A fundamental quantum physics problem has been proved unsolvable

For the first time a major physics problem has been proved unsolvable, meaning that no matter how accurately a material is mathematically described on a microscopic level, there will not be enough information to predict its macroscopic behaviour.

The research, by an international team of scientists from UCL, the Technical University of Music and the Universidad Complutense de Madrid – ICMAT, concerns the spectral gap, a term for the energy required for an electron to transition from a low-energy state to an excited state.

Spectral gaps are a key property in semiconductors, among a multitude of other materials, in particular those with superconducting properties. It was thought that it was possible to determine if a material is superconductive by extrapolating from a complete enough microscopic description of it, however this study has shown that determining whether a material has a spectral gap is what is known as “an undecidable question”.

“Alan Turing is famous for his role in cracking the Enigma, but amongst mathematicians and computer scientists, he is even more famous for proving that certain mathematical questions are `undecidable’ – they are neither true nor false, but are beyond the reach of mathematics code,” said co-author Dr Toby Cubitt, from UCL Computer Science.

“What we’ve shown is that the spectral gap is one of these undecidable problems. This means a general method to determine whether matter described by quantum mechanics has a spectral gap, or not, cannot exist. Which limits the extent to which we can predict the behaviour of quantum materials, and potentially even fundamental particle physics.”


The research, which was published today in the journal Nature, used complex mathematics to determine the undecidable nature of the spectral gap, which they say they have demonstrated in two ways:

“The spectral gap problem is algorithmically undecidable: there cannot exist any algorithm which, given a description of the local interactions, determines whether the resulting model is gapped or gapless,” wrote the researchers in the journal paper.

“The spectral gap problem is axiomatically independent: given any consistent recursive axiomatisation of mathematics, there exist particular quantum many-body Hamiltonians for which the presence or absence of the spectral gap is not determined by the axioms of mathematics.”

In other words, no algorithm can determine the spectral gap, and no matter how the maths is broken down, information about energy of the system does not confirm its presence.


The research has profound implications for the field, not least for the Clay Mathematics Institute’s infamous $1m prize to prove whether the standard model of particular physics, which underpins the behaviour of the most basic particulars of matter, has a spectral gap using standard model equations.

“It’s possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable,” said Cubitt.

“We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s,” agreed co-author Professor Michael Wolf, from the Technical University of Munich.

“So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”

“It’s not all bad news, though,” added Professor David Pérez-García, from the Universidad Complutense de Madrid and ICMAT. “The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them.

“But this bizarre behaviour also predicts some new and very weird physics that hasn’t been seen before. For example, our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology.”

Researchers discover remains of “Triassic Jaws” who dominated the seas after Earth’s most severe mass extinction event

Researchers have discovered the fossil remains of an unknown large predatory fish called Birgeria: an approximately 1.8-meter-long primitive bony fish with long jaws and sharp teeth that swallowed its prey whole.

Swiss and US researchers led by the Paleontological Institute and Museum of the University of Zurich say the Birgeria dominated the sea that once covered present-day Nevada one million years after the mass extinction.

Its period of dominance began following “the most catastrophic mass extinction on Earth”, which took place about 252 million years ago – at the boundary between the Permian and Triassic geological periods.

Image courtesy of UZH. Featured image courtesy of Nadine Bösch

Up to 90% of the marine species of that time were annihilated, and before the discovery of the Birgeria, palaeontologists had assumed that the first predators at the top of the food chain did not appear until the Middle Triassic epoch about 247 to 235 million years ago.

“The surprising find from Elko County in northeastern Nevada is one of the most completely preserved vertebrate remains from this time period ever discovered in the United States,” emphasises Carlo Romano, lead author of the study.

Although, species of Birgeria existed worldwide. The most recent discovery belongs to a previously unknown species called Birgeria Americana, and is the earliest example of a large-sized Birgeria species, about one and a half times longer than geologically older relatives.

The researchers say the discovery of Birgeria is proof that food chains recovered quicker than previously thought from Earth’s most devastating mass extinction event.

According to earlier studies, marine food chains were shortened after the mass extinction event and recovered only slowly and stepwise.

However, finds such as the newly discovered Birgeria species and the fossils of other vertebrates now show that so-called apex predators (animals at the very top of the food chain) already lived early after the mass extinction.

“The vertebrates from Nevada show that previous interpretations of past biotic crises and associated global changes were too simplistic,” said Romano.

Revolutionary DNA sunscreen gives better protection the longer its worn

Researchers have developed a ground-breaking sunscreen made of DNA that offers significant improvements over conventional versions.

Unlike current sunscreens, which need to be reapplied regularly to remain effective, the DNA sunscreen improves over time, offering greater protection the longer it is exposed to the sun.

In addition, it also keeps the skin hydrated, meaning it could also be beneficial as a treatment for wounds in extreme or adverse environments.

Developed by researchers from Binghamton University, State University of New York, the innovative sunscreen could prove essential as temperatures climb and many are increasingly at risk of conditions caused by excessive UV exposure, such as skin cancer.

“Ultraviolet (UV) light can actually damage DNA, and that’s not good for the skin,” said Guy German, assistant professor of biomedical engineering at Binghamton University.

“We thought, let’s flip it. What happens instead if we actually used DNA as a sacrificial layer? So instead of damaging DNA within the skin, we damage a layer on top of the skin.”

The DNA sunscreen has the potential to become a standard, significantly improving the safety of spending time in the sun

The research, which is published today in the journal Scientific Reports, involved the development of thin crystalline DNA films.

These films are transparent in appearance, but able to absorb UV light; when the researchers exposed the film to UV light, they found that its absorption rate improved, meaning the more UV is was exposed to, the more it absorbed.

“If you translate that, it means to me that if you use this as a topical cream or sunscreen, the longer that you stay out on the beach, the better it gets at being a sunscreen,” said German.

The film will no doubt attract the attention of sunscreen manufacturers, who will likely be keen to commercialise such a promising product. However, the researchers have not said if there is any interest as yet, and if there is any clear timeline to it becoming a commercial product.


The film’s properties are not just limited to sun protection, however. The DNA film can also store water at a far greater rate than conventional skin, limiting water evaporation and increasing the skin’s hydration.

As a result, the film is also being explored as a wound covering, as it would allow the wound to be protected from the sun, keep it moist – an important factor for improved healing – and allow the wound to be monitored without needing to remove the dressing.

“Not only do we think this might have applications for sunscreen and moisturizers directly, but if it’s optically transparent and prevents tissue damage from the sun and it’s good at keeping the skin hydrated, we think this might be potentially exploitable as a wound covering for extreme environments,” said German.