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.”

Russia announces testing of country-wide drone control network, paving way for commercial boom

Roscosmos, the Russian space agency, has announced that it will begin testing a vast drone control network that will run across the nation.

The network, which is based on the country’s extensive existing satellite system, will allow small UAVs to safely operate in massive numbers within Russian airspace.

Once established, it will likely lead to an explosion in the commercial use of drones in the country, with drone deliveries in particular becoming viable on an unprecedented scale.

The announcement was made at Navitech 2017 in Moscow yesterday by experts from Russian Space Systems, a space hardware company owned by Roscosmos. Outlining the details of the system, they said that testing would begin this year, but did not provide a precise date for its start.

Each drone in the network will follow a route determined by the system, with ground-based infrastructure continuously receiving real-time data about its location and flight parameters.

This will immediately be processed and disseminated across the network, to ensure that large numbers of drones can be safely flown at any time, without interfering with both each other and traditional airspace traffic.

The network will not require the establishment of major new infrastructure, as all data will be transmitted through a combination of existing systems: FM transmitters, the country’s established cellular communication systems and GLONASS, Russia’s global satellite navigation system, which has provided 100% coverage of the country since 2011.

The system will also provide real-time data about no-fly zones, allowing routes to be adjusted immediately in response to changing information, and will offer a “platform of integrated applications” to UAV operators, content providers and insurance companies.

Roscosmos believes that the system will significantly reduce operating costs for drone owners by limiting the risks involved with running a commercial drone operation, as well as creating the conditions for new industries to emerge.

Among the industries the space agency expects to blossom through the adoption of the network are drone insurance, cloud software that would increase the capabilities of drones and what it calls “convenient services” – a term that likely refers to drone deliveries.

If the platform does deliver on this hope, it is likely Russia would become the first country with an extensive drone delivery network, realising a dream that was first brought to prominence by Amazon back in 2013. However, the US-based company is unlikely to become the main player in the Russian market, having as yet shown little interest in the country for its Prime Air operations.

As with many countries, drone deliveries are currently a rare occurrence in Russia, with notable exceptions including DoDo Pizza, a Syktyvkar-based company that began delivering pizzas to local residents back in 2014.

NFL players’ union signs historic deal that will enable players to sell their own performance data and make them “healthier and wealthier”

The NFL players association (NFLPA) has signed a landmark deal with human performance company WHOOP that will give players access to, ownership of and the option to sell their individual health data.

All current and future NFL players will be issued with a WHOOP Strap 2.0, which allows them to, without interference from their clubs, monitor their own performance, recovery and sleep.

WHOOP’s strap contains five sensors that measure data 100 times per second and automatically transmit it to accompanying mobile and web apps. WHOOP has also developed a Team Dashboard, which it says has “27 levels of privacy to ensure sharing data is completely secure and comfortable for all parties involved”.

“Our mission at WHOOP is to empower athletes. This partnership with the NFLPA is truly the first of its kind in that athletes will finally become both healthier and wealthier by collecting, controlling, and ultimately having the ability to sell their own health and performance data,” said Will Ahmed, founder and CEO at WHOOP.

“We applaud the NFLPA’s vision and share its commitment to work with athletes to better monitor their recovery and enable longer careers.”

Image and featured image courtesy of Alan Kotok

The partnership between the NFLPA and WHOOP is the first of its kind and was secured through the OneTeam Collective, which is an initiative designed to give companies like WHOOP the opportunity to leverage the NFLPA’s exclusive player rights.

WHOOP has hinted at seeking further partnerships with players’ unions in future.

In addition to owning their own data, as part of the agreement NFL players can design custom licensed bands for the WHOOP Strap, which will be made available commercially and allow players to further monetise the arrangement between the two parties.

“Every day, NFL players produce data that can translate into physiological and financial opportunities. We see partnering with WHOOP as the first step in harnessing this exciting technology,” said Ahmad Nassar, President of NFL Players Inc.

“We are excited to have WHOOP and its innovative, holistic monitoring technology serve as our first OneTeam Collective deal. Together, we’re paving the way towards a new frontier where athletes are empowered by data.”

Russell Okung playing for the Denver Broncos in 2016. Image courtesy of By Jeffrey Beall – Own work, CC BY 4.0

Along with the commercial opportunities WHOOP will offer players, the partnership also promises to help players optimise training and recovery, improve performance and reduce injuries.

The NFLPA and WHOOP will both study the effects travel, sleep, scheduling and injuries have on recovery and generate reports for players aimed at boosting athletic performance.

“WHOOP and the NFLPA are putting the power of data directly in the players’ hands. I want to recover faster, avoid injuries, and have a longer career. This partnership has the potential to contribute to my health, which is imperative to my career in football,” said Russell Okung of the Los Angeles Chargers.