Order and chaos. Nature and nurture. Yin and yang. We are fond of carving the world into two. And physics, at first, seems to oblige. Take the universe’s unruly zoo of fundamental particles and it seems to fall into two camps. Boil it all down and you have matter and forces. Together, they make up a pleasingly simple recipe for reality.
Except physics has a way of spoiling simple recipes. In recent mathematical work, researchers have discovered a potential third category of particles. These so-called paraparticles would be neither matter nor force, but something stranger in between. And unlike either bosons or fermions, they would obey an alternate set of quantum rules, first proposed decades ago, then largely dismissed.
Thanks to new mathematical insights, paraparticles may be more viable than anyone thought. No one has seen one in nature, but the stakes are high. If paraparticles exist, it would shake our understanding of reality.
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The standard model of particle physics, our best current theory of the fundamental ingredients of the universe, already has gaps: it omits gravity and can’t explain dark matter or dark energy. But paraparticles might offer a new way into those missing parts. “This would be huge,” says at the University of Oxford. “It could mean the standard model is badly wrong.”
The binary at the heart of reality
To understand why paraparticles once seemed impossible, it helps to return to the two kinds of particle we know exist. There are fermions, such as electrons and quarks, which make up matter. And there are bosons, such as photons and gluons, which carry forces. Together, they compose all the fundamental particles in the standard model. Matter and messenger: the division between the two isn’t merely superficial; it seems to be written into the very mathematical structure of quantum mechanics.
Quantum mechanics treats particles in a strange but strict way. Two electrons aren’t just very alike. As far as the theory is concerned, they are interchangeable. Swap them in the maths and no experiment should be able to tell that anything has happened.
The maths in question is the wave function: a mathematical object that encodes the probabilities of finding them in particular states, defined by properties such as location, energy and spin – a kind of internal angular momentum. Wave functions contain odd-looking components, including negative signs and imaginary numbers. But experiments only ever yield ordinary probabilities. To get these, physicists square the wave function, making some of the mathematical oddness disappear from view.
All this means that, when two identical particles are swapped, there are two possible outcomes: the wave function can stay as it is or it can flip sign. After squaring, both options give the same positive probabilities. But physically, they describe very different kinds of particles.
In one case, identical particles can crowd together. These are bosons, a family that includes photons, which mediate the electromagnetic force, and gluons, which carry the strong nuclear force that binds quarks into protons and neutrons. Because bosons can have the same quantum properties at the same time, they tend to be quite gregarious. Photons, for instance, can pile together in the beam of a laser.
In the other case, identical particles are barred from sharing a quantum state. These are fermions, including electrons, quarks and ghostly particles known as neutrinos. They are mathematically forbidden from overlapping, making electrons antisocial and explaining why they occupy different shells around atomic nuclei. It is also what gives ordinary matter its stubborn solidity: squeeze atoms too tightly and their electrons have nowhere new to go, producing a quantum pressure that resists further compression.
For decades, that seemed to exhaust all the possibilities. There was no obvious third option. But in 1953, physicist Herbert Green found one. He suggested that the wave function might have more structure inside it than physicists had assumed. When two identical particles were swapped, the wave function needn’t simply stay the same or flip sign. It could also rearrange hidden internal states that don’t show up directly in ordinary measurements.
Think of two identical-looking boxes. From the outside, swapping them changes nothing: the same boxes are still there, and any ordinary inspection gives the same result. But what if there are unseen compartments inside? If so, the external sameness is preserved, even though something concealed within has changed. These are often referred to as “hidden states”, and the particles that possessed them were named “paraparticles”.
These hidden states became a source of scepticism around paraparticles. No one knew what they corresponded to physically. They might be nothing more than a mathematical trick. Or they might turn out to be similar to spin – a quantum mechanical property with no straightforward classical equivalent – except hidden from ordinary measurement. “The physical meaning attached to them is going to be to be dependent on what they actually are in a real physical system,” says at Rice University in Texas.
Because of this, Green faced an uphill struggle. “Already at the beginning, people started asking: ‘If these exist, why don’t we observe them?’” says , a theoretical physicist at the Brazilian Center for Research in Physics in Rio de Janeiro. “People argued you can’t see them because they are actually equivalent to bosons and fermions.”
In 1971, that argument seemed to triumph. Three physicists – Sergio Doplicher, Rudolf Haag and John E. Roberts, known as DHR – showed that, in a three-dimensional world, any theory of paraparticles could be recast as ordinary standard-model physics in disguise. Space itself would force paraparticles to behave as either fermions or bosons, and their verdict soon hardened into textbook wisdom: paraparticles were a fun idea, but not real.
Still, some were undeterred. In the 1980s, Nobel laureate Frank Wilczek showed that particles confined to two dimensions – as they can be within thin layers of materials – could indeed obey different rules. He called them “anyons” and they were a remarkable challenge to the accepted orthodoxy. “When I first proposed anyons, I thought of it as just kind of a lark and a curiosity,” says Wilczek. “But soon they turned up experimentally.”
Not as free-floating fundamental particles, however. Anyons emerge in certain materials and are known as “quasiparticles” – collective disturbances that behave like particles. A phonon is a simpler example. It is essentially a packet of sound, produced by atoms vibrating in a material, rather like a Mexican wave travelling through a packed stadium. No single person is the wave, yet the wave moves as if it were an object in its own right.
Still, anyons are now taken seriously as possible building blocks for fault-tolerant quantum computers. showed how swapping them around allows information to be stored in a form that is more resilient to errors. But anyons looked like a special loophole to the rule DHR had established: exotic and useful in the laboratory, but nowhere close to a rebuttal of the standard model’s grand binary.
Code cracked
In three dimensions, making paraparticles work is quite a bit more difficult. In 2021, Toppan tried to introduce a different type of algebra for describing paraparticles in the laboratory. With this maths, he found that ordinary space no longer forced paraparticles to collapse back into fermions or bosons. The trick was to stop looking at particles one by one. On their own, they could still pass for ordinary particles, but in groups their shared quantum state carried an extra mathematical fingerprint, unique to paraparticles.
But serious problems remained. For bosons or fermions, swapping two identical particles in a wave function doesn’t mean this has to happen in the real world. No one is dragging one electron around another. Instead, you are just changing the labels: the particle called A is now B, and vice versa. Since electrons are identical, nothing measurable should change.
Paraparticles seemed different. Swapping their labels also changed something else: their hidden states. Even if it is unclear what that physically corresponds to, the relabelling seemed to have real consequences. Now, put one paraparticle on Earth and another on Pluto, and you’ll find that swapping their labels violates a principle known as “locality”, which says that distant objects can’t influence one another instantaneously.
But a solution to this once-fatal problem has recently come to light. , then a PhD student at Rice University and now at the Max Planck Institute of Quantum Optics in Germany, was stuck indoors during a covid-19 lockdown and was entertaining himself with maths. “It’s kind of funny,” says Hazzard, his colleague and former supervisor. Wang’s response to lockdown boredom was “playing around with representations of algebra”. But when Wang showed him his calculations, Hazzard was immediately intrigued.
Using a similar but extended version of Toppan’s algebra, Wang and Hazzard tied the mathematics of re-labelling particles back to physical motion. , they showed how a swap could change a paraparticle’s hidden states only if the particles were actually exchanged by moving one around the other. This process would take time, so wouldn’t allow for a faster-than-light signal.
“It’s an absolutely brilliant paper,” says Toppan. Wilczek describes the finding as “interesting” and “intriguing”, but says more theory is needed. Wang and Hazzard have shown how paraparticles behave when exchanged, but not yet the full story of how they move or interact with one another. “Anyons are different in that we can keep track of the whole history of how particles have moved,” he says.
Even so, Wang and Hazzard’s work suggests that paraparticles could exist as quasiparticles that can exist in higher dimensions than anyons. “New types of quasiparticles may give us materials with properties that we just didn’t realise were possible,” says Hazzard. Materials hosting paraparticles could conduct heat or electrical charge in unfamiliar ways, for instance.
Wang also thinks there could be interesting applications in secret communications. Imagine two parties wanting to exchange information without sending a conventional signal that could be intercepted. In principle, swapping paraparticles might allow information to be encoded in their exchange without leaving the same kind of measurable trace.
A new fundamental particle
While the possibility of new quasiparticles could unlock technologies, the bigger prize lies elsewhere: paraparticles not just inside materials, but as a new type of fundamental particle. “The idea that these could be fundamental particles is extremely speculative. It seems a little bit of a desperate idea,” says Hazzard. “But when you talk to people in the community of finding new fundamental particles, it turns out we’re a little desperate.”
No one yet knows quite what role such particles would play, or how they would interact with the particles we already know. But they would almost certainly behave unlike anything in the standard model. Bosons are happy to crowd together, while fermions are barred from doing so. Paraparticles would obey a stranger rule of togetherness: not quite free to pile up, but not quite forbidden from overlapping. They would introduce a new way for particles to share the universe’s quantum real estate.
One especially tempting problem to apply them to would be the mystery of dark matter. We know that galaxies are wrapped in vast halos of unseen matter, but we still don’t know what this is made of. Hazzard has already begun exploring whether paraparticles could fit the bill with cosmologists and , also at Rice University.
They say that the inability of fermions to share the same quantum state imposes a limit. “If the mass of the dark matter particle is below about 1/500,000th of the electron’s mass, then dark matter cannot be made of fermions,” says Long. Very light dark matter candidates – such as the hypothetical particles known as axions, which interact very weekly with ordinary matter and light – are usually treated as bosons for that reason.
But Amin realised that the new social rules of paraparticles could allow them to be light enough to form dark matter halos. The idea is still preliminary, but it is an intriguing proposition. “I think people who work on dark matter would be very receptive to the idea that there’s a whole new knob to turn,” says Long.
Proving paraparticles
Demonstrating that paraparticles exist won’t be easy. Their defining hidden states can’t be measured directly. Instead, physicists must look for them indirectly.
Toppan has recently proposed one such test. Imagine two scientists monitoring a pair of particles before and after they are exchanged. For ordinary bosons or fermions, the measurements should match perfectly. For paraparticles, the hidden states would subtly alter the underlying wave function, creating a telltale asymmetry in the data even though the particles themselves still appear identical.
Hazzard and at Penn State University hope to look for this effect in paraparticle-like states in chains of ultracold atoms. It wouldn’t amount to the discovery of a fundamental paraparticle, but it would show that their strange behaviours can emerge in a real physical system.
Finding a fundamental paraparticle, on the other hand, would be an even taller order. One possible route to this is through particle accelerators. “What you’d do is accelerate some particles, create a cascade reaction and then observe the outcomes,” says Vedral. That means smashing particles together, letting the collision spray out new particles and then looking for patterns in the debris. In principle, paraparticles could carry the imprint of hidden states changing as particles swap places.
But there might be a way to see evidence in data we already have. If paraparticles contribute to dark matter, dark energy or other cosmic phenomena, their fingerprints might already be hiding in observations of the universe. Vedral and others have suggested looking for their influence in the cosmic microwave background, the relic radiation left over from the big bang. “One of the possibilities is that there is a contribution from some kind of paraparticle interactions,” he says. at the University of York, UK, says this is “the simplest, cheapest way to look for them”.
For now, paraparticles remain a mathematical possibility rather than a physical reality. Much is still unknown, including their mass, spin and full dynamics. Wang and Hazzard are now working to place them within a fully relativistic quantum field theory, the language of modern particle physics. Whether that effort ultimately reveals a new kind of particle or closes the door once again remains to be seen.
But if paraparticles survive such efforts, they may change the standard model in ways we can barely imagine. There is even the possibility, says Hazzard, that some particles we already know as fermions or bosons might reveal paraparticle-like behaviour if measured precisely enough. “Some people have reached out to us saying: ‘How well do we know the electron actually is a fermion?’” he says.
It is a revealing question. Physics can sometimes see reality in black and white. But paraparticles are a vital reminder that nature’s cleanest divisions are often places to look again.
