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 develop painkiller with no side effects

Tests of a new painkiller, Tiovyurtsin, have shown that it works for longer, suppresses pain symptoms of various etiologies and has no toxic effects on the body. Prolonged use (28 days) of the drug does not induce drug dependence, so the drug could be used as a replacement for morphine.

New species of giant herbivorous dinosaur found in outback Australia

A new species of giant herbivorous dinosaur, called Savannasaurus elliottorum, has been found in outback Australia. The new specimen has led researchers to propose a new theory of how the species spread across the ancient megacontinent of Gondwana, which joined Australia, Africa, Antarctica and South America.

Source: The Guardian

Our theory on how solar systems are formed might be wrong

The discovery of the first "binary–binary" – two massive companions around one star in a close binary system, one so-called giant planet and one brown dwarf, or "failed star" – has led a University of Florida astronomer to question whether what we understand about solar system formation is correct.

Source: PHYS.ORG

Mars lander lost on its descent, ESA confirms

A space probe that was developed to look for signs of life on Mars has been lost, the European Space Agency has confirmed. Mission controllers said they are in the dark about the fate of the Schiaparelli probe, which is believed to have touched down on Wednesday after a seven-year journey.

Source: Sky News

Nintendo's new console is a hit with fans but not with investors

Shares in Nintendo fell by as much as 7% following the release of a teaser video for its upcoming hybrid games console the Nintendo Switch. Despite a largely positive reception from fans and media alike, Switch failed to wow Japanese investors, with many, it seems, not ready to forgive Nintendo for the performance of the Wii U.

Source: Ars Technica

Tesla to make all its new cars self-driving

Electric carmaker Tesla has said all of its cars will have the hardware – basically a super-computer in a car – needed to drive completely on their own. But despite cameras, sensors and radars being introduced, it is still expected to be years before Tesla's vehicles become fully self-driving.

Source: BBC

Factor Magazine Issue 29: The Future of Politics – Out Now

In a Venn diagram of politics and unbelievable events, 2016 represents the meeting point, where we finally acquiesced to madness and accepted that it is perfectly reasonable for Donald Trump to run for president.

But beyond Trump’s potential presidency there are loads of examples that prove 2016 is the maddest year in Western politics in living memory. Britain has voted to leave the European Union; the US Democratic nominee was investigated by the FBI and – I don’t know if we mentioned – the US Republican nominee is Donald Trump. Add the alleged Russian hack of the Democratic National Committee (DNC) and Recep Tayyip Erdoğan’s increasingly bizarre behaviour following the totally-not-fake Turkish coup, and you have a year where nothing, no matter how improbable, is definitely off the political table.

So in this, our politics issue, we attempt to make sense of the madness and find out how technology is turning the tables on “post-truth politics”.


With the presidential election just weeks away, we look at how technology has played a role on the campaign trail, and ask whether a growth in support for third-party candidates could ever one day lead to them being a viable alternative to president.

Plus with accusations of Russia ordering a state-sponsored cyber attack on the DNC, we hear from Shawn Henry, former executive assistant director of the FBI, to consider the impact hacking is having on democracy.

On the other side of the Atlantic, the European Union is in peril. We discover how Brexit is just the start, and find out what lies ahead for the stricken community. Plus we look at Turkey’s bizarre move to ban cloud-based file sharing services, and ponder the motives behind such a decision.


On both sides of the pond, truth has become highly mutable within politics this year. We look at whether automated fact checking could allow technology to bring truth back to politics, consider the statistics behind Trump and Clinton’s statements and find out how The Simpsons predicted Trump’s rise 16 years ago.

Plus, we look at how deep learning could be used to more accurately predict election results, and consider the technology being used to better engage voters. And if that wasn’t enough, we’ll also look at the UK financial system’s tentative embrace of cryptocurrencies.

And if you’re sick of politics, we also hear from ESA astronaut Tim Peake about his six-month stay on the International Space Station, and discover how a simple change of camera angle laid the foundations for the Total War games we know and love.

As well as this there’s all the latest news, reviews, and we’ll look at Marty McFly’s Nike Mags and see how the sewing industry is about to be automated in Issue 29 of Factor magazine – out now on iPad and online.

Scientists unlock wireless charging for airborne drones

Using inductive coupling, scientists have made a breakthrough that allows them to wirelessly transfer power to a drone while it is still flying. The technology could open up a host of possibilities, including allowing drones to fly indefinitely, simply hovering over a ground support vehicle when in need of a recharge.

Inductive coupling is a concept originally demonstrated over 100 years ago by Nikola Tesla, the principle being that by tuning two copper coils into each other with electronics, you can enable the wireless exchange of power at a certain frequency.

Inductive coupling has been experimented with for decades, but until now researchers have failed to utilise the technology to wirelessly power flying devices.

The researchers behind the breakthrough, from Imperial College London, demonstrated their method by altering the electronics and removing the battery of an off-the-shelf quadcopter drone.

A receiving antenna was made by encircling the drone’s casing with a copper foil ring, and a transmitter device on the ground was made out of a circuit board and connected to electronics and a power source, creating a magnetic field. The researchers believe that this is the first demonstration to show how this wireless charging method can be efficiently used with a flying object, and expect it to open up a range of potential applications.

“Imagine using a drone to wirelessly transmit power to sensors on things such as bridges to monitor their structural integrity,” explained Professor Paul Mitcheson, from the Department of Electrical and Electronic Engineering at Imperial College London. “This would cut out humans having to reach these difficult-to-access places to re-charge them.

“Another application could include implantable miniature diagnostic medical devices, wirelessly powered from a source external to the body. This could enable new types of medical implants to be safely recharged, and reduce the battery size to make these implants less invasive.”

Images courtesy of Imperial College London

Images courtesy of Imperial College London

Drones are currently limited in their commercial usage by the distance they can travel and the duration for which they can do so.

Despite growing possibilities for usage, the limited availability of power and re-charging requirements means that it is hard to make full use of drones in their capacity for roles such as surveillance or search and rescue. The development of efficient wireless power transfer technology would solve these endurance problems and enable a wide range of advancements.

“In the future, we may also be able to use drones to re-charge science equipment on Mars, increasing the lifetime of these billion dollar missions,” added Mitcheson.

“We have already made valuable progress with this technology and now we are looking to take it to the next level.”

For now, the technology is still very much in its infancy and the Imperial team’s technology only allows the drone to fly ten centimetres above the magnetic field transmission source.

However, they are now exploring collaborations with industrial partners, and have estimated that a commercially available product could be ready in a year.