Sometimes the study is a quiet contemplation, as with Rey or Yoda in Star Wars, sages in classic Daoist texts such as the Zhuangzi, or martial artists such as Katara and Aang in the epic TV series Avatar: The Legend of Aang. Often the study takes the form of exploring and experiencing the world, as with Gandalf in The Lord of the Rings, Morgana and Merlin in Arthurian legend, and Tenar and Ged in Ursula K. Le Guin’s classic Earthsea novels. In many modern examples, the wizard is a supernaturally gifted scientist. Doc Brown’s achievements in Back to the Future, Rick’s in Rick and Morty, or those of Doctor Who are presented as scientific, but the technology is so far beyond the experiences of the other characters and the audience that it is more like magic. It is apparent that the Rules of Wizardry implicitly assume an important hidden rule, the Rule of Rebellion:

A wizard understands that rules are made to be broken.

Look again at the five and a half rules of wizardry, and replace the word “wizard” with “scientist.” That seems about right, doesn’t it? J. G. Frazer, in his chronicle of magical practices, The Golden Bough, put it poetically:

Magic like science postulates the order and uniformity of nature; hence the attraction both of magic and of science, which open up a boundless vista to those who can penetrate to the secret springs of nature.

Frazer’s quote makes a link between magic and science. But wizardry is a particular type of magic; a particular type of science. And its name is condensed matter physics.
The Magic of True Names
Zoology is the study of animals. Botany is the study of plants. What is physics the study of? Its name derives from the ancient Greek, ta physika, meaning “natural things,” taken from the title of Aristotle’s collected works on the physical world. That doesn’t narrow things down much. Perhaps the best answer is that physics is defined not so much by the set of phenomena studied, but rather by a distinctive approach and set of tools. Broadly, these tools divide into three groups. A physicist will tend to specialize in just one of them, although it takes all three working together to obtain the desired knowledge of natural things.

The three categories of tools are experiment, numerics, and theory. Experimental physicists—experimentalists—carry out practical tests to see how the world behaves. However exotic and unfamiliar our scientific theories may become, they must always lead to testable predictions. These predictions can be confirmed or falsified through observation: wizards don’t invent spells, they learn them. When our fictional accounts of wizards give us glimpses of how wizards learn their spells, it is invariably through observation of the world itself. In Avatar, for example, certain individuals are born with a magical influence over water, which their ancestors learned from observing the Moon’s influence on the tides.

Numerical physicists—numericists—build and test computer simulations of the world. Simulations can be conducted under more controlled conditions, and repeated more frequently, than if the experiments were carried out in reality. The trade-off is that numericists need to know that their simulation shares all the relevant properties with its real-world counterpart.

Theoretical physicists—theorists or theoreticians—also work with models of reality. But whereas numericists would generally prefer the most accurate simulation, theorists generally seek the simplest model that captures the essence of the phenomenon. A theorist must learn to see through to the true essence of a thing; this process surely lies at the heart of all magic.

I am a theorist, although I also work closely with experimentalists and numericists. This guide to modern wizardry will present a theoretical physicist’s perspective—partly because this is the perspective I have, and partly because it is in the nature of a book such as this to boil complex stories down to their essence. Theorists build analogies; fables. But as a fellow theorist, Dr. Jans Henke, once put it to me, mathematical models are the most powerful kind of analogy, because they don’t just relate phenomena to familiar cases: they also allow us to say, in detail, how they will behave in new, untested situations. Experimentalists can then test the phenomena and see if they behave as the model predicted. Often the experimental observation comes first and the fable is woven around it. Suppose a model’s prediction is verified experimentally in a repeatable, controllable way. That lends weight to the idea that the simple elements which went into the model captured the essence of the phenomenon. Theoretical physics often comes close to mathematics; the difference enters via the gap between the mathematical model—perfect and predictable—and reality, the messy world we experience. Theoretical physics is the storytelling we do to make the mathematical model more intuitive.

The work of the theorist has always reminded me of the magic of true names. From ancient Egypt to modern hacking culture, the idea has persisted that learning something’s true name grants us power over it. Ursula K. Le Guin’s Earthsea books, which are said to be the first example in fiction of the wizard being the protagonist rather than a supporting character, provide a great example in a fantasy setting. In the world of Earthsea, wizards gain their magic by listening to the world and learning the true names of things. Now, the day-to-day names we use for things are simply labels we attach so we can refer to them in conversation. In Earthsea these are called use names, but things also have a true name. These names are said to belong to the Language of the Making. We are told the true name for pebble is “tolk,” for example. When we say something’s use name to someone else, a little bit is lost in translation. When I say “pebble,” I conjure certain associations in my mind that other people will not have. My fiancée, Dominique, explained it to me like this. If you were to speak something’s true name, then by definition nothing could be lost in translation; anyone would have the same perfect understanding of what is meant. So it is natural to associate true names with conjuration. How can you guarantee perfect understanding unless the thing itself is present? When I say “pebble,” I may be referring to some more general property shared by all pebbles. To speak the name “tolk,” however, I must first have understood the essence of a pebble.

People, too, can have true names. In the graphic novel The Invisibles, a person must take a magical name when they become a wizard. Grave warnings are issued against flippant name choices because the name shapes their personality. I have a friend who belongs to a religion in which a holy person has to be consulted when naming babies. They are believed to have some mystical understanding of the essence of the child, and name them accordingly. This holy person then assigns new names as the person grows throughout their life. It is true that names can dictate elements of one’s life. My own name, Felix Flicker, is absurd and demands attention; I can’t help but wonder whether I internalized those traits. The effect can be more serious, though. A 2012 study found that when identical applications were assessed for a scientific job, the application was deemed of lower quality when a female name was attached to it than when a male name was attached, and a significantly lower salary was deemed appropriate.1 Even in our world, a name is more than an arbitrary label.

Theorists study models of things, not the things themselves. Say that one day a theorist drops her crystal ball down the steps of her tower. Imbued as it is with potent magic, the ball will survive intact. But she needs to know when it will arrive at the bottom, in order to summon an eagle to collect it in a timely manner.II Quick as a flash, she decides to use Newton’s laws of motion to construct a mathematical equation to model the ball’s descent. But she will not attempt to capture every feature of the physical scenario. Probably she will assume the stairs are frictionless; probably she will ignore air resistance; probably she will ignore little gusts of wind that might come about, because these can’t be predicted with any certainty. Our theorist hopes that the outcome—which she can calculate with certainty in her model—matches the reality in which she has found herself by tossing her orb about. The crystal ball is the use name—this particular ball—while the mathematical model is the true name: perfect, and untainted by reality. Once you understand a piece of mathematics, you understand it in exactly the same way as anyone else who understands it, regardless of what language you speak. Two plus two equals four however you write it. There is no approximation in a model; the approximation appears in getting from the model to reality. It is a source of much philosophical debate as to whether the model “exists.” If it does, then it might not be too much of a stretch to suppose that understanding the model conjures it into that existence. To view the world as a theoretical physicist, you must learn to listen for the true names of things: you must learn to conjure perfect mathematical models. The art lies in choosing the simplest models that capture the essence of the thing being studied. This simplicity is important: a map with a 1:1 scale would be entirely accurate, but it would also be entirely useless because it would give no simplification.

Physics is a set of tools that can be applied to anything, from the invisibly small to the unknowably large. But the wizard’s focus is more specific, lying in the here and now. Between the extremes lies a middle realm: the familiar world we inhabit.
The Middle Realm Has Its Own Ways
All disciplines of physics do pretty magical things. Cosmologists study the birth and life of the universe, and also predict its fate. Astrophysicists have listened to gravitational waves to hear black holes collide. Particle physicists excite quantum fields to create elementary particles that have never before been detected. These are very grand magics, and many excellent books have been devoted to them. Yet between the microcosm of the quantum and the macrocosm of the universe lies a middle realm. It is no less magical, but its magic takes a different form—a familiar form—and as such it has been largely overlooked in popular books. Yet it is the largest area within physics, occupying around a third of all researchers.

The study of the middle realm is condensed matter physics. It is the physics of the things you see around you: matter—lumps of stuff you can hold in your hand—and their description, right down to the quantum realm from which they emerge. Wolfgang Pauli, one of the creators of quantum mechanics, famously dismissed condensed matter physics as Schmutzphysik (the physics of dirt). It’s the perfect description of the wizard’s art.

I think it is fair to say that condensed matter physics’ closest cousin is particle physics. It is important to understand the similarities and differences between these disciplines. Particle physics is the study of elementary particles—electrons, protons, and so forth; a reasonable definition might be something like this:

An elementary particle can exist by itself in the vacuum of space, and cannot be reduced to other things with that property.

An electron meets these criteria. An atom, however, does not, because while it may be able to exist by itself, it is made up of other things (electrons, protons, and neutrons), which also have that property. Protons are themselves made up of three quarks; but quarks cannot exist in isolation, so by the definition above they are also not elementary.

Now, condensed matter physics is the study of what emerges when many elementary particles interact. If that’s so, doesn’t it simply reduce to particle physics? In this book I’ll try to convince you that the answer is no. If condensed matter physics had a tagline, it would be this:

The whole is more than the sum of the parts.

Perhaps the most important illustration is given by the behavior of particles within matter—to my mind the central set piece in the magic show of reality. When an electron shoots through the vacuum of space, it has a specific mass, charge, and magnetic field (called its “spin”). These uniquely define it to be an electron, and all electrons are alike. If that electron travels into a material, it interacts with the other particles in the material according to the rules of quantum mechanics. In doing so, its properties change; since all electrons have the same mass, it can no longer be an electron. Indeed, it is no longer an elementary particle: it has transformed into an “emergent quasiparticle,” the whole that is more than the sum of its parts.

To explain how this works, I will rephrase an elegant analogy devised by Professor David J. Miller to explain the behavior of the Higgs boson, an elementary particle. Miller mentioned that he had borrowed the central conceit from condensed matter physics, so I trust he won’t mind a temporary return loan. Imagine a collection of avid ghost hunters has packed into the dilapidated ballroom of a haunted mansion, unbeknownst to the ruff-wearing specter who is happily floating down the corridor with his detached head held under his arm. The ghost enters the ballroom, and suddenly all eyes (and dubious measurement devices) are on him. The crowd, previously spread out, squashes around him. Unfortunately for the ghost, he’s the kind from Tom’s Midnight Garden that can’t pass effortlessly through people. His pace dramatically slows as he has to push his way through the crowd of ghost hunters failing to capture him on camera. The ghost’s mass has increased, in the sense that it would take a greater force to accelerate him than when he was strolling alone down the corridor: he now has a surrounding crowd that also needs to be moved. To bring the analogy a bit closer to reality’s true quantum weirdness, we might imagine that he is instead the kind of ghost from Bill & Ted’s Bogus Journey: rather than push through the crowd in his original form, he hops between host bodies as he possesses them one after the other. He again slows down and effectively gains mass, but there is now nothing in the ballroom resembling the original ghost at all; yet when he pops out onto the veranda he reappears in his original form. When the electron is in the material, it is changed; yet it can leave the material and return to being an elementary particle.

Other emergent quasiparticles have no precedent in the world of elementary particles. For example, while light is conveyed by its elementary particles of photons, sound cannot be described by elementary particles, for it cannot exist in the vacuum of space. Sound, being a vibration, requires a medium through which to travel. Yet it can travel through matter—and when it does, it, too, can be described by emergent quasiparticles, known as “phonons.”III To borrow again from Miller’s analogy, this time a ghost hunter merely imagines they “have felt a presence” and tells the person next to them. That person’s neighbor overhears and leans in, and soon the rumor is moving around the room. Wherever the rumor goes, the crowd squashes together as if there were a ghost there—but there’s not. This dense region of crowd behaves like an object with mass, resisting changes to its motion, just as a phonon does. Matter that doesn’t contain any quasiparticles can be thought of as the condensed matter version of the vacuum of space—after all, a vacuum is simply the absence of elementary particles. Phonons provide an illustrative example. They can be understood as the vibrations of the atoms in a crystal; when the crystal is cooled down, the atoms vibrate less and the phonons disappear. When all phonons are gone, the crystal is in its lowest energy state, called its “ground state.” Were you to speak to the crystal in your quiet, practiced tone, you’d give it energy, causing its atoms to vibrate and conjuring phonons into existence. This motivates the following definition:

An emergent quasiparticle can exist by itself above the ground state of a material, and cannot be reduced to other things with that property.

Emergent quasiparticles cannot be reduced to elementary particles without losing an essential part of the description: think of the crowd squashing together to hear the rumor of a ghost. It’s true that everything can be described in terms of individual ghost hunters, but that would miss the bigger picture. This is the essential idea of “emergence,” the concept that the whole can be more than the sum of its parts: the crowd has properties, such as moving constrictions, that are not properties of the individuals who comprise it. In condensed matter physics the individuals will usually be the atoms and elementary particles, and the emergent properties will be the large-scale behavior of matter, understood in terms of emergent quasiparticles.

Quasiparticles are unique to condensed matter physics. Many have a dreamy sense of unreal wonder: phonons can be measured in experiments—but if you look for them at the level of elementary particles, there is nothing there. They are simply the collective vibrations of atoms.

Now, it may seem tempting on that basis to dismiss quasiparticles as less “real” than the elementary particles from which they emerge. But look at it like this: we consider the world around us—the middle realm—to be real. By contrast, we think the quantum realm from which it emerges is full of mystical hocus-pocus. Yet our familiar world only avoids quantum tomfoolery because it is emergent. To reject the reality of quasiparticles is to reject the reality of everyday existence. There is no elementary particle that carries sound, yet you are able to hear the distant hoot of owls in a nearby wood.
The Owls Are Not What They Seem
Theoretical physicists can be found in all branches of the subject, boiling reality down to its essence. But this boiling down can take many forms. Particle physicists are trying to identify the individual building blocks of the universe—the smallest moving parts of reality. This program has had phenomenal success, culminating in the Standard Model, which accounts for all known elementary particles. Perhaps the ultimate aim of this quest is the “theory of everything,” which would add the final missing ingredient to the Standard Model: gravity. If found, this theory would then encompass all the forces in nature. It would explain dark matter and dark energy, and it would contain within it the key to understanding the fate of the universe. But you can probably see that it wouldn’t really be a theory of everything. In fact, it would not really describe anything you actually experience day to day. It would be a theory of all the elementary particles and their interactions, but it would not be a theory of, say, owls.

There is no elementary owl particle, yet we believe owls exist. They are made up of many different types of atom. Each atom is made up of protons, neutrons, and electrons. So owls are not elementary; they are emergent. Owls are complex, messy, sets of traits; they are more than the sum of the parts from which they emerge. The simpler parts could be elementary particles, atoms, cells, genes, or other things. These lower-level descriptions are not mutually exclusive, and none of them is wrong, as such. But they do not account for the owl’s talons, its screech, its beak, or its popular association with magic.

Condensed matter physics is not the study of owls (at least, not yet). But it is the study of what emerges when many things interact, and this is what distinguishes the middle realm from the microscopic world. A well-worn saying has it that two heads are better than one. What is less frequently observed is that two heads are more than twice as good as one: the extra bit is emergence. And when many, many particles get together to form a lump of stuff, new worlds can emerge.

This book asks what form these new worlds can take. If you were to boil the story down to its essence, the tincture you would create would provide an answer to the following question: What is matter?

There are many ways to understand the answer, and we will encounter a complementary approach in each chapter. Ours will be a journey of discovery, undertaken in three stages.
There and Back Again
Once, when walking through the desert, I chanced upon a magician. Our conversation drifted this way and that, and we found our way to the subject of stage magic. I asked the magician if he knew of my favorite performer, Derren Brown, the master illusionist who reminds us at the start of each show that he employs a combination of “magic, suggestion, psychology, misdirection, and showmanship.” The magician knew of him.

I told the magician that my appreciation of Derren Brown had grown in two stages. When I first watched him, I enjoyed the brilliant feats of mentalism. He can read your mind, he can make you see things that aren’t there, he can make you perform impossible stunts. He exploits gaps in our perceptions of reality to show us that our models of the world are susceptible to manipulation. But after obsessively rewatching his act, I came to realize that a lot could be accomplished using clever sleight of hand and traditional magic, rather than psychological manipulation. This was when I reached the second stage of my appreciation. This was the real magic trick! He made a rational skeptic like me believe in magic again, and he accomplished this by appealing to a scientific blind spot: the mysteries of the mind.

The magician in the desert told me that he considered Derren Brown to be the greatest living magician. He agreed that, as with all truly great magic, there exist the two stages of appreciation I’d glimpsed. But he added that there was also a third stage: that of the professional colleague watching the tricks. A magician will know many of the techniques being used and how the tricks are performed—but it is still a marvel to watch Derren Brown working because his technical ability is unparalleled. It is a joy for a professional to see the tricks performed so deftly.

I heard in the magician’s words a parallel to the scientist’s journey of understanding. It is a three-stage journey that we have all begun. When we are young, we are fascinated by the world. It is all new to us, and we marvel at its wonders. This is the first stage: enjoying the performance. As we get older, we begin to learn how things work. We approach the second stage: understanding how the world performs its magic. It is easy to get lost here, stumbling into a cold, dark cavern of rationality. But if you can keep that fire of excitement smoldering inside you, it takes little more than a short puff of breath to reignite it. With patience, and a little luck, you can kindle that fire and proceed to the third stage of understanding: that of the scientist, who understands how the world works its magic and loves it all the more for the skill of its performance.

Our understanding of the stuff around us is a story that has been updated and retold through the ages. As we progress through this book, we will meet different takes on the nature of matter. We will begin in the distant past, where all was earth and air and fire and water, and we will progress toward the far future, in which our lives are transformed by things condensed matter physicists are only now beginning to comprehend. In the earlier chapters, we will put together our essential spells: the knowledge, passed down through generations, representing the understanding that all condensed matter physicists must develop in their training. Thus prepared, in the later chapters we will push on to the future, meeting spells condensed matter physicists are still learning to cast.

If there is one message you take away from this book, I hope it is this. Wizards are real, and if you are interested in becoming one, the condensed matter physics community will welcome you. If you are concerned that you do not fit a traditional idea of a physicist, you are needed all the more. There are condensed matter physicists from all walks of life, and increasingly so. I will give a snapshot of contributions to the subject made by some individual physicists past and present, and I hope these give some idea of the breadth of backgrounds of people behind the science.

On the other hand, any small insight into the characters of the past should not be taken as an endorsement of all they have said. J. G. Frazer, quoted above, had an elegant turn of phrase, but his views were regressive even for their time. And there are battles still to be won. For example, until 2017, only two of the 216 physics Nobel laureates were women; it took thirty years for the first prize to be awarded outside Europe or North America, and to this day it has never been awarded to anyone from Africa, South America, or the Middle East. Nobel Prizes are merely one symptom of a much wider problem in which only a narrow cross section of society is encouraged to pursue science, and in which the contributions of people who don’t fit the stereotype are devalued or ignored. I will occasionally highlight Nobel Prizes as a convenient shorthand to indicate the importance of certain work, but it should be understood that the lack of a prize is often an indicator of nothing more than bias. Things are improving: the physics prize was awarded to women in 2018 and again in 2020 (although seven men won it in the same period). This improvement is vital for the future of science: the best way to solve a complicated problem is to have as many views and approaches represented as possible. So if you’ve ever felt excluded by past depictions of scientists or wizards, it is because you are the future of the subject.

I wish I could tell you that I was inspired to study physics by a desire to be a wizard, or a love of fantasy fiction. I do recall being drawn to the arcane words and the idea of an esoteric knowledge available to the initiated, but it was really something deeper that drew me to both: a love of imagination. The same power that is used to create imaginary worlds is used to realize those worlds in physical theories, and to invent ways to access them in experiments. I will employ this connection throughout the book, using both fictional passages, and references to classic books and films, to emphasize the magic behind the physics. As with the opening passage of the book, it is often easier to see magic when it is presented as fiction; but by the close of the book I hope you will agree that the real world is as magical as the most enchanting tales it contains.

Let us proceed, then, with learning the physics of dirt. There are many spells that don’t appear in this book, and it is not the purpose of this book to teach you them. The world is already telling you its spells; the purpose of this book is to help you to listen.

1. I. I have tended not to use the term “witch” because of its historical associations with persecution. The term “wizard” is intended to cover magic workers of all types and backgrounds.
2. II. Eagles, as Tolkien taught us, are always happy to oblige with a convenient rescue.
3. III. Some physicists prefer to call phonons “collective excitations” rather than “quasiparticles.” I will not draw this distinction.