On a quiet pandemic afternoon in 2021, Zhiyuan Wang, then a graduate student at Rice University, was alleviating his boredom by working on a weird mathematical problem. After he found an exotic solution, he started to wonder if the math could be interpreted physically. Eventually, he realized that it seemed to describe a new type of particle: one that’s neither a matter particle nor a force-carrying particle. It appeared to be something else altogether.
Wang was eager to develop the accidental discovery into a full theory of this third kind of particle. He brought the idea to Kaden Hazzard, his academic adviser.
“I said, I’m not sure I believe this can be true,” Hazzard recalled, “but if you really think it is, you should put all your time on this and drop everything else you’re working on.”
This January, Wang, now a postdoctoral researcher at the Max Planck Institute of Quantum Optics in Germany, and Hazzard published their refined result in the journal Nature. They say that a third class of particles, called paraparticles, can indeed exist, and that these particles could produce strange new materials.
When the paper appeared, Markus Müller, a physicist at the Institute for Quantum Optics and Quantum Information in Vienna, was already contending with the notion of paraparticles for a different reason. According to quantum mechanics, an object or observer can be in multiple locations at once. Müller was thinking about how you can, on paper, switch between the perspectives of observers in these coexisting “branches” of reality. He realized that this came with new constraints on the possibility of paraparticles, and his team described their results in a preprint in February that’s now under review for publication in a journal.
The close timing of the two papers was a coincidence. But taken together, the work is reopening the case of a physics mystery that was believed to be solved decades ago. A basic question is being reevaluated: What kinds of particles does our world allow?
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Hidden worlds
All known elementary particles fall into one of two categories, and the two behave almost as opposites. There are the particles that make up matter, called fermions, and the particles that impart the fundamental forces, called bosons.
The defining characteristic of fermions is that if you switch the positions of two fermions, their quantum state gains a minus sign. The presence of that measly minus sign has enormous ramifications. It means that no two fermions can be in the same place at the same time. When packed together, fermions cannot be compressed past a certain point. This feature prevents matter from collapsing in on itself — it’s why the electrons in every atom exist in “shells.” Without this minus sign, we couldn’t exist.
Bosons have no such restriction. Groups of bosons will happily all do exactly the same thing. Any number of particles of light, for instance, can be in the same place. This is what makes it possible to build lasers, which emit many identical light particles. This ability comes down to the fact that when two bosons swap places, their quantum state stays the same.
It’s not obvious that fermions and bosons should be the only two options.
That’s in part due to a fundamental feature of quantum theory: To calculate the probability of measuring a particle in any particular state, you have to take the mathematical description of that state and multiply it by itself. This procedure can erase distinctions. A minus sign, for example, will disappear. If given the number 4, a Jeopardy! contestant would have no way to know if the question was “What is 2 squared?” or “What is negative 2 squared?” — both possibilities are mathematically valid.
It’s because of this feature that fermions, despite gaining a minus sign when swapped around, all look the same when measured — the minus sign disappears when quantum states are squared. This indistinguishability is a crucial property of elementary particles; no experiment can tell two of a kind apart.
But a minus sign may not be the only thing that disappears. In theory, quantum particles can also have hidden internal states, mathematical structures not seen in direct measurements, which also go away when squared. A third, more general category of particle, known as a paraparticle, could arise from this internal state changing in a myriad of ways while the particles swap places.
While quantum theory seems to allow it, physicists have had difficulty finding a mathematical description of a paraparticle that works. In the 1950s, the physicist Herbert Green made a few attempts, but further inspection revealed that these paraparticle models were really just mathematical combinations of typical bosons and fermions.
In the 1970s, the mystery of why no one could find a proper model of paraparticles seemed to be solved. A collection of theorems called DHR theory, after the mathematical physicists Sergio Doplicher, Rudolf Haag and John Roberts, proved that if certain assumptions are true, only bosons and fermions are physically possible. One assumption is “locality,” the rule that objects can only be affected by things in their vicinity. (“If I poke my table, I better not affect the moon instantaneously,” as Hazzard put it.) The DHR proof also assumed that space is (at least) three-dimensional.
The results discouraged new ventures into paraparticles for decades, with one exception. In the early 1980s, the physicist Frank Wilczek came up with a theory of particles called anyons that can’t be described as either bosons or fermions. To get around the DHR theorems, anyons come with a big catch: They can only exist in two dimensions.
Physicists now widely study anyons for their potential in quantum computing. Even confined to two dimensions, they could manifest on a flat surface of a material, or in a 2D array of qubits in a quantum computer.
But paraparticles in three dimensions that could form a solid still seemed impossible. That is, until now.
Shifting sights
While developing their model, Wang and Hazzard noticed that the assumptions behind DHR theory went beyond typical concerns of locality. “I think people overinterpreted what limitations or constraints were actually imposed by these theorems,” Hazzard said. Paraparticles, they realized, may be theoretically possible after all.
In their model, in addition to the usual properties of a particle like charge and spin, groups of paraparticles share extra hidden properties. As with the minus sign that gets squared away during a measurement, you can’t directly measure these hidden properties, but they change how the particles behave.
When you swap two paraparticles, these hidden properties change in tandem. As an analogy, imagine that these properties are colors. Start with two paraparticles, one that’s internally red and another that’s internally blue. When they swap places, rather than keeping these colors, they both change in corresponding ways, as prescribed by the mathematics of the particular model. Perhaps the swap leaves them green and yellow. This quickly turns into a complex game, where paraparticles affect each other in unseen ways as they move around.
Meanwhile, Müller was also busy rethinking the DHR theorems. “It’s not always super transparent what they mean, because it’s in a very complicated mathematical framework,” he said.
His team took a new approach to the paraparticle question. The researchers considered the fact that quantum systems can exist in multiple possible states at once — what’s called a superposition. They imagined switching between the perspectives of observers who exist in these superposed states, each of whom describes their branch of reality slightly differently. If two particles are truly indistinguishable, they figured, then it won’t matter if the particles are swapped in one branch of the superposition and not in the other.
“Maybe if the particles are close by, I swap them, but if they are far away I do nothing,” Müller said. “And if they’re in a superposition of both, then I do the swapping in one branch, and nothing in the other branch.” Whether observers across branches label the two particles in the same way should make no difference.
This stricter definition of indistinguishability in the context of superpositions imposes new restrictions on the kinds of particles that can exist. When these assumptions hold, the researchers found that paraparticles are impossible. For a particle to be truly indistinguishable by measurement, as physicists expect elementary particles to be, it must be either a boson or fermion.
Although Wang and Hazzard published their paper first, it’s as though they saw Müller’s constraints coming. Their paraparticles are possible because their model rejects Müller’s starting assumption: The particles are not indistinguishable in the full sense required in the context of quantum superpositions. This comes with a consequence. While swapping two paraparticles has no effect on one person’s measurements, two observers, by sharing their data with each other, can determine whether the paraparticles have been swapped. That’s because swapping paraparticles can change how two people’s measurements relate to each other. In this sense, they could tell the two paraparticles apart.
This means there’s a potential for new states of matter. Where bosons can pack an endless number of particles into the same state, and fermions can’t share a state at all, paraparticles end up somewhere in the middle. They are able to pack just a few particles into the same state, before getting crowded and forcing others into new states. Exactly how many can be crammed together depends on the details of the paraparticle — the theoretical framework allows for endless options.
“I find their paper really fascinating, and there’s absolutely no contradiction with what we do,” Müller said.
The road to reality
If paraparticles exist, they’ll most likely be emergent particles, called quasiparticles, that show up as energetic vibrations in certain quantum materials.
“We might get new models of exotic phases, which were difficult to understand before, that you can now solve easily using paraparticles,” said Meng Cheng, a physicist at Yale University who was not involved in the research.
Bryce Gadway, an experimental physicist at Pennsylvania State University who sometimes collaborates with Hazzard, is optimistic that paraparticles will be realized in the lab in the next few years. These experiments would use Rydberg atoms, which are energized atoms with electrons that roam very far from their nuclei. This separation of the positive and negative charge makes Rydberg atoms especially sensitive to electric fields. You can build quantum computers out of interacting Rydberg atoms. They are also the perfect candidates for creating paraparticles.
“For a certain kind of Rydberg quantum simulator, this is kind of just what they would do naturally,” Gadway said about creating paraparticles. “You just prepare them and watch them evolve.”
But for now, the third kingdom of particles remains wholly theoretical.
“Paraparticles might become important,” said Wilczek, the Nobel Prize–winning physicist and inventor of anyons. “But at present they’re basically a theoretical curiosity.”
Original story reprinted with permission from Quanta Magazine, an editorially independent publication supported by the SimonsFoundation.
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