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.”

Robot takes first steps towards building artificial lifeforms

A robot equipped with sophisticated AI has successfully simulated the creation of artificial lifeforms, in a key first step towards the eventual goal of creating true artificial life.

The robot, which was developed by scientists at the University of Glasgow, was able to model the creation of artificial lifeforms using unstable oil-in-water droplets. These droplets effectively played the role of living cells, demonstrating the potential of future research to develop living cells based on building blocks that cannot be found in nature.

Significantly, the robot also successfully predicted their properties before they were created, even though this could not be achieved using conventional physical models.

The robot, which was designed by Glasgow University’s Regius Chair of Chemistry, Professor Lee Cronin, is driven by machine learning and the principles of evolution.

It has been developed to autonomously create oil-in-water droplets with a host of different chemical makeups and then use image recognition to assess their behaviour.

Using this information, the robot was able to engineer droplets to have different properties­. Those which were found to be desirable could then be recreated at any time, using a specific digital code.

“This work is exciting as it shows that we are able to use machine learning and a novel robotic platform to understand the system in ways that cannot be done using conventional laboratory methods, including the discovery of ‘swarm’ like group behaviour of the droplets, akin to flocking birds,” said Cronin.

“Achieving lifelike behaviours such as this are important in our mission to make new lifeforms, and these droplets may be considered ‘protocells’ – simplified models of living cells.”

One of the oil droplets created by the robot

The research, which is published today in the journal PNAS, is one of several research projects being undertaken by Cronin and his team within the field of artificial lifeforms.

While the overarching goal is moving towards the creation of lifeforms using new and unprecedented building blocks, the research may also have more immediate potential applications.

The team believes that their work could also have applications in several practical areas, including the development of new methods for drug delivery or even innovative materials with functional properties.

Mac spyware stole millions of user images

A criminal case brought against a man from Ohio, US has shed more light on a piece of Mac malware, dubbed Fruitfly, that was used to surreptitiously turn on cameras and microphones, take and download screenshots, log keystrokes, and steal tax and medical records, photographs, internet searches, and bank transactions from users.

Source: Ars Technica

Drone swarm attack strikes Russian military bases

Russia's Ministry of Defence claims its forces in Syria were attacked a week ago by a swarm of home-made drones. According to Russia's MoD Russian forces at the Khmeimim air base and Tartus naval facility "successfully warded off a terrorist attack with massive application of unmanned aerial vehicles (UAVs)"

Source: Science Alert

Las Vegas strip club employs robot strippers

A Las Vegas strip club has flown in robot strippers from London to 'perform' at the club during CES. Sapphire Las Vegas strip club managing partner Peter Feinstein said that he employed the robots because the demographics of CES have changed and the traditional female strippers aren’t enough to lure a crowd to the club anymore.

Source: Daily Beast

GM to make driverless cars without steering wheels or pedals by 2019

General Motors has announced it plans to mass-produce self-driving cars without traditional controls like steering wheels and pedals by 2019. “It’s a pretty exciting moment in the history of the path to wide scale [autonomous vehicle] deployment and having the first production car with no driver controls,” GM President Dan Ammann told The Verge.

Source: The Verge

Russia-linked hackers "Fancy Bears" target the IOC

Following Russia's ban from the upcoming 2018 Winter Olympics, the Russia-linked hacking group "Fancy Bears" has published a set of apparently stolen emails, which purportedly belong to officials from the International Olympic Committee, the United States Olympic Committee, and third-party groups associated with the organisations.

Source: Wired

Scientists discover ice cliffs on Mars

Using images provided by the Mars Reconnaissance Orbiter, scientists have described how steep cliffs, up to 100 meters tall, made of what appears to be nearly pure ice indicate that large deposits of ice may also be located in nearby underground deposits. The discovery has been described as “very exciting” for potential human bases.

Source: Science Mag