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.”

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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.

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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.”

Mark Zuckerberg: VR goal is still 5-10 years away

Mark Zuzkerberg has said that the true goal of virtual reality could still be a decade away, in a testimony during a high-profile court case against his company.

Facebook, as owner of Oculus, is currently in the middle of being sued by ZeniMax Media for allegedly stealing technology for the virtual reality device. If proved guilty, they will be pursued for the amount of $2bn by ZeniMax.  However, perhaps more pertinent to the actual future of virtual reality are comments arising from Mark Zuckerberg’s testimony.

As it currently stands, virtual reality is still a far cry from being integrated into everyday life on a wide scale. Oculus, HTC Vive and Playstation VR are still largely targeting gamers and the idea of entertainment experiences. While they have found varying levels of success, all three platforms are being held back by the youth of the technology and, in the case of Vive and Oculus, the limited by the need for a high performing computer to plug into.

Image and featured image courtesy of Oculus

“I don’t think that good virtual reality is fully there yet,” said Zuckerberg. “It’s going to take five or 10 more years of development before we get to where we all want to go.”

The revelation isn’t a particularly shocking one; even the most ardent believer in virtual reality has to admit that we’re a fair way off the goal. Indeed, we can be seen as being in the first wave of mainstream virtual reality, with the main players in the tech using gaming as a way to introduce the technology to a group that are most likely to be interested from the off.

Zuckerberg has far grander plans than simply expanding the user base however, as seen with projects such as Facebook Social VR. If games are the entry, the idea is to expand virtual reality to become a whole new computing platform used for a bevy of experiences and containing a whole load of tools. The ambition is high, the reality slightly lagging behind.

Mark Zuckerberg with Priscilla Chan in 2016

When asked about the realisation of VR as this new computing platform, Zuckerberg replied: “These things end up being more complex than you think up front. If anything, we may have to invest even more money to get to the goals we had than we had thought up front.”

He then went on to add that the probable investment for Facebook to reach that goal is likely to top the $3bn mark over the next ten years. Considering the social media giant spent $2bn just to acquire Oculus, this represents a truly colossal investment in something that seemed to be initially set to hit a lot sooner. Admittedly the goal is rather grand: providing hundreds of millions of people with a good virtual reality experience transcending gaming alone.

Oh, and in case you were wondering, it’s very important that you know that Mark Zuckerberg did in fact wear a suit to trial. Whether Palmer Luckey, making his first public appearance since his Gamergate/Trump support scandal last year, will manage to ditch the flip flops when he testifies is yet to be seen.

Historic Seasteading agreement to see floating city built in French Polynesia

A landmark agreement has been signed between the government of French Polynesia and the Seasteading Institute that lays the foundations for the establishment of a floating city in the country’s waters.

Signed on Friday, 13th January, the agreement will see the government and non-profit cooperate to develop a legal framework for what they are now calling The Floating Island Project.

Although located within the territorial waters of French Polynesia, the floating island will have its own governing framework and economic regulations, allowing it to attract businesses with offers of low – if any – taxation and little red tape.

However, it should also offer significant benefits to the nation, by not only bringing jobs and preventing a brain drain on the archipelagos, but also offering resilience to rising sea levels associated with climate change.

“Our seasteading collaboration with French Polynesia was initiated by the Tahitians themselves and will bring jobs, economic growth, and environmental resiliency to the region,” explained Randolph Hencken, executive director of the Seasteading Institute.

“Signing the memorandum of understanding with French Polynesia is an important first step, and a huge milestone for seasteading.”

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The agreement is a vital step in what has already been a long journey towards the development of such a floating city. Back in September, a delegation from the Seasteading Institute examined multiple sites around French Polynesia, as well as meeting with several of the nation’s senior ministers.

Now a memorandum of understanding (MOU) has been signed, the next steps will be to complete and extensive environmental assessments of the ocean and seabed, as well as the completion of an economic analysis by the Seasteading Institute to demonstrate the financial benefits to the nation.

“The Seasteading Institute and the government of French Polynesia will draw from the best practices of more than 4,000 existing Special Economic Zones around the world to create a ‘Special Economic SeaZone,’” added Hencken.

“The SeaZone will combine the advantages of French Polynesia’s geopolitical location with unique regulatory opportunities specifically designed to attract businesses and investors.”

When construction finally begins on the floating islands, it will be funded by investors in the Seasteading Institute, with a total anticipated cost somewhere between $10m and $50m. The floating platforms that will house the city have already been designed by Dutch engineering firm Blue21, meaning the focus now is on making the concept work for the area.

The organisation plans for many businesses on the floating island to be areas of clean-tech, meaning there are likely to be numerous skilled jobs available to the people of French Polynesia.

“We need to create new clean-tech and blue economy jobs for our youth, and this project has the potential to be a real game-changer locally,” said Marc Collins, former Minister of Tourism for French Polynesia. “This project could help us retain our bright minds, who would otherwise emigrate for work.”

However, with many of the country’s islands under threat from rising sea levels, the project also could provide a long-term survival solution for the nation.

“Polynesian culture has a long history of seafaring across the Pacific Ocean that will contribute to this ambitious project. More than most nations, our islands are impacted by rising sea levels, and resilient floating islands could be one tangible solution for us to maintain our populations anchored to their islands,” added Collins.

“For many Polynesians, leaving our islands is not an option.”