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.”

Volkswagen wants its driverless, zero-emission car to know everything about you

Volkswagen has taken to the stage at the Paris Motor Show 2016 to announce that by 2025 it will release a fully-automated, zero-emission car.

The Volkswagen I.D. will be ready to launch as a zero-emission vehicle, powered by a 125 kW / 170 PS electric motor and offering a range of up to 600 kilometres, in 2020.

Driverless technology will then be added by 2025.

“In 2020 we will begin to introduce an entire family of electric vehicles on the market. All of them will be based on a new vehicle architecture which was specially and exclusively developed for all-electric vehicles,” explained the chairman of the Board of Management for Volkswagen Brand, Dr Herbert Diess.

“Not for combustion engine or plug-in hybrid vehicles. The I.D. stands for this new era of all-electric vehicles, for a new automotive era: electrical, connected and autonomously driving.”

I.D. owners have the option of either taking control of the car themselves or taking advantage of car’s driverless technology and activate “I.D. Pilot” mode, which can be switched on by touching the VW logo on the steering wheel.

Once I.D. pilot is activated, the steering wheel disappears into the instrument panel, which Volkswagen promises “gives the driver an entirely new feeling of space”.


Volkswagen’s I.D. won’t use a conventional car key; instead, a smartphone can be used as a “digital key” to open the car and enable the vehicle to start.

Using a digital key will enable the I.D. to recognise who is in the car and load up a customisable “Volkswagen ID”.

This ID is an individual profile that stores such information as personal seat and climate control settings, favourite radio stations and playlists, settings of the sound system, contact data for friends and business partners and the navigation system configuration.

Images courtesy of Volkswagen

The Elon Musk Offer: Extinction or Explosion

Elon Musk wants to take you to Mars. He also wants you to know that there’s a very good chance you’ll die doing so. Yesterday, at the International Astronautical Congress, Musk announced a lot more about SpaceX’s plans to get to Mars and opened up a little about the notion of colonising the Red Planet. He was also, almost shockingly, upfront about just how much such a mission is likely to kill you.

Musk’s speech, entitled Making Humans a Multiplanetary Species, largely consisted of explaining more about SpaceX’s Interplanetary Transport System and how the company plans to get people and supplies to Mars.

The plan involves 28,730,000 pounds of thrust and reusable booster rockets. And while Musk spoke about colonisation, it was in a way that very much avoided any kind of commitment on how such a colony would work and what role SpaceX would possibly play in it.

For now it seems the entrepreneur is very much focused on just getting there.

Images courtesy of SpaceX

Images courtesy of SpaceX

What was mentioned was the idea of a self-sustaining civilisation, presumably making some sort of use of Musk’s various clean energy ventures, and the goal of making the cost of a trip to Mars that of a median price house in the United States.

In order to do so we need four things: reusable rockets, refuelling the spaceship in space, using methane fuel rather than traditional propellant and harvesting methane fuel from Mars itself.

If it sounds like a lot of work, be assured it is; Musk made no mention of the infrastructure that would support this though he did point out that there would be no shortage of jobs on Mars if successful. Provided you get there of course.

Even allowing for the overcoming of technical challenges, there is still a very good chance that our initial tries at getting people there will fail horribly.

“The risk of fatality will be high,” Musk told the audience. “There’s no way around it. It would be basically, are you prepared to die? If that’s okay, you’re a candidate for going.

“The probability of death is quite high on the first mission.”

Elon Musk during the talk

Elon Musk during the talk

Musk’s honesty is kind of refreshing, even if it’s distinctly bleak. The chances of such a mission going perfectly on the first try are very low and it’s important to remember for anyone caught up in the excitement of going multiplanetary that there is a good chance of a cold death in space waiting out there.

That said, as Musk pointed out, staying on Earth indefinitely almost certainly ends in some kind of extinction event.

There is currently far too much uncertainty around the way in which a colony on Mars would actually work, the likelihood is that there would have to be some kind of governmental oversight of the colonisation and there are obviously chances of a whole new space race that come along with that.

Musk’s presentation was there to offer up a choice: stay on Earth and face extinction in what may be the far future or go to Mars now and almost definitely go out in a blaze of glory.

The rollout of 4G has transformed our ability to communicate on the go. The former CEO of EE, the first company to bring 4G to the UK, explains how our browsing habits have been forever changed, and what it has meant for the country

It’s quite a claim to call something a “revolution”.

However, in the right circumstances it’s entirely appropriate. Going back to the dictionary definition, one meaning for revolution is “A sudden, complete or marked change in something.”

I would say that the launch of 4G mobile technology was such a change. My experience of it came at the helm of EE, which launched the UK’s first and leading 4G network in 2012.

To explain why it was so revolutionary, we should first cast our minds back ten years or so. At that time, there was relatively little movement in the UK’s mobile market. It was all about calls, texts and a little bit of web on the move. Third-generation, or 3G, mobile networks had been built for these services and further investment was lacking.

Meanwhile, the world had been changing. The Internet had been with us for twenty years, and the smartphone market really started to boom in 2007, catapulting “anytime, anywhere” online access (and expectations) into our pockets.

The existing 3G infrastructure just hadn’t been set up to cater for the surge in data traffic that resulted. If you think back, I’m sure you can remember the days of waiting on tenterhooks for an email to send, or looking at a flickering screen as you waited for a webpage to load on your phone. As for watching video on the go? Forget it.

The launch of 4G

It was time for something new. My company decided to take the plunge and introduce Britain’s first 4G network, which would have the speeds and capacity to manage the needs of data-hungry devices and customers. (How we did it is another story in its own right.)

EE came into the world on 30th October 2012.

We paid close attention to what was happening on the new 4G network and started to review the findings in the EE 4GEE Mobile Living Index report. Within a year of its launch, we saw a rapid rise in the use of social media over the network. In the six months leading up to December 2013 this rose from 13% to 18% of our overall 4G traffic.

Within a year of its launch, we saw a rapid rise in the use of social media over the network

We also surveyed customers and found that those set to do their Christmas shopping via mobile had nearly tripled. 57% of our customers were accessing the Internet via mobile for more than one hour every day, with 21% spending more than three hours.

Later reports showed a sharp hike in the amount of time our customers were spending streaming music, TV programmes and movies on the go – and a reduction in the amount of time they were spending connected to their home broadband supply. New connected devices – like cameras and in-car Wi-Fi – started to take off. The availability of 4G connectivity had started to change people’s daily habits.

People were doing more online, on the move, because they could.

Revolutionary impact

But the true value of 4G and its impact on the way we communicate was really brought home to me at the end of last year.

We were able to demonstrate the significant impact of enhanced connectivity on British businesses, including its most vital public services:

  • In the NHS, improved communication between patients and care providers has the potential to reduce missed and unnecessary appointments by 65%, which would represent a saving of £585m
  • Public housing providers could get connected on site to 4G within three days, rather than waiting a month for a broadband connection, enabling homes to be built more quickly and cost-effectively
  • Police forces deploying 4G mobile devices could save hundreds of thousands of hours of staff time per year, the equivalent of more than 100 officers on the beat

Olaf Swantee is the co-author of new book, The 4G Mobile Revolution – Creation, innovation and transformation at EE, published by Kogan Page, priced £19.99.

At the same time, new research we released with the Centre for Economic & Business Research (CEBR) and YouGov estimated that the efficiency and productivity gains made from 4G would give an £8.9bn boost to UK Plc in 2015, and continue to rise each year.

Finally, EE was selected by the Home Office to provide Britain’s new Emergency Services network, giving 300,000 of these critical workers access to 4G voice and data for the first time.

That’s why I say that the launch of 4G was a revolution. We really did pioneer a sudden, complete and marked change for the UK and kick-started a new communications age. It was fantastic to be a part of it.

There’s more to come, by the way. Just wait until 5G arrives! That’s when things are going to get really interesting… Watch this space.