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.”

Insects might be touted as the food of the future, but many of us remain unconvinced about bug-based meals. However, scientists have identified another approach to tackling future food shortages, and it’s set to be a lot more appetising to the average Westerner

As the global population continues to grow, we may need to search further afield for cheap, sustainable food alternatives.

A 2013 report from the World Resources Institute warned that Earth’s agricultural system faces a challenging balancing act. The challenge: “To meet different human needs, by 2050 it [the world] must simultaneously produce far more food for a population expected to reach about 9.6 billion, provide economic opportunities for the hundreds of millions of rural poor who depend on agriculture for their livelihoods, and reduce environmental impacts, including ecosystem degradation and high greenhouse gas emissions.”

Despite their high protein levels, many refuse to accept insects as the future of food

Despite their high protein levels, many refuse to accept insects as the future of food

Since then, a number of solutions have been proposed. Insects, for example, have been touted as a meat replacement for some time – they are high in protein, highly sustainable and represent a cheaper alternative to meat.

They have also been eaten widely in many parts of the world for years, including much of Asia.

And a 2014 study from Ghent University in Belgium revealed that one in five meat eaters from the Western world were ready to adopt bugs into their diet – with men more likely than women to accept them.

But researchers from the University of Hohenheim in Germany have recently proposed an alternative ‘future food’ that could be more palatable than adding crushed crickets to your dinner.

Forgotten grains

Friedrich Longin and Tobias Würschum believe that untapped consumer markets exist for ancient foods – such as einkorn, emmer and spelt – which fed large sections of the global population for thousands of years before industrial farming and the green revolution took centre stage.

In an opinion piece published in the journal Trends in Plant Science, the two plant breeders argue that consumer demand in the US and Europe for high quality, healthy food presents an opportunity to reintroduce ancient wheat varieties and other plant species, in turn increasing agricultural biodiversity (without the need for creepy crawlies).

“People are interested in diversity, in getting something with more taste, with healthier ingredients, and ancient grains deliver interesting things,” Longin explains.

By testing and analysing some of the thousands of varieties of ancient wheat species found in gene banks, agronomists and cereal scientists can select those best suited to both modern farming needs and consumer preferences.

And in terms of consumer preferences, I think we can safely argue that a new (or ancient) wheat variety would trump insects as an addition to the 21st century menu.

Take your pick

The wheat flour in widely available breads and baked goods comes almost exclusively from bread wheat – just one of three species, 20 subspecies and thousands of varieties of wheat cultivated and eaten across the world for centuries.

Ancient grain einkorn is one of those being considered

Ancient grain einkorn is one of those being considered

But the development of industrial agriculture and the green revolution in the mid-1900s focused on developing cultivars that produce a high yield and have short stalks which are less likely to collapse and expose the grains to pests or mould. And as other varieties ceased to be commercially viable, traditional dishes and regional food diversity also began to disappear.

However, many of these varieties still exist in gene banks.

In their research, Longin and Würschum screened hundreds of varieties of einkorn and emmer and tested the 15 best candidates at four different locations in Germany. The results proved the importance of looking at the plants holistically.

“When you look at einkorn, it is really fantastic looking in the field, but when you get the agronomic performance, it is low-yielding and it falls down in the rain. But then we found there were so many healthy ingredients, and you taste and even see it in the end product,” says Longin.

Leading by example

Spelt is an example of an ancient grain that has successfully been reintroduced into modern markets. The main cereal crop in Southern Germany, Austria and Switzerland, spelt had almost completely disappeared by the early 20th century. But after a rediscovery that started in the 1970s, today more than 100,000 hectares of spelt are grown every year in and around Germany, with an annual turnover of €1bn across Europe and an annual growth rate of over 5%.

The potential for these ancient grains is considerable, and the end results, according to the scientists, could create a self-financing strategy for providing high quality foods and preserving ancient species.

So let’s not forget about these grains of yesteryear. They may certainly prove to be more appetising than other ‘leggier’ alternatives.

Bioink made from cow cells paves way for scaffold-free 3D printed replacement joints

A research team of engineers has developed a method to create artificial cartilage using 3D printing that may one day allow us to grow replacement patches for worn out joints.

“Our goal is to create tissue that can be used to replace large amounts of worn out tissue or design patches,” said Ibrahim T Ozbolat, associate professor of engineering science and mechanics. “Those who have osteoarthritis in their joints suffer a lot. We need a new alternative treatment for this.”

Cartilage represents a good target for bioprinting due to its simple structure, consisting of only one cell type and with no blood cells in the tissue. Additionally, its inability to repair itself means that the prospect of artificial patches represents an important medical opportunity.

Previous attempts to create cartilage did so by embedding cells in a hydrogel, a substance comprising of polymer chains and water that acts as a scaffold for the tissue’s growth. This method didn’t allow cells to grow as normal, however, meaning that the created tissues lacked sufficient mechanical integrity. Ozbolat’s team’s new method allows them to produce larger scale tissues without the need for a scaffold.

The multiarmed 3D bioprinter used to print the cartilage

The multiarmed 3D bioprinter used to print the cartilage

The method consists initially of creating a tiny tube from algae extract. Cartilage cells taken from cows are then injected into the tube and allowed to grow for about a week and adhere to each other. Because cells do not stick to alginate, the tube can be removed to leave a strand of printable cartilage.

This strand substitutes for ink in the 3D printing process. Using a specially designed prototype nozzle, the 3D printer lays down rows of cartilage strands in a pattern chosen by the researchers. After about half an hour, the cartilage patch self-adheres enough to move to a petri dish containing nutrient media. The nutrient media allows the patch to further integrate into a single piece of tissue.

“We can manufacture the strands in any length we want,” said Ozbolat. “Because there is no scaffolding, the process of printing the cartilage is scalable, so the patches can be made bigger as well. We can mimic real articular cartilage by printing strands vertically and then horizontally to mimic the natural architecture.”

A plug of 3D bioprinted cartilage sits in nutrient media. Images courtesy of Ozbolat, Penn State

A plug of 3D bioprinted cartilage sits in nutrient media. Images courtesy of Ozbolat, Penn State

The cartilage produced by the team is currently inferior to natural cartilage, but better than the cartilage made using hydrogel scaffolding. However, Ozbolat believes mechanical pressure on the artificial cartilage will improve its mechanical properties, mimicking the way in which natural cartilage forms with pressure from the joints.

Applying the process to human cartilage will likely involve each individual treated providing their own source material to avoid tissue rejection.

However, once successful, we will have proven the possibility of artificially repairing tissues, as opposed to our current limitation to replacement or support.

Other tissues are far more complex than cartilage but if we consider it a starting point, this developing method could potentially lead to the ability to create “patches” for a variety of tissues, enabling us to combat the degradation of cells that leads to a variety of medical problems.

Virtual reality is often perceived as a solitary activity, but VR sociable network vTime are showing just how wrong that notion is. vTime CEO and founder of Evolution Studios Martin Kenwright speaks exclusively to Factor about the social future of VR

Virtual reality is often a very solitary activity, using imagined worlds to firmly separate the user and the rest of humanity. But a growing number of apps are transforming the virtual experience into a highly social one, and at the top of the tree is ‘sociable network’ vTime.

Already out for Gear VR and Cardboard, and set for release on Oculus Rift, HTC Vive, Playstation VR and Google Daydream by the end of the year, the network is completely cross-platform, and has already collected a slew of accolades and positive reviews.

Most recently, vTime was named a Gartner Cool Vendor for 2016 in the consumer mobile market. Put simply, vTime is on the up, and looks set for virtual reality stardom.

“It’s incredible. We’ve been thrilled and delighted at this validation because, as you can imagine, it’s quite frightening doing something as audacious as what we did right at the start of the lifecycle,” says vTime CEO Martin Kenwright. “You need to be very brave. But I think, now that people have realised the potential and the opportunity, we’re just in remarkable shape.”

vTime’s success is likely to be largely due to its unique offering. Placing users in avatars that animate in response to their voice, the system allows friends, family, colleagues and even strangers to meet up in a stunning selection of virtual environments, and hold conversations as if they were in the same room. And, in part because it suffers from fewer buffering and lag problems than VOIP services such as Skype, it’s quickly being embraced by users as a reliable and regular means of online communication.

“Anyone can create a web-based front-end using graphics and UIs, but I think the idea of VR is for people to fall in love with it,” says Kenwright. “We want to create ultimate presence and immersion, to suspend disbelief. And I think that’s what’s unique about what we’re doing.”

VR’s Evolution

Perhaps the biggest reason vTime is doing so well is its technology, and in particular its ability to run with high levels of stability while rendering striking and very detailed environments. It’s an impressive show for a smartphone-run VR, and one that could only be achieved by a team that has some pretty serious experience behind them.

Back at DID, before even Evolution, we worked on some of the first VR in the world, and worked on secret projects for the military, that even now I don’t know if I can tell you about

But Martin Kenwright isn’t just any tech CEO. His last company was gaming legend Evolution Studios, which he founded and ran until 2007, and before that he founded Digital Image Design (DID), the first company in the world to develop accelerated 3D games for PC.  Some of the vTime team have been with him since the beginning.

“VR is something we’ve always been heavily involved with. Back at DID, before even Evolution, we worked on some of the first VR in the world, and worked on secret projects for the military, that even now I don’t know if I can tell you about!” says Kenwright.

“I felt when VR was coming it was like ‘ah, finally, our time has come’. And I genuinely think we have the talent, the skill and the resources to do something quite incredible, right at the start of the lifecycle. Something incredible like we did with [Evolution Studios PS3 launch title] Motorstorm, and just what we’d done before countless times: create an app of genuine use and value – beautiful, slick, lovely – that you’d want to use every day, that adds real value.“

Taking on Facebook

When Kenwright first put together the team that now is vTime, his sights were not on VR, but its augmented cousin.

“I thought, initially, it would be more about AR than VR, and we massively invested in AR. We’ve got some incredible demos that people should see one day from years and years ago, movies, everything in augmented reality,” he says. But that changed in 2014, when Kenwright started to see the social potential of a virtual reality device being touted by a certain startup.

“vTime really all began just over two years ago when we were gearing up for GDC,” he explains. “We’d spotted and liked this little company called Oculus and wanted to talk to them about our ideas for a social network in VR. But they cancelled the appointment that day, in San Francisco.”

That day, as it turned out, was quite an important one for Oculus.

“I was really angry and then we found out that Facebook acquired them that very day for $2bn. So there you go, the mould was set. I ended up thrilled and angry at the same time. Damn, my idea was good!”


Images courtesy of vTime

But that didn’t stop Kenwright from ploughing on with his VR social network idea, regardless of the fact that the biggest social network in the world would likely be a major rival in the future.

“When I reflected on this acquisition I thought ‘how crazy would you be to go up against the format holder now and try and do this?’” he says. “But again, when you understand the calibre and skill we have, I figured that our team could create a consumer front-end that would be the envy of the world. We could do it – very few could.”

As it is, of course, vTime is growing by the day, while Facebook is yet to release a VR version of its social network. What happens in the future, of course, remains to be seen, but for now Kenwright’s offering is certainly top of the pile.

Mobile importance

For many developers dipping their toe in the VR pool, the obvious first target is the Oculus Rift or the HTC Vive. After all, they’re the highest quality headsets around, and have been enthusiastically embraced by well-off early adopters around the world.

However, vTime focused instead on mobile, producing an experience that feels extremely high-quality for a budget VR solution while positioning itself as available to the techy and the non-techy alike.

“With vTime we made big bets and big gambles on certain things. We bet big on mobile,” explains Kenwright. “We felt VR, like digital photography, would go the same way. You know, not bigger digital cameras, but cheaper, smaller, built into mobile devices. We thought the low end would be the mass market; not the high-end PCs with tethers and things.

“I’m not belittling that, but I’m just saying, to be able to build something from the ground up working on the lowest end devices, that scales across all formats, was really the idea; to create an incredible vision of what we think social environments could be like in virtual reality.”

This approach may prove to be vTime’s making. More and more people are trying the platform, and for many their first headset will be one with a smartphone in it. And with Google’s Daydream set to dominate within a year, this is only going to widen the smartphone market at a pace that far outstrips the high-end offerings.

“For us the focus was creating the first baby steps to the metaverse, you know, in terms of having something with a really low barrier to entry that normal people could use everyday, for people who don’t think they like VR,” adds Kenwright.

Sociable network

The very notion of a social network in virtual reality is an intriguing one, but vTime has widened this definition to a “sociable network” in a bid to distinguish the service from more traditional shout-to-the-world approaches.

“Using the term ‘sociable network’, rather than social network, is to explain that it’s a whole different format,” explains Kenwright. “Social networks simply aren’t very sociable. You post stuff on your own using your phone, tablet or PC.

There are stories – and they’re all true – of people falling in love, meeting someone and getting engaged in vTime. They may actually be getting married in the metaverse

“You can only be sociable when you’re in the same place, face-to-face, talking to someone. There are a lot of lonely people out there, a lot of people who want to escape and meet up and just chat and share and be sociable.”

And for some, vTime has certainly filled that niche. “There are stories – and they’re all true – of people falling in love, meeting someone and getting engaged in vTime. They may actually be getting married in the metaverse!” he exclaims.

There are, of course, many features to encourage interaction. Aside from the regular worlds, where up to four people can meet up in spaces that include the Arctic, a Victorian train, a space station and  cliff face, users can also host meetings inside 3D photographs, or in a specialist image viewing room.

However, while many are using the platform to chat with family, friends and potential friends, businesses are also starting to see a serious benefit to the platform.

“There’s also businesses using vTime for meetings instead of Facetime or Skype, people giving spoken foreign language lessons – all sorts, really,” says Kenwright. “They’re using vTime for the reason we designed it: to allow people to do what they’ve done since the beginning of time – meet up with family, friends, strangers and sit around telling stories – chatting, singing, laughing, all that stuff. The difference now is that by using vTime you can be anywhere in the real world but still be together.”

vTime in context

Although vTime is already enjoying considerable success, with downloads already in the “hundreds of thousands” despite not yet being out on some major platforms, Kenwright has his sights set on something greater.

“We see vTime becoming the very heart of users’ VR world,” he says. “There are clues for where vTime is going in the next couple of releases, but as you can imagine these are just the first babysteps to where it’s going.”


Kenwright is staying tight-lipped about exactly what the company has planned in the long-term, saying “expect the unexpected” when asked whether there were plans to connect the technology to other platforms, but it’s clear that there are plans afoot to take the service to new heights.

“We can’t tell you too much of our strategy, our roadmap, but obviously people who look back over the past 30 years can see what we’ve created, we’re just fairly addicted to creating fantastic products we’re proud of,” he says.

“We’ve always tried to be the very first or the very best in every sector we’ve been in, and we don’t fear anything. All we want to do is have fun and be happy. And you know, if you’re happy you can do anything.”

Future of VR

With vTime set to be a part of virtual reality for the foreseeable future, what does Kenwright predict for the industry as a whole?

“There are going to be huge trends. Everyone is talking about how it creates a bit of a new world order in terms of society, how people might engage together, the social society of the future as it were, how we do business together, how you buy and sell things. And I just think it will be,” he says.

“Gaming will lead, as it has done with new tech before, but I think it’s all the things outside of games where it will evolve too.“

As someone who has been a part of the games industry for three decades, Kenwright has watched VR’s slow approach on the horizon for many years.

“I remember one particular quote when we started a few years ago, from someone far more clever than I, saying ‘in a few hundred years historians will look back to the 20th century and see it as a stopgap between reality and virtual reality’,” he explains.

“I’m not sure it’ll be quite as dramatic as that, but there’s certainly a huge element of it, you know. You can see it now. With an app for $5 or $10 and a few clicks of your phone you can have an experience you’d have paid half a million dollars for just a few years ago.”

But now, with VR developing at pace, Kenwright is facing the prospect of seeing decades-old ideas finally become reality.


“30 years ago, when I started getting into games, I asked myself: ‘one day, would we be able to create something that was so close to reality that you wouldn’t know?’ And my answer was:  ‘maybe not in my lifetime’,” he muses. “But since VR, I’ve been thinking ‘you know what? I think it might be in my lifetime’.“

However, as experienced as the vTime team are, there is still a distinct element of entering the unknown when it comes to VR and the future.

“We are still very much making it up as we go along, everyone in VR is very much fighting for their lives,” he says.

“We don’t know if there is the market yet; there’s no big revenues yet. We’re still all figuring out how we’re going to make money, so it’s a very, very exciting but dangerous time as well.”