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Physicists believe a third class of particles – anyons – could exist, but only in 2D. As Elay Shech asks, what kind of existence is that?…

Everything around you – from tables and trees to distant stars and the great diversity of animal and plant life – is built from a small set of elementary particles. According to established scientific theories, these particles fall into two basic and deeply distinct categories: bosons and fermions.

Bosons are sociable. They happily pile into the same quantum state, that is, the same combination of quantum properties such as energy level, like photons do when they form a laser. Fermions, by contrast, are the introverts of the particle world. They flat out refuse to share a quantum state with one another. This reclusive behaviour is what forces electrons to arrange themselves in layered atomic shells, ultimately giving rise to the structure of the periodic table and the rich chemistry it enables.

At least, that’s what we assumed. In recent years, evidence has been accumulating for a third class of particles called ‘anyons’. Their name, coined by the Nobel laureate Frank Wilczek, gestures playfully at their refusal to fit into the standard binary of bosons and fermions – for anyons, anything goes. If confirmed, anyons wouldn’t just add a new member to the particle zoo. They would constitute an entirely novel category – a new genus – that rewrites the rules for how particles move, interact, and combine. And those strange rules might one day engender new technologies.

Although none of the elementary particles that physicists have detected are anyons, it is possible to engineer environments that give rise to them and potentially harness their power. We now think that some anyons wind around one another, weaving paths that store information in a way that’s unusually hard to disturb. That makes them promising candidates for building quantum computers – machines that could revolutionise fields like drug discovery, materials science, and cryptography. Unlike today’s quantum systems that are easily disturbed, anyon-based designs may offer built-in protection and show real promise as building blocks for tomorrow’s computers.

Philosophically, however, there’s a wrinkle in the story. The theoretical foundations make it clear that anyons are possible only in two dimensions, yet we inhabit a three-dimensional world. That makes them seem, in a sense, like fictions. When scientists seek to explore the behaviours of complicated systems, they use what philosophers call ‘idealisations’, which can reveal underlying patterns by stripping away messy real-world details. But these idealisations may also mislead. If a scientific prediction depends entirely on simplification – if it vanishes the moment we take the idealisation away – that’s a warning sign that something has gone wrong in our analysis.

So, if anyons are possible only through two-dimensional idealisations, what kind of reality do they actually possess? Are they fundamental constituents of nature, emergent patterns, or something in between? Answering these questions means venturing into the quantum world, beyond the familiar classes of particles, climbing among the loops and holes of topology, detouring into the strange physics of two-dimensional flatland – and embracing the idea that apparently idealised fictions can reveal deeper truths…

[Shech explains anyons, and considers the various strategies for making sense of them. (They”paraparticles” like anyons don’t actually exit. Or we simply lack the theoretical framwork and experimental work to follow to find them. Or in ultra-thin materials physics, we’ve already found them.) Considering the latter two possibilities, he concludes…]

So, if anyons exist, what kind of existence is it? None of the elementary particles are anyons. Instead, physicists appeal to the notion of ‘quasiparticles’, in which large numbers of electrons or atoms interact in complex ways and behave, collectively, like a simpler object you can track with novel behaviours.

Picture fans doing ‘the wave’ in a stadium. The wave travels around the arena as if it’s a single thing, even though it’s really just people standing and sitting in sequence. In a solid, the coordinated motion of many particles can act the same way – forming a ripple or disturbance that moves as if it were its own particle. Sometimes, the disturbance centres on an individual particle, like an electron trying to move through a material. As it bumps into nearby atoms and other electrons, they push back, creating a kind of ‘cloud’ around it. The electron plus its cloud behave like a single, heavier, slower particle with new properties. That whole package is also treated as a quasiparticle.

Some quasiparticles behave like bosons or fermions. But for others, when two of them trade places, the system’s quantum state picks up a built-in marker that isn’t limited to the two familiar settings. It can take on intermediate values, which means novel quantum statistics. If the theories describing these systems are right, then the quasiparticles in question aren’t just behaving oddly, they are anyons: the third type of particles.

In other words, while none of the elementary particles that physicists have detected are anyons – physicists have never ‘seen’ an anyon in isolation – we can engineer environments that give rise to emergent quasiparticles portraying the quantum statistics of anyons. In this sense, anyons have been experimentally confirmed. But there are different kinds of anyons, and there is still active work being done on the more exotic anyons that we hope to harness for quantum computers.

But even so, are quasiparticles, like anyons, really real? That depends. Some philosophers argue that existence depends on scale. Zoom in close enough, and it makes little sense to talk about tables or trees – those objects show up only at the human scale. In the same way, some particles exist only in certain settings. Anyons don’t appear in the most fundamental theories, but they show up in thin, flat systems where they are the stable patterns that help explain real, measurable effects. From this point of view, they’re as real as anything else we use to explain the world.

Others take a more radical stance. They argue that quasiparticles, fields and even elementary particles aren’t truly real: they’re just useful labels. What really exists is not stuff but structure: relations and patterns. So ‘anyons’ are one way we track the relevant structure when a system is effectively two-dimensional.

Questions about reality take us deep into philosophy, but they also open the door to a broader enquiry: what does the story of anyons reveal about the role of idealisations and fictions in science? Why bother playing in flatland at all?

Often, idealisations are seen as nothing more than shortcuts. They strip away details to make the mathematics manageable, or serve as teaching tools to highlight the essentials, but they aren’t thought to play a substantive role in science. On this view, they’re conveniences, not engines of discovery.

But the story of anyons shows that idealisations can do far more. They open up new possibilities, sharpen our understanding of theory, clarify what a phenomenon is supposed to be in the first place, and sometimes even point the way to new science and engineering.

The first payoff is possibility: idealisation lets us explore a theory’s ‘what ifs’, the range of behaviours it allows even if the world doesn’t exactly realise them. When we move to two dimensions, quantum mechanics suddenly permits a new kind of particle choreography. Not just a simple swap, but wind-and-weave novel rules for how particles can combine and interact. Thinking in this strictly two-dimensional setting is not a parlour trick. It’s a way to see what the theory itself makes possible.

That same detour through flatland also assists us in understanding the theory better. Idealised cases turn up the contrast knobs. In three dimensions, particle exchanges blur into just two familiar options of bosons and fermions. In two dimensions, the picture sharpens. By simplifying the world, the idealisation makes the theory’s structure visible to the naked eye.

Idealisation also helps us pin down what a phenomenon really is. It separates difference-makers from distractions. In the anyon case, the flat setting reveals what would count as a genuine signature, say, a lasting memory of the winding of particles, and what would be a mere lookalike that ordinary bosons or fermions could mimic. It also highlights contrasts with other theoretical possibilities: paraparticles, for example, don’t depend on a two-dimensional world, but anyons seem to. That contrast helps identify what belongs to the essence of anyons and what does not. When we return to real materials, we know what to look for and what to ignore.

Finally, idealisations don’t just help us read a theory – they help write the next one. If experiments keep turning up signatures that seem to exist only in flatland, then what began as an idealisation becomes a compass for discovery. A future theory must build that behaviour into its structure as a genuine, non-idealised possibility. Sometimes, that means showing how real materials effectively enforce the ideal constraint, such as true two-dimensionality. Other times, it means uncovering a new mechanism that reproduces the same exchange behaviour without the fragile assumptions of perfect flatness. In both cases, idealisation serves as a guide for theory-building. It tells us which features must survive, which can bend, and where to look for the next, more general theory.

So, when we venture into flatland to study anyons, we’re not just simplifying – we’re exploring the boundaries where mathematics, matter and reality meet. The journey from fiction to fact may be strange, but it’s also how science moves forward…

Eminently worth reading in full: “Playing in flatland,” from @elayshech.bsky.social in @aeon.co.

Pair with: “Is Particle Physics Dead, Dying, or Just Hard?“

* Edwin A. Abbott, Flatland: A Romance of Many Dimensions

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As we brood over the boundaries of “being” (and knowing), we might spare a thought for Bertand Russell; he died on this date in 1970. A philosopher, logician, mathematician, and public intellectual, he influenced mathematics, logic, and several areas of analytic philosophy.

He was one of the early 20th century’s prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British “revolt against idealism“. Together with his former teacher Alfred North Whitehead, Russell wrote Principia Mathematica, a milestone in the development of classical logic and a major attempt [if ultimately unsuccessful, pace Godel] to reduce the whole of mathematics to logic. Russell’s article “On Denoting” is considered a “paradigm of philosophy.”

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