In a ground-breaking theoretical study, two physicists have identified a new class of quasiparticle called the paraparticle. Their calculations suggest that paraparticles exhibit quantum properties that are fundamentally different from those of familiar bosons and fermions, such as photons and electrons respectively.

Using advanced mathematical techniques, Kaden Hazzard at Rice University in the US and his former graduate student Zhiyuan Wang, now at the Max Planck Institute of Quantum Optics in Germany, have meticulously analysed the mathematical properties of paraparticles and proposed a real physical system that could exhibit paraparticle behaviour.

“Our main finding is that it is possible for particles to have exchange statistics different from those of fermions or bosons, while still satisfying the important physical principles of locality and causality,” Hazzard explains.

Particle exchange

In quantum mechanics, the behaviour of particles (and quasiparticles) is probabilistic in nature and is described by mathematical entities known as wavefunctions. These govern the likelihood of finding a particle in a particular state, as defined by properties like position, velocity, and spin. The exchange statistics of a specific type of particle dictates how its wavefunction behaves when two identical particles swap places.

For bosons such as photons, the wavefunction remains unchanged when particles are exchanged. This means that many bosons can occupy the same quantum state, enabling phenomena like lasers and superfluidity. In contrast, when fermions such as electrons are exchanged, the sign of the wavefunction flips from positive to negative or vice versa. This antisymmetric property prevents fermions from occupying the same quantum state. This underpins the Pauli exclusion principle and results in the electronic structure of atoms and the nature of the periodic table.

Until now, physicists believed that these two types of particle statistics – bosonic and fermionic – were the only possibilities in 3D space. This is the result of fundamental principles like locality, which states that events occurring at one point in space cannot instantaneously influence events at a distant location.

Breaking boundaries

Hazzard and Wang’s research overturns the notion that 3D systems are limited to bosons and fermions and shows that new types of particle statistics, called parastatistics, can exist without violating locality.

The key insight in their theory lies in the concept of hidden internal characteristics. Beyond the familiar properties like position and spin, paraparticles require additional internal parameters that enable more complex wavefunction behaviour. This hidden information allows paraparticles to exhibit exchange statistics that go beyond the binary distinction of bosons and fermions.

Paraparticles exhibit phenomena that resemble – but are distinct from – fermionic and bosonic behaviours. For example, while fermions cannot occupy the same quantum state, up to two paraparticles could be allowed to coexist in the same point in space. This behaviour strikes a balance between the exclusivity of fermions and the clustering tendency of bosons.

Bringing paraparticles to life

While no elementary particles are known to exhibit paraparticle behaviour, the researchers believe that paraparticles might manifest as quasiparticles in engineered quantum systems or certain materials. A quasiparticle is particle-like collective excitation of a system. A familiar example is the hole, which is created in a semiconductor when a valence-band electron is excited to the conduction band. The vacancy (or hole) left in the valence band behaves as a positively-charged particle that can travel through the semiconductor lattice.

Experimental systems of ultracold atoms created by collaborators of the duo could be one place to look for the exotic particles. “We are working with them to see if we can detect paraparticles there,” explains Wang.

In ultracold atom experiments, lasers and magnetic fields are used to trap and manipulate atoms at temperatures near absolute zero. Under these conditions, atoms can mimic the behaviour of more exotic particles. The team hopes that similar setups could be used to observe paraparticle-like behaviour in higher-dimensional systems, such as 3D space. However, further theoretical advances are needed before such experiments can be designed.

Far-reaching implications

The discovery of paraparticles could have far-reaching implications for physics and technology. Fermionic and bosonic statistics have already shaped our understanding of phenomena ranging from the stability of neutron stars to the behaviour of superconductors. Paraparticles could similarly unlock new insights into the quantum world.

“Fermionic statistics underlie why some systems are metals and others are insulators, as well as the structure of the periodic table,” Hazzard explains. “Bose-Einstein condensation [of bosons] is responsible for phenomena such as superfluidity. We can expect a similar variety of phenomena from paraparticles, and it will be exciting to see what these are.”

As research into paraparticles continues, it could open the door to new quantum technologies, novel materials, and deeper insights into the fundamental workings of the universe. This theoretical breakthrough marks a bold step forward, pushing the boundaries of what we thought possible in quantum mechanics.

The paraparticles are described in Nature.

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Striking evidence that string theory could be the sole viable “theory of everything” has emerged in a new theoretical study of particle scattering that was done by a trio of physicists in the US. By unifying all fundamental forces of nature, including gravity, string theory could provide the long-sought quantum description of gravity that has eluded scientists for decades.

The research was done by Caltech’s Clifford Cheung and Aaron Hillman along with Grant Remmen at New York University. They have delved into the intricate mathematics of scattering amplitudes, which are quantities that encapsulate the probabilities of particles interacting when they collide.

Through a novel application of the bootstrap approach, the trio demonstrated that imposing general principles of quantum mechanics uniquely determines the scattering amplitudes of particles at the smallest scales. Remarkably, the results match the string scattering amplitudes derived in earlier works. This suggests that string theory may indeed be an inevitable description of the universe, even as direct experimental verification remains out of reach.

“A bootstrap is a mathematical construction in which insight into the physical properties of a system can be obtained without having to know its underlying fundamental dynamics,” explains Remmen. “Instead, the bootstrap uses properties like symmetries or other mathematical criteria to construct the physics from the bottom up, ‘effectively pulling itself up by its bootstraps’. In our study, we bootstrapped scattering amplitudes, which describe the quantum probabilities for the interactions of particles or strings.”

Why strings?

String theory posits that the elementary building blocks of the universe are not point-like particles but instead tiny, vibrating strings. The different vibrational modes of these strings give rise to the various particles observed in nature, such as electrons and quarks. This elegant framework resolves many of the mathematical inconsistencies that plague attempts to formulate a quantum description of gravity. Moreover, it unifies gravity with the other fundamental forces: electromagnetic, weak, and strong interactions.

However, a major hurdle remains. The characteristic size of these strings is estimated to be around 10⁻³⁵ m, which is roughly 15 orders of magnitude smaller than the resolution of today’s particle accelerators, including the Large Hadron Collider. This makes experimental verification of string theory extraordinarily challenging, if not impossible, for the foreseeable future.

Faced with the experimental inaccessibility of strings, physicists have turned to theoretical methods like the bootstrap to test whether string theory aligns with fundamental principles. By focusing on the mathematical consistency of scattering amplitudes, the researchers imposed constraints based on basic quantum mechanical requirements on the scattering amplitudes such as locality and unitarity.

“Locality means that forces take time to propagate: particles and fields in one place don’t instantaneously affect another location, since that would violate the rules of cause-and-effect,” says Remmen. “Unitarity is conservation of probability in quantum mechanics: the probability for all possible outcomes must always add up to 100%, and all probabilities are positive. This basic requirement also constrains scattering amplitudes in important ways.”

In addition to these principles, the team introduced further general conditions, such as the existence of an infinite spectrum of fundamental particles and specific high-energy behaviour of the amplitudes. These criteria have long been considered essential for any theory that incorporates quantum gravity.

Unique solution

Their result is a unique solution to the bootstrap equations, which turned out to be the Veneziano amplitude — a formula originally derived to describe string scattering. This discovery strongly indicates that string theory meets the most essential criteria for a quantum theory of gravity. However, the definitive answer to whether string theory is truly the “theory of everything” must ultimately come from experimental evidence.

Cheung explains, “Our work asks: what is the precise math problem whose solution is the scattering amplitude of strings? And is it the unique solution?”. He adds, “This work can’t verify the validity of string theory, which like all questions about nature is a question for experiment to resolve. But it can help illuminate whether the hypothesis that the world is described by vibrating strings is actually logically equivalent to a smaller, perhaps more conservative set of bottom up assumptions that define this math problem.”

The trio’s study opens up several avenues for further exploration. One immediate goal for the researchers is to generalize their analysis to more complex scenarios. For instance, the current work focuses on the scattering of two particles into two others. Future studies will aim to extend the bootstrap approach to processes involving multiple incoming and outgoing particles.

Another direction involves incorporating closed strings, which are loops that are distinct from the open strings analysed in this study. Closed strings are particularly important in string theory because they naturally describe gravitons, the hypothetical particles responsible for mediating gravity. While closed string amplitudes are more mathematically intricate, demonstrating that they too arise uniquely from the bootstrap equations would further bolster the case for string theory.

The research is described in Physical Review Letters.

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