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.”

Scientists implant device to boost human memory

Scientists have enhanced human memory for the first time with a “memory prosthesis” brain implant. The team behind the device say it can boost performance on memory tests by up to 30%, and a similar approach may work for enhancing other brain skills, such as vision or movement.

Source: New Scientist

Astronomers discover Earth-sized world 11 light years away

A planet, Ross 128 b, has been discovered in orbit around a red dwarf star just 11 light years from the Sun. The planet is 35% more massive than Earth, and it likely exists at the edge of the small, relatively faint star's habitable zone even though it is 20 times closer to its star than the Earth is to the Sun.

Source: Ars Technica

An algorithm can see what you've learned before going to sleep

Researcher fed the brain activity from sleeping subjects to a machine learning algorithm, and it was able to determine what the subject had learned before falling asleep. In other words, an algorithm was able to effectively ‘read’ electrical activity from sleeping brains and determine what they were memorising as a result.

Source: Motherboard

Elon Musk unveils Tesla Truck and Tesla Roadster

Elon Musk has unveiled the long-anticipated 'Tesla Semi' – the company's first electric articulated lorry. The vehicle has a range of 500 miles on a single charge, and will go into production in 2019. Unexpectedly, Tesla also revealed a new Roadster, which will have a range of close to 1,000km (620 miles) on a single charge and will do 0-100mph in 4.2 seconds.

Source: BBC

Arrivo plans to build 200mph hyperloop-lite track

Arrivo, the company founded by former Hyperloop One engineer Brogan BamBrogan, has announced a partnership with Colorado’s Department of Transportation. Arrivo will now build a magnetised track to transport existing vehicles, cargo sleds and specially designed vehicles alongside preexisting freeways at 200mph in the city of Denver.

Source: The Verge

Boston Dynamics' Atlas robot can now do backflips

It's been a busy week for Boston Dynamics, first the company revealed it SpotMini robot dog was getting an upgrade, and now the company has shared a video of its Atlas humanoid robot leaping from platforms and doing a backflip. It seems like an obvious thing to say, but it's not easy to make a robot do a backflip, so how Boston Dynamics has managed it is anyone's guess.

Source: WIRED

The all new Factor Magazine is here – your guide to how today, tomorrow and beyond are being shaped

Guess who’s back, back again.

It’s been a few months, but Factor has returned with a bigger and better format, bringing the same future news and discussion, but on a platform that you can read on any device.

We’ve been working towards this for a long, long time: this is how we’ve always wanted the magazine to look, and we’re so happy to share this with you. It can be viewed on any web browser, on anything from a mobile to a monster PC, and if you’re on a desktop or laptop, click the button in the bottom right-hand corner for the ultimate shiny reading experience. A digital magazine has never looked this good. Probably.

Unfortunately that means no more iPad app, but as you can easily read the magazine from an iPad web browser, we hope you’ll agree that what we’ve gained is so much better than what’s been lost.

So anyway, here it is: the Winter 2017 issue of Factor, the first issue of the quarterly version of the magazine.

In case any of you are worrying about us publishing the magazine quarterly, trust us you don’t need to. We’ve produced the biggest issue of Factor ever, so packed with futuristic awesomeness, that we’ve had to divide it into three sections: Today, Tomorrow and Beyond.

Today deals with the futuristic present, as much of what we think of as ‘the future’ already exists today. We look at how humanoid robots are being employed as co-workers, hear from the legendary Richard Stallman about the vanishing state of privacy and discover how automation is already taking jobs. Plus, we take a light hearted look at the futuristic world of Mr Tesla, Elon Musk, and provide our festive present suggestions in a bumper futuristic gift guide.

Moving on to Tomorrow, and it’s all about the world of the next few decades, as technologies that are in development now reach fruition and seep into our everyday lives. We consider how flying cars are inching towards reality, with a look at both Lilium and the newly announced UberAir, and find out how driverless delivery may be the first true instance of the self-driving future.  Plus, we also look at the Christmas dinners of the future, because why the hell not.

Finally, in Beyond we look at the way-out future that many of us probably won’t live to see, but is supremely cool to think about. We ask leading futurists to predict what’s in store in the 22nd century – not the most positive of pictures, unfortunately – and consider what jobs will remain in a post-automation world. Plus, we look at the potential first homes of the human race beyond the solar system, and check out how asteroid mining is set to shape off-earth development.

Take a look, and if you like what you see and read, please share the magazine with your friends, or tell us what you think. This is a completely free magazine, with not an ad in sight, so it’s always good to know that it’s worth the effort.