For decades, physicists have been looking for a quantum-gravity model that will combine quantum physics, the rules of the very tiny, and gravity. One important impediment has been the difficulty of empirically validating the predictions of potential theories. However, some of the models predict an impact that can be tested in the lab: a very modest violation of a basic quantum tenet known as the Pauli exclusion principle, which governs how electrons are grouped in atoms, for example.
A study conducted at the INFN subterranean laboratory under the Gran Sasso mountains in Italy has been looking for evidence of radiation created by such a breach in the form of atomic transitions prohibited by the Pauli exclusion principle. The team states in two publications published in the journals Physical Review Letters (September 19, 2022) and Physical Review D (accepted for publication on December 7, 2022) that no evidence of violation has been detected so far, ruling out certain quantum-gravity theories.
We learn in chemistry class that electrons can only organise themselves in particular certain patterns in atoms, which is related to the Pauli exclusion principle. The atomic nucleus is located at the middle of the atom and is surrounded by orbitals filled with electrons. For example, the first orbital can only hold two electrons. The Pauli exclusion principle, proposed by Austrian physicist Wolfang Pauli in 1925, states that no two electrons may have an identical quantum state; hence, two electrons in an atom’s initial orbital have oppositely directed “spins” (a quantum internal property usually depicted as an axis of rotation, pointing up or down, although no literal axis exists in the electron).
The good news for humans is that this implies matter cannot flow through other matter. “It’s everywhere—you, me, we’re Pauli-exclusion-principle-based,” explains Catalina Curceanu, a member of the Foundational Questions Institute, FQXi, and the principal physicist on the INFN experiments. “Another practical consequence is that we can’t traverse barriers.”
The concept applies to all basic particles called fermions that belong to the same family as electrons and was derived mathematically from a fundamental theory known as the spin-statistics theorem. It has also been experimentally proven so far, seeming to hold for all fermions in testing. One of the key concepts of the standard model of particle physics is the Pauli exclusion principle.
Infringing on the principle
However, certain speculative physics theories outside the standard model show that the principle may be broken. Physicists have been looking for a basic theory of reality for decades. The standard model is excellent at understanding particle behaviour, interactions, and quantum processes at the microscale. It does not, however, include gravity. As a result, physicists have been working on developing a unified theory of quantum gravity, some versions of which predict that many features underlying the standard model, such as the Pauli exclusion principle, may be broken under extreme conditions.
“Many of these violations arise naturally in so-called ‘noncommutative’ quantum-gravity theories and models, such as the ones we investigated in our studies,” Curceanu explains. String theory, which defines basic particles as small vibrating strands of energy in multidimensional spaces, is one of the most prominent candidate quantum-gravity frameworks. Some string theory models anticipate such a violation as well.
“Our approach disfavours certain specific realisations of quantum gravity,” Curceanu argues.
It has previously been considered that testing such predictions would be difficult since quantum gravity is only important in venues where there is a massive quantity of gravity concentrated into a compact space—think of the core of a black hole or the beginning of the cosmos. Curceanu and her colleagues, on the other hand, discovered that there may be a minor effect—a hint that the exclusion principle and the spin-statistics theorem had been violated—that could be detected in lab studies on Earth.
Curceanu’s team is working on the VIP-2 (Violation of the Pauli Principle) lead experiment deep under the Gran Sasso mountains in L’Aquila, Italy. The apparatus’s heart is a thick block of Roman lead, with an adjacent germanium detector that can detect minuscule amounts of radiation emitted by the lead. If the Pauli exclusion principle is broken, a prohibited atomic transition inside the Roman lead will occur, resulting in an X-ray with a unique energy signature. The germanium detector can detect this X-ray.
The cosmic stillness
Because the radiation signal from such a process would be so tiny, it would otherwise be washed out by the ambient background radiation on Earth from cosmic rays, the lab must be situated underground. “Our laboratory provides ‘cosmic stillness,’ in the sense that the Gran Sasso mountain suppresses cosmic ray flow by a million times,” Curceanu explains. However, this is insufficient.
“Our signal has a potential rate of one or two incidents per day or fewer,” Curceanu explains. This implies that the materials used in the experiment must be “radio-pure,” meaning they must not release any radiation, and the equipment must be insulated from radiation emitted by the mountain rocks and radiation emitted from beneath.
“What’s very fascinating is that we can explore certain quantum-gravity models with such high precision, which is difficult to achieve with today’s accelerators,” Curceanu explains.
The team says in their recent articles that they discovered no indication of a breach of the Pauli principle. “FQXi financing was critical for establishing data analytic tools,” Curceanu explains. This enabled the scientists to confine certain suggested quantum-gravity models by limiting the scale of any conceivable violation.
The scientists examined the predictions of the so-called “theta-Poincaré” model in detail and were able to rule out certain variants of the model to the Planck scale (the scale at which the known classical laws of gravity break down). Furthermore, “the analysis we provided disfavours several actual realisations of quantum gravity,” Curceanu claims.
With theoretical colleagues Antonino Marcian from Fudan University and Andrea Addazi from Sichuan University, the team now wants to expand their study to additional quantum-gravity models. “On the experimental side, we will look for small signals to reveal the fabric of spacetime using novel target materials and new analytic tools,” Curceanu explains.
“What’s really fascinating is that we can explore certain quantum-gravity models with such great accuracy,” Curceanu says. “This is a significant advance, both theoretically and experimentally.”
